Answers
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
What is meant by an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]
Multiply both sides by 0.038 / 12, we get
[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]
Subtract 5225 / 6 from both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]
Simplify
[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]
By using exponent rules, we get
[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]
Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]
[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]
Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
To learn more about exponent rules refer to:
https://brainly.com/question/11975096
#SPJ13
Related Questions
PLEASE SOLVE!
x+146=546
I tried but can't get it
Answers
[tex]x+146=546[/tex]
Subtract 146 from both sides:
[tex]x+146-146=546-146\\[/tex]
[tex]x=400[/tex]
Answer:
x = 400
Step-by-step explanation:
x + 146 = 546
We need to subtract 146 on both sides.
146 - 146 is equal to 0 so we cancel out. 546 - 146 is equal to 400.
So now x is alone and we have our answer.
x = 400
Describe all the x-values within or including a distance of the given value.
(Enter your answer using interval notation.)
Distance of 2 units from the number 7
Answers
The range of values, in interval notation is [-6,14] .
What is interval notation in math?
Continuous sets of real numbers can be represented by the integers that bound them using interval notation. When written, intervals resemble ordered pairs in several ways. They don't necessarily indicate a particular point, though. They are intended to serve as a shortened manner of expressing an inequality or system of inequalities.the values with a distance of 10 units from 4.
Maximum value to the right, 10 units from 4 is 4+10 = 14
Maximum value to the left, 10 units from 4 is 4 - 10 = -6
So, all the range of values, in interval notation is [-6,14]
Learn more about interval notation
brainly.com/question/17249352
#SPJ13
A car rental service charges an initial fee of $250 and 25$ for every hour using the car. If a customers bill totals $1,275 then how long did they rent the car for?
Answers
======================================================
Explanation:
x = number of hours
y = total cost
The equation is y = 25x+250 since 250 is the initial cost, aka y intercept, and 25 is the slope telling us how much the cost goes up per hour (aka rate of change).
I recommend making a table of values to help see how/why that equation works out.
Plug in y = 1275 and isolate x.
y = 25x+250
1275 = 25x+250
1275-250 = 25x
1025 = 25x
25x = 1025
x = 1025/25
x = 41 hours
----------------
Check:
If the customer rents the car for 41 hours, then they pay 25*41 = 1025 dollars on top of the initial fee of $250.
The total cost is therefore 1025+250 = 1275 dollars to confirm the answer.
----------------
Extra info:
41 hours = 24 hours + 17 hours = 1 day + 17 hours
41 hours = 41/24 = 1.70833 days approximately
A student claimed that reflect a triangle in a line, translating a triangle , rotating a triangle, and reflecting it in a point result in an image that is congruent to the original( pre-image) triangle. explain why they are correct.
Answers
If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.
This is a problem from triangular geometry. We can solve this problem by following a few steps.
Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.
After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.
After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.
∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''
( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )
To know more about congruent triangle visit,
https://brainly.com/question/27848509?referrer=searchResults
#SPJ1
find the length of the arc shown in red. Leave your answer in terms of pie
Answers
EXPLANATION
Given the circle, we can see the following facts:
Diameter= 24 ft ----> radius= 12 ft
Total arc length = 360°
The arc of a semi-circle is equal to 360/2 = 180 degrees
The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,
360° - 180° - 60° = 120°
So, representing this as a radian form:
[tex]\text{arc length = 2}\cdot\pi\cdot r\cdot(\frac{\theta}{360})[/tex][tex]\text{arc length = 2}\cdot\pi\cdot12\cdot(\frac{120}{360})[/tex]Multiplying terms:
[tex]\text{arc length = 24}\cdot\pi\cdot\frac{1}{3}[/tex]Simplifying:
[tex]\text{arc length= 8}\cdot\pi[/tex]So, the answer is 8π ft
What is the probability that A occurs given that B occurs ?
