Answer:
10:7
Step-by-step explanation:
40:28 are both divisible by 4. 40/4 is 10. 28/4 is 7. So the ratio would be 10:7 since neither is divisible by both the same number, this is the final ratio.
Brad invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
The time needed for the investment to triple is approximately 32.59 years.
What is the time taken for the investment to triple?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $2,500Accrued amount A = tripled = 3 × $2,500 = $7,500Interest rate r = 3.4%Compounded semi-annually n = 2Time t = ?Plug the given values into the above formula and solve for t.
A = P(1 + r/n)^(n*t)
t = In( A/P) / n[In( 1 + r/n ) ]
t = In( 7500 / 2500) / (2[In( 1 + 3.4%/2 ) ])
t = In( 7500/2500 ) / ( 2[In( 1 + 0.017 ) ]
t = 32.59 years
Therefore, the required time for the investment to $7,500 is is 32.59 years.
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Solve linear differential equations.
a. (x + 2)² (dy/dx) = 5-8y - 4xy
The value of y for the linear differential equation is:
y= [5(x³+6x²+12x)/3(16+32x+24x²+8x³+4x⁴)] + c₁ /(16+32x+24x²+8x³+x⁴)
How to solve the differential equation?You should know that a differential equation is in which we find the value of y with respect to x
The given parameter is
(x-2)² dy/dx = 5-8y-4xy
Differentiate y with respect to x to have
y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
Recall that the differential equation is (x-2)² dy/dx = 5-8y-4xy
Solving the Ordinary Differential Equation we have
y= y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
In conclusion, the value of y is: y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
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Examine the four different companies in the table, which shows their yearly income and their tax rate. Which type of taxation does this table best represent?
A. Indirect
B. Progressive
C. Pegreative
D. Proportional
The type of taxation that this table best represent is B. Progressive
What is a progressive tax?A progressive tax is one in which the tax rate rises (or progresses) as taxable income rises. It imposes a lower tax rate on low-income earners and a higher tax rate on higher-income earners. This is usually accomplished by establishing tax brackets that categorize taxpayers based on their income levels.
A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.
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Answer:
I got c
Step-by-step explanation:
Took the test and that’s what it told me 4nem
Solve 3 (8-x) -6x + 15
A. -3
B. -1
C. 2
D. -2
E. 3
By solving 3 (8-x) -6x + 15 , x = -1
How do solve equations ?Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.the three phases of the problem-solving cycle: comprehend, plan, and put into action. That is, we must first comprehend the issue, then consider potential solutions, and ultimately put those solutions into practise to see where they take us.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.Find the attachment answer
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During a fireworks display, a shell is shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t-20t^2
Find velocity when t=0.5
The velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t - 20t² is 38 m / s.
What is velocity?When anything is moving, its velocity tells us how quickly that something's location is changing from a certain vantage point and as measured by a particular unit of time.
If a point moves along a path and covers a certain distance in a predetermined amount of time, its average speed over that period of time is equal to the distance covered divided by the travel time. A train traveling 100 kilometers in two hours, for instance, is doing it at an average speed of 50 km/h.
Given:
Height equation, y = 58t - 20t²,
The time, t = 0.5 seconds,
The initial velocity, u = 58 m/s,
Calculate the height at 0.5 sec,
y = 58 × 0.5 - 20 × 0.5²
y = 24 m
Calculate the acceleration at 0.5 sec by using the motion equation given below:
[tex]s = ut+1/2at^2[/tex]
24 = 58 × 0.5 + 1 / 2 × a × 0.5²
-5 = 0.125 × a
a = - 40 m / s²
Calculate the velocity by using the formula given below,
[tex]v = u + at[/tex]
v = 58 + (-40) × 0.5
v = 38 m /s
Therefore, the velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y = 58t - 20t² is 38 m / s.
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Solve the following inequality
8n+4n< -4+8n
Answer:
n < –1
Step-by-step explanation:
8n + 4n < –4 + 8n
12n < –4 + 8n
12n – 8n < –4
4n < –4
divide both sides by (4) to obtain
n < –1
i hope this helps please rate the answer as brainliest
y varies inversely as x. y = 18 when x = 7. Find y when x = 6.
The value of y is 21, when x = 6.
What are Inverse variations?
The link between two variables known as "inverse variation" occurs when the value of one variable rises while the value of the other variable falls.
Here, we have
Inverse variations look like this: y = k/x
We need to make our own inverse variation given y = 18 and x = 7. We can plug this into the standard inverse variation with variables.
y = k/x
18 = k/7
k = 126
We've determined that k =126. Now we have what it takes to create an inverse variation. This is our final equation:
y = 126/x
We still need to find what y equals when x is 6. Let's plug in 6 for x
y = 126/6
y = 21
Hence, the value of y is 21, when x = 6.