Answers
This is an instance of conditional probability and the formula to use is;
[tex]P(\text{AIB)}=\frac{P(A\cap B)}{P(B)}[/tex]Where:
P(A|B) = the probability of event A occurring given that event B occurred
P(A ∩ B) = the probability that both events A and B occur
P(B) = the probability of event B
[tex]\begin{gathered} P(\text{AnB)}=\frac{1}{3} \\ P(B)=\frac{2}{5} \end{gathered}[/tex][tex]P(\text{AIB)}=\frac{\frac{1}{3}}{\frac{2}{5}}=\frac{1}{3}\times\frac{5}{2}=\frac{5}{6}[/tex]Therefore, the probability that A occurs given that B occurs is 5/6
There is a line that includes the point (1, – 2) and has a slope of 10. What is its equation in point-slope form?
Answers
The equation of line in point - slope form will be;
⇒ y + 2 = 10 (x - 1)
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line = (1, -2)
And, The slope of the line = 10
Now,
Since, The equation of line in point-slope form is;
⇒ y - y₁ = m (x - x₁)
Where, (x₁ , y₁) is the point on the line and m is slope of the line.
Hence, The equation of line in point-slope form passing through the points (1, -2) with slope 10 is;
⇒ y - y₁ = m (x - x₁)
⇒ y - (-2) = 10 (x - 1)
⇒ y + 2 = 10x - 10
⇒ y = 10x - 10 - 2
⇒ y = 10x - 12
Thus, The equation of line in point - slope form will be;
⇒ y + 2 = 10 (x - 1)
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ1
Answer for both A, B, and C. Need help asap!!! Giving brainliest.
Answers
Answer:
Step-by-step explanation:
Question a: Solve for c
0.9c = 17.01 - 18.9r
c = 17.01-18.9r/0.9
c = 18.9 - 2.1r
Question b: Solve for r
18.9r = 17.01-0.9c
r = 9 - [tex]\frac{0.9}{18.9}[/tex]c
r = -10/21c + 9
(0.9/18.9 = 10/21)
Question c:
It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.
c = 18.9 - 2.1r
Substitute r with 3.25
c = 18.9 - 2.1(3.25)
c= 18.9 - 6.825
c = 12.075
1.2x10-8 x 4.0×10-3
Scientific Notation
Answers
Answer:
−3.11×10^2
Step-by-step explanation:
The measure of an acute angle is represented by (3x + 12)°. Which is not a possible value for x?
A 26
B 21
C) 23
D25
Answers
a)26 is not a possible value for x as the angle becomes a right angle and doesn't remain acute
An acute angle is one whose measure is less than 90 degrees. The given acute angle in the question is represented by (3x+12)°
if x=26 then the angle is 90°
if x= 21 then the angle is 75°
if x=23 then the angle is 81°
if x=25 then the angle is 87°
∴26 cannot be a possible value for x as the angle becomes 90 degrees (right angle) and doesn't remain acute any longer.
Thus the correct answer is option a)26
Know the type of angle:
brainly.com/question/16492238
#SPJ4
The musical note e can be modeled by the function, y = asin(1320Ï€x), where a = 1 and x is the time in seconds. playing note e on your computer, you notice that it is not loud enough to be heard across the room. what change can you make to the function to make note e louder than the original? let a < 0. let a > 0. let a > 0 and a < 1. let a > 1 or a < â€"1.
Answers
The change that increases the loudness is a > 1
How to determine the change?From the question, the equation of the function that represents the musical note is given as
y = a sin(1320πx)
Where
a = 1 i.e. the amplitudex represents the timeIn sound, the sound loudness is directly proportional to the amplitude.
This means that an increment in the amplitude, would cause the note to become louder
This change is represented as a > 1
This is so because a represents the amplitude, and the initial value is 1
Read more about amplitude at
https://brainly.com/question/25699025
#SPJ1
On a cold January day, Klara noticed that the temperature dropped 21 degrees over the course of the day to –9°C. Write and solve an equation to determine what the temperature was at the beginning of the day.
Answers
x = 12
The temperature at the beginning of the day was 12* C
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answers
A custodian must move a shipment of books from the first floor to the sixth floor. The elevators weight limit is 900 pounds. If the custodian weighs 160 pounds and each box of books weighs 37 pounds , find the maximum number of boxes the custodian can move on the elevator at one time
Answers
Step-by-step explanation:
160 + 37x <= 900
37x <= 740
x <= 20
the custodian can move max. 20 boxes on the elevator at one time.
if he/she is always riding with the boxes.
if the custodian would climb the stairs and let the books ride alone, there could be
37x <= 900
x <= 900/37 = 24.32432432 ≈ 24
boxes on the elevator at one time.
3. At a carnival, of the games cost $1. Another 2.5% of the games cost $2. What
percent of the games do not cost $1 or $2?
Answers
Percent of the games do not cost $1 or $2 is 35%.
What is percentage?
A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Given,
games = 58
5/8 is 62.5%
2.5% + 62.5% = 65%
100%-65% = 35%
A third of the games (35%) are free.
To learn more about percentage from given link
https://brainly.com/question/24877689
#SPJ9
Complete question -
At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?
Help me out please :))
Answers
Answer:
The answer is C
Step-by-step explanation:
an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone. use 3.14 for π. round your answer to the nearest tenth.
Answers
an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone then The lateral surface area of the cone is 105.2 cm².
What is lateral surface area?
The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.
Lateral surface area = πr√(h² + r²)
Where:
π = pi = 3.14
r = radius = 8/2 = 4cm
h = √8.4² - 4² = 7.38
3.14 x 4 x √(7.38² + 4²)
= 105.4 cm
learn more about of cone, here
https://brainly.com/question/26414506
#SPJ4
A study on the average minutes spent by students on internet usage is 300 with a standard deviation of 102. Answer the following questions assuming a bell-shaped distribution and using the empirical rule. What percentage of students use the internet for more than 402 minutes?.
Answers
The percentage of students that use the internet for more than 402 minutes = 16%
Percentage
Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.
calculate the percentage-
The empirical rule states that
68% of the population lies within 1 standard deviation of the mean
95% of the population lies within 2 standard deviations of the mean
99.7% of the population lies within 3 standard deviations of the mean
Standard Deviation
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
The percentage will be illustrated in this:
P(X > 402) = P(X > 30 + 1 × 102)
= (1-0.68) / 2
= 0.32/2
= 16%
The percentage of students that use the internet for more than 402 minutes = 16%.
To learn more about Standard Deviation visit:
brainly.com/question/13905583
#SPJ4
Help!! i’ll give brainlest
Answers
The equivalent expression is 54 divided by 18, and the quotient is 3.
a length of black steel pipe is 21'-0" long. how much if the length remains of two pieces 7'-9 5/8" are cut from the length?
Answers
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.
Remain length = 13.2' = 13' 2 2/5 ".
What is a mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognized fraction.Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction's value doesn't change. We can assert that the actual mixed number and the simplified mixed number are fractions of the same size.Length of black steel pipe is 21'-0".
7' 9 5/8" =7.8 '
Remain length = 13.2' = 13' 2 2/5 ".
To learn more about : Mixed fraction
Ref : https://brainly.com/question/21446512
#SPJ1
A car park charges £1.20 to each car entering.
The payment station only accepts £1 coins and 20p coins.
Here are the coins collected from the payment station on a particular day:
Number of £1 coins
176
Number of 20p coins
320
Assuming each driver paid the exact amount due on that day, work out the
percentage of drivers that paid with six 20p coins.
Optional working
+
Answer:
Answers
Answer: 12%
Step-by-step explanation:
12%
Explanation:
If has 176 £1 coins then 176 drivers paid £1 and 20 p coins.
The rest of the driver paid with 20 p coins.
So the number of 20 p coins is:
320 - 176 = 144
Since £1 and 20 p need 6 coins of 20 p, the number of drivers who paid only for 20 p coins is:
144 / 6 = 24
The total number of drivers is:
176 + 24 = 200
The percentage of drivers who paid only with coins id 20 p is:
24 / 200 • 100% =
0.12 • 100% = 12%
Max is designing a hot tub for a local spa.