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Give the prime factorization of 300 in exponential form
Answer: 2^2*3^1*5^2
Step-by-step explanation:
1st step: find the factors
2 x 2 x 3 x 5 x 5
2nd step: simplify
2^2*3^1*5^2
Convert 110 kilograms to pounds. (1 kilogram = 2.204 pounds)
110 kilograms is equal to 242.44 pounds.
To convert kilograms to pounds, you can use the conversion factor:
1 kilogram = 2.204 pounds.
Given that you want to convert 110 kilograms to pounds, you can multiply 110 by the conversion factor:
110 kilograms x 2.204 pounds/kilogram = 242.44 pounds
Therefore, 110 kilograms is equal to 242.44 pounds.
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A softball team is participating in a tournament where the team will spend three nights at a hotel. Each hotel offers a 50%
discount for the third night. The coach wants to keep the total cost for each player at $225 with an absolute deviation of at
most $25. Write an absolute value of inequality. Use x for the variable.
Hotel Price per night
Hotel A
$80
Hotel B
$105
Hotel C
$75
Hotel D $90
12.5x2251>25
The inequality will be;
For Hotel A; 80x + 25 < 225
For Hotel B; 105x + 25 < 225
For Hotel C; 75x + 25 < 225
For Hotel D; 90x + 25 < 225
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.
Now,
Since, The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.
Hence, We get;
The inequality will be;
For Hotel A;
⇒ 80x + 25 < 225
For Hotel B;
⇒ 105x + 25 < 225
For Hotel C;
⇒ 75x + 25 < 225
For Hotel D;
⇒ 90x + 25 < 225
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5. Mr. Roberson created this frequency table to record the favorite color of each of his students. Which of the following statements are true based on the frequency table?
More students prefer red than green.
Twice as many students prefer green than purple.
More students prefer yellow than blue.
Two more students prefer blue than purple.
The same number of students prefer yellow or purple as the number who prefer blue.
Statments Two more students prefer blue than purple and Twice as many students prefer green than purple are true.
What is frequency distribution table?
A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table.
All of the results are presented in the first column as individual values or as class intervals.
The table's second column contains the results' totals, which also display the frequency as vertical lines. It's not required.
The frequency of each result is revealed in the third column.
From the given frequency distribution table we will first calculate the numeric value of the number of students with their favourite colour.
Number of students like red colour = 6
Number of students like yellow colour = 2
Number of students like blue colour = 5
Number of students like purple colour = 3
Number of students like green colour = 6
Now according to above data we find that number of students prefer red colour is equal to number of students prefer green colour.
Twice as many students prefer green than purple.
More students prefer blue than yellow.
Two more students prefer blue than purple.
Therefore, statments Two more students prefer blue than purple and Twice as many students prefer green than purple are true.
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Evaluate. Write your answer as a fraction or whole number.
(1/2)²=___
Answer: 0.25 or 1/4
Hope this helps :)
Step-by-step explanation:
Answer:
0.25 or 1/4
Step-by-step explanation:
1/2 as a decimal is 0.50 and that squared is 0.25, which as a fraction is 1/4.
Jacob wants to save $175 for a trip to an amusement park. He sets aside $14 of his allowance at the end of each week. How many weeks will it take him to save enough money for the whole trip?
Luke is completing a science experiment at home. He bought two hibiscus plants for his experiment. One of the plants was 5 cm tall. Each week he measured and recorded the
height of the plant, H, in cm. After collecting data for several weeks, he determined that the height of the plant, H, in cm, could be represented by the function H (t) = 5 +0.5t,
where t is the number of weeks since he purchased the plant.
Part A
What is the value of H(4)?
Part B
What does H (2) = 10 mean in this situation?
The height of the plant was 2 cm after 10 weeks.
The height of the plant was 7 cm after 4 weeks.
The height of the plant was 4 cm after 7 weeks.
The height of the plant was 10 cm after 2 weeks.
a) The numeric value at t = 4 is of H(4) = 7.
b) The meaning of the numeric value H(2) = 10 is given as follows:
The height of the plant was 10 cm after 2 weeks.
What is the meaning of the function?The function in this problem has the definition presented as follows:
H(t) = 5 + 0.5t.
The variables of the function are given as follows:
t is the number of weeks.H(t) is the height after t weeks.The numeric value at t = 4 is calculated replacing the lone instance of t in the function by 4, as follows:
H(4) = 5 + 0.5(4) = 5 + 2 = 7 cm.
H(2) = 10 means that when t = 2, H(t) = 10, that is, after 2 weeks, the height is of 10 cm, and thus the last option is correct.
(considering the interpretation of each variable).
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Alicia cashed half of her paycheck and set aside the other half to take her friends out to dinner. She spent on dinner and brought home more than Write an inequality to represent the situation, using to represent the amount of Alicia’s paycheck.
An inequality that uses Alicia's salary as the unit of measurement is x > $124.3.
Explain the term inequality?Inequalities specify the link between two things that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two parameters are not equal. But several inequalities are utilized to compare the numbers, regardless it is less than or higher than.Data for the stated question-
'x' is the Alicia's Paycheck
Half money is taken for dinner x/2
Total spending on dinner = $42.15
Cost of home she bought home more than $20.00.
Thus, inequality to represent the situation becomes-
x/2 - $42.15 > $20.00
Add both side by 42.15.
x/2 > $62.15
Divide the number by 2.
x > $124.3
Therefore, an inequality that uses Alicia's salary as the unit of measurement is x > $124.3.
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The complete question is-
Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck.
In AJKL, m/J = (4x − 10)°, m/K = (3x − 7)°, and m/L = (4x − 1)º.
-
Find m/K.
Answer:
K = 17
Step-by-step explanation:
x = 8
Measures of Central Tendency ->
Barry has scores of 93, 84, 86, and 75. He wants to raise the mean to 86.
what is the answer?
Measures of Central Tendency
A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of central tendency.
[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]
There are 6 numbers and their sum is 525
Therefore, their mean is
[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]
Mode is the number with the highest frequency i .e which number appears the most in the sequence
In this case, there is NO mode because each number there appears only once
Median is the middle number when you place the numbers in ascending order
79,85,86,90,92,93
The middle number is between 86 and 90 . So your middle number can be found by [tex]\frac{86+90}{2}=88[/tex]
So your median is 88
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Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 3 > 3
The graph for |x| + 3 > 3 is attached below.
What is open sentence?It is unknown if a mathematical sentence is true or false since it uses variables, which is known as a "open sentence" in mathematics. On the other hand, a closed sentence is a mathematical statement that is known to be either true or untrue.
Given:
|x| + 3 > 3
|x| > 3- 3
|x| > 0
Now, The open sentence is an absolute inequality, so we start by analyzing the inequality sign > 0 means that, the x-values of the inequality is not less than 0.
So, the shaded area of the graph are: x >0 then right side of the graph is shaded.
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How much money does Dana Jones have after 7 years if she invests $ 1100 at 5 % interest compounded continuously? Use the formula A =Pе⁺ to solve.
Dana Jones has $____ after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
When compounded continuously , the Compound Interest Amount is calculated by the formula ,
A = Pe^rt
Given data ,
Let the investment be P
The value of P = $ 1100
The rate of interest r = 5 %
The number of years t = 7 years
The Compound Interest Amount when compounded continuously is calculated by the formula ,
A = Pe^rt
Substituting the values in the equation , we get
A = 1100 x e ^ 0.05 x 7
A = 1100 x e ^ 0.35
A = 1100 x 2.718 ^ 0.35
A = 1100 x 1.419067
A = $ 1560.97
Therefore , the value of the amount is A = $ 1560.97
Hence ,
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
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In which direction does the parabola defined by the equation y = -x + 2 open?
Answer:
Downward
Step-by-step explanation:
A parabola is a curve that is shaped like a U. The direction in which a parabola opens depends on the sign of the coefficient of the x^2 term in the equation defining the parabola. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downward.
In the equation y = -x + 2, the coefficient of the x^2 term is 0, so the direction of the parabola does not depend on it. However, the coefficient of the x term is -1, which is negative. This means that the parabola defined by this equation opens downward.
23. For the data in the table, does y vary directly with x? If it does, write an equation for the direct (1 point) variation.
yes; y=2 x
yes; y=5 x
yes; y=7 x
no; y does not vary directly with x.
The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
What is the constant of variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
We have,
x y
2 10
4 24
6 36
To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.
If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.
If the ratio y/x is not constant for all the data points, then y does not vary directly with x.
so, let's see the k constant of variation,
k = y/x
k = 2/10 =1/5
k = 4/24 = 1/6
k = 6/36 = 1/6
so, k = 1/5, k=1/6, k=1/6.
Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
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there are 80 houses being built in a neighborhood last month 1/4 of them were sold. This month 2/5 of the remaining houses were sold. How many houses are left to be sold?
36 houses are left to be sold.
Step-by-step explanation:Here are the steps to find out the answer to your question:We need to convert 1/4 and 2/5 into decimals. We do this by dividing the numerator by the denominator:
1 ÷ 4 = 0.25
2 ÷ 5 = 0.4
Now, we can set up this equation to find out how many were sold in the first month:
0.25 x 80 = 20
Now, 20 isn't the answer, it is 60 houses left, because 80 - 20 = 60.
Let's do the next one:
0.4 x 60 = 24
60 - 24 = 36
Solution:
36 houses are left to be sold.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
To convert Celsius temperatures to Fahrenheit temperatures, the function F defined by F(x) = 32 + 1.87 is useful. Confirm this, then find a formula for the function C (which could also be called F-1) that converts Fahrenheit temperatures to Celsius temperatures.
Answer: The function F(x) = 32 + 1.87x converts Celsius temperatures to Fahrenheit temperatures. To confirm this, you can plug in a few different values for x (the Celsius temperature) and see if the corresponding value of F(x) (the Fahrenheit temperature) is correct.
For example, if x = 0, the function gives us F(0) = 32 + 1.87 * 0 = 32, which is the correct conversion from Celsius to Fahrenheit for 0 degrees Celsius.
If you want to find a formula for the function C that converts Fahrenheit temperatures to Celsius temperatures, you can start by rearranging the formula for F(x). The Fahrenheit temperature is equal to the Celsius temperature plus 32, multiplied by 1.8.
If we solve for the Celsius temperature, we get:
x = (F - 32) / 1.8
This is the formula for the function C that converts Fahrenheit temperatures to Celsius temperatures. To use this function, you would plug the Fahrenheit temperature into the function as the input, and it will give you the corresponding Celsius temperature as the output.
For example, if you want to convert 100 degrees Fahrenheit to Celsius, you would plug 100 into the function as the input:
C(100) = (100 - 32) / 1.8 = 37.78 degrees Celsius.
Pls help, I can’t figure this out .
Answer:
Step-by-step explanation:
y = 4×[tex]5^{0}[/tex] y=4
y=4×[tex]5^{2}[/tex] y=100
y=4×[tex]5^{4}[/tex] y=2500
y=4×[tex]5^{6}[/tex] y=62500
y=4×[tex]5^{7}[/tex] y=312500
How many different roots does the polynomial function, y= (x+4)(x-2)^2(x+7) have?
The polynomial function, y= (x+4)(x-2)²(x+7) has three different roots
How to determine the number of roots?From the question, we have the following parameters that can be used in our computation:
y = (x+4)(x-2)^2(x+7)
Rewrite the equation properly
So, we have the following representation
y= (x+4)(x-2)²(x+7)
Set the factor to 0
So, we have
x + 4 = 0, x - 2 = 0 and x + 7 = 0
When these equations are solved, we have
x = -4 , x = 2 and x = -7
See that the counts of the values of x is 3
Hence, it has three different roots
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Question 1: Write down the square numbers from the list below
91 101 1024
81 200
A water tank initially contained 55 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 2 minutes? Round answers to the nearest whole liter.
Answer:
50 liters
Step-by-step explanation:
2.5 liters drained per minute x 2 minutes = 5 liters drained total
(2.5 x 2 = 5)
55 liters at the start - the 5 liters drained = 50 liters remaining
(55 - 5)
whole equation would be
55 - (2.5 x 2) = 50
The price of a CD player was reduced from $80to $52. What was the decent decrease in the price of the CD player?
Answer:
it was decreased by $28
Step-by-step explanation:
$80 – x = $52
–x = $52 – $80
–x = $28
x = $28
i hope this answer helped
Find using Function Notation
Given the f(x) graph below, find the value of each expression.
Find f(0)
Find f(x) = -3
The set of all x for which the f(x) graph crosses the x-axis is the solution of f(x) = 0. The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0
What is function notation?A simple and clear approach to write functions is in function notation. When we use function notation, the independent variable (often x) and the dependent variable (often F) for a function are both listed (x).A function provides an output after receiving an input. When writing a function, the name of the function is written as f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, f, x is the input variable, and f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, f is the output.a set of symbols that are used to represent unique objects. Example: "" stands for "infinity" in mathematical notation. Numerous symbols are used in mathematics.Given data :
f(0) =
The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0
f (x) = -3
x = − 3 is a vertical line that crosses the -axis at -3. y = 3 is a horizontal line that crosses the -axis at 3. y = − 3 is a horizontal line that crosses the -axis at -3.
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Determine whether the following equation defines y as a function of x.
100x² = y²
Does the equation defines y as a function of x?
No
Yes
Yes, the equation defines the value of y in terms of x which is ±10x.
What is the equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Given, the equation defines y as a function of x.
100x² = y²
Hence,
Y² = (10x)²
Taking square root on both sides.
y = ±10x
Since the value of the y is in the term of x. Therefore, The value of y is defined in terms of x, which is 10x, in the equation.
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