He wants the hot tub to have a diameter of 90 inches, what is the approximate area required for the installation of the hot tub? (Use 3.14 for.)
Answers
The area of the hot tub to be installed for local spa is 6358.5 in².
What is defined as the circle?A circle is a round figure with no corners as well as edges.A circle is defined in geometry as a closed, double curved shape.The center of the a circle is the point in a circle where all distances to the circle's points are equal. This distance is known as the circle's radius.The diameter of a circle is a line segment that passes through center of a circle and has its endpoints just on circle.Diameter = 2 × radiusFor the given question;
The diameter of the hot tub to be installed for local spa is 90 inches.
Then, radius is 90/2 = 45 inches.
The area of the circle is;
Area = πr²
Where, π = 3.14
Put the values;
Area = 3.14×45²
Area = 6358.5
Thus, the area of the hot tub to be installed for local spa is 6358.5 in².
To know more about the circle, here
https://brainly.com/question/24375372
#SPJ13
can anyone help me with these questions
Answers
Answer:
Nah
Step-by-step explanation:
M
Given the diagram below, solve for x.
X%
87° 87°
Xº
87
N
Acute Geometry Class, 2021
Answers
The angle x= 33 degree.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle measurement between the two rays. If different types of angles, such as a positive angle and a negative angle.
Positive Angle: If angle goes in counterclockwise, then it is called a positive angle.
Negative Angle: If angle goes clockwise direction, then it is called a negative angle.
360= 87*3+3x
360-261=3x
33=x
To know more about angles visit: https://brainly.com/question/28451077
#SPJ9
You plan to retire in 35 years, and would like to have 1,000,000$ in investments. How much money would you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 35 years. Assume all years have 365 days round your answer to the nearest cent
Answers
Given:
You plan to retire in 35 years and would like to have 1,000,000$ in investments.
So, the time = 35 years
And A = 1,000,000
compounded daily, n = 365
Rate of the interest = r = 7% = 0.07
We will find the initial investment = P
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the values of A, r, n, and t
[tex]\begin{gathered} 1000000=P\cdot(1+\frac{0.07}{365})^{365\cdot35} \\ \end{gathered}[/tex]Solve the equation to find P
[tex]\begin{gathered} 1000000=P\cdot11.5856 \\ \\ P=\frac{1000000}{11.5856}=86,313.86 \end{gathered}[/tex]So, the answer will be $86,313.86
Find the multiplicative inverse of −1 x -3/10.
Answers
Step-by-step explanation:
-1 × -3/10
=> 3/10
Multiplicative Inverse/Reciprocal of 3/10 = 10/3
“If the sum of two angles is 180 then the angles are supplementary
Answers
If the sum of two angles is 180 then the angles are supplementary.This is true.
What are supplementary angles?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.
If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined.
If two angles add up to 180 degrees, they are considered to be supplementary angles in geometry. For example, if A + B = 180°, A and B are referred to as supplementary angles. When supplementary angles are combined, they always yield a straight angle (180 degrees).
Learn more about angles on:
https://brainly.com/question/25716982
#SPJ1
1. You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long
will it be before you and your sister have the same amount of money? Write an equation and solve.
Answers
It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.
How to write equation?A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.
What is equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given condition,
You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.
Let x be the time period in weeks. So we need same amount of money.
60+7x=120+5x
This is the equation needed.
2x=60
x=30 weeks
If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.
To know more about equations,
https://brainly.com/question/28868504
#SPJ13
Write the equation of each parabola in vertex form
Answers
Answer: 9. y=[tex](x+4)^2-3[/tex]
10. y=[tex]-(x-5)^2+5[/tex]
11. y=[tex](x-2)^2+1[/tex]
12. y=[tex]x^2-3[/tex] or y=[tex](x-0)^2-3[/tex]
Step-by-step explanation:
can someone please help?
Answers
Answer:
No
Step-by-step explanation: