It will take approximately 12 years and 9 months for Sienna Rose's money to grow to $7000.
What is compound interest?
Compound interest is interest that is calculated not only on the original principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, the interest earned on an investment or the interest charged on a loan is added to the principal, and then the interest for the next period is calculated on the new total amount.
For example, if you invest $1,000 at an annual interest rate of 5%, and the interest is compounded annually, you would earn $50 in interest at the end of the first year. Instead of receiving that $50, it would be added to your principal, so your new balance would be $1,050. The following year, you would earn 5% interest on $1,050, which would be $52.50. This process would continue for each year of the investment.
Compound interest can be very beneficial for long-term investments, as the interest earned on the accumulated interest can significantly increase the total return. However, it can also work against you in the case of loans, as the interest charged on the accumulated interest can quickly increase the total amount owed.
We can use the formula for compound interest to solve this problem:
[tex]A= P (1+\frac{r}{n} )^{nt}[/tex]
where
A is the amount of money after t years,
P is the principal (starting amount),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year, and
t is the time (in years).
In this case,
P = $4000,
r = 0.036 (since the interest rate is given as 3.60% per year),
n = 12 (since the interest is compounded monthly), and
we want to find t when A = $7000.
Substituting these values into the formula, we get:
$7000 = $4000(1 + 0.036/12)^(12t)
Dividing both sides by $4000 and taking the natural logarithm of both sides, we get:
ln(1.75) = 0.003 t
Solving for t, we get:
t = ln(1.75)/(0.003)
t ≈ 153.71 months
Therefore, it will take approximately 153 months, or 12 years and 9 months (since there are 12 months in a year), for Sienna Rose's money to grow to $7000.
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how many hours until tomorrow
The time right now and the time zone you are in determine how many hours are left before tomorrow. Assuming you mean the following calendar day, tomorrow's hours would be:
The amount of hours until tomorrow if it is currently before midnight is 24 minus the current hour. For instance, if it is 9:00 PM right now, there are 24 – 21 = 3 hours left until tomorrow.
In this case, the number of hours until tomorrow would be equal to the time difference between now and midnight + 24. If it is 1:00 AM, for instance, there are (24 - 1) + 1 = 24 hours until tomorrow.
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How to convert 9 into cm?
9 inches is equal to 22.86 centimeter
To convert 1 inches to cm, we can use the following formula:
1 inch = 2.54 cm
The conversion factor is 2.54
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in cm = conversion factor × The length in inches
Substitute the values in the equation
9 inches = 9 × 2.54 cm
Multiply the numbers
= 22.86 cm ( rounded to two decimal places )
Therefore, 9 inch is 22.86 cm
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You need a 40% alcohol solution. On hand, you have a 120 mL of a 5% alcohol mixture. You also have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired solution?
In order to create a 40% alcohol solution, we must combine 280 mL of 55% alcohol combination with 120 mL of the 5% alcohol mixture.
How does drinking affect the body?Alcohol can change how the brain functions and appears by interfering with the body's communication networks. In addition to altering attitude and behaviour, these disturbances can also make it more difficult to think effectively and move to coordination.
Let's designate the quantity of a mixture of 55% booze that needs to be added "x" (in mL).
We know that the finished solution must contain 40% pure alcohol by volume in order to achieve our goal of a 40% alcohol solution.
The amount of pure alcohol in the 120 mL of 5% alcohol mixture is:
0.05 * 120 = 6 mL
When we add "x" mL of the 55% alcohol mixture, we will add:
0.55x mL of pure alcohol
In the end, we want the total amount of pure alcohol in the final solution to be:
0.40 * (120 + x) mL
Now we can set up an equation:
0.55x + 6 = 0.40(120 + x)
Simplifying and solving for "x", we get:
0.55x + 6 = 48 + 0.40x
0.15x = 42
x = 280
So we need to add 280 mL of the 55% alcohol mixture to the 120 mL of 5% alcohol mixture to obtain a 40% alcohol solution.
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Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The height of a randomly selected giraffe b. The number of points scored during a basketball game c. The gender of college students d. The amount of rain in City Upper B during April e. The number of fish caught during a fishing tournament f. The number of bald eagles in a country
The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.
a. Continuous random variable
b. Discrete random variable
c. Discrete random variable
d. Continuous random variable
e. Discrete random variable
f. Not a random variable
a. The height of a randomly selected giraffe is a continuous random variable because it can take on any value within a certain range.
b. The number of points scored during a basketball game is a discrete random variable because it is a countable number.
c. The gender of college students is a discrete random variable because it is a categorical variable with two possible values.
d. The amount of rain in City Upper B during April is a continuous random variable because it can take on any value within a certain range.
e. The number of amount fish caught during a fishing tournament is a discrete random variable because it is a countable number.
f. The number of bald eagles in a country is not a random variable because it is a fixed number and not a random sample.
The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.
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PLEASE HELP!!!
There are 87 marbles in a bag and 68 of them are green. If one marble is chosen, what is the probability that it will be green?
Probability =
specific: green (68)
total: all (87)
= 68 ÷ 87 = 0.781609...
Watch the instructions carefully to determine how many decimals places to round, or if the number should be converted to a percent. In the example above, if we round to two decimal places, we get 0.78.
Review
Directions: Use the Spinner to answer questions 1-6.
THE SPINNER IS AT THE BOTTOM OF THE PAGE!!!
1) In which color, is the pointer more likely to land?
2) In which color, is the pointer less likely to land?
3) In which colors, is the pointer equally likely to land?
4) What is the chance the pointer will land on white?
a) More likely b) less likely c) equally likely d) unlikely
5) Is any color certain?
6) If green is replaced by blue, which colors have equally likely chances?
7) There are 5 white balls, 8 red balls, 7 yellow balls, and 4 green balls in a container. A ball is chosen at random. What is the probability of choosing red?
8) What is the probability of choosing green?
9) What is the probability of choosing either red or white?
10) What is the probability of choosing neither white nor green?
11) What is the probability of choosing other than yellow?
12) What is the probability of choosing black?
13) A card is drawn from a deck of 52 cards. Find the probability of drawing a black card.
14) Find the probability of drawing a red card.
15) Find the probability of drawing a red or black.
16) Find the probability of drawing an ace.
17) Find the probability of drawing either a jack or queen or king.
Challenge: Create three probability application problems of your own. Solve your problems. Explain your answers.
18)
19)
20)
Answer:32222
Step-by-step explanation: i dont really think thats the answer, i just did it for the points
Jay's unpaid credit card balance is $3390.88. His APR is 18.6%. What is his new balance if he made one new transaction of $128?
Jay's new balance if he made one transaction of $ 128, given the credit card balance is
How to find the new balance ?To find the new balance, you first need to find the interest on the old balance by the formula :
= 3, 390.88 x 18. 6 % / 12 months per year
= $ 52. 56
Jay's new balance is :
= Old balance + Interest + New transaction
= 3, 390. 88 + 52. 56 + 128
= $ 3, 571. 44
The new credit card balance is $ 3, 571. 44.
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the function f is continuous and ∫80f(u)du=6. what is the value of ∫31xf(x2−1)dx?
Using integration by substitution, the value of ∫31xf(x^2-1)dx is 6.
What is the value using integration by substitutionTo solve this problem, we can use integral by substitution.
Let's set u = x^2 - 1, then du/dx = 2x, or dx = du / (2x).
Using this substitution, we can rewrite the integral as:
∫(3^2-1)^(8^2-1) f(u) * (du / 2)
Next, we can use the fact that f is continuous and the integral of f from 8 to 0 is 6. We can split the integral into two parts:
∫(3^2-1)^(8^2-1) f(u) * (du / 2) = ∫0^(8^2-1) f(u) * (du / 2) - ∫0^(3^2-1) f(u) * (du / 2)
The first integral on the right-hand side is the integral we're given:
∫0^(8^2-1) f(u) * (du / 2) = 6
The second integral can be rewritten using our substitution:
∫0^(3^2-1) f(u) * (du / 2) = ∫(3^2-1)^(0) f(u) * (du / 2)
Notice that we've switched the limits of integration, which means we need to negate the integral:
∫(3^2-1)^(0) f(u) * (du / 2) = -∫0^(3^2-1) f(u) * (du / 2)
Substituting back into our original integral and using these results, we get:
∫(3^2-1)^(8^2-1) f(u) * (du / 2) = 6 - (-∫0^(3^2-1) f(u) * (du / 2)) = 6 + ∫0^(3^2-1) f(u) * (du / 2)
Finally, we can substitute back in for x and simplify to get our answer:
∫31xf(x^2-1)dx = (1/2) * ∫(3^2-1)^(8^2-1) f(u) * du = (1/2) * (6 + ∫0^(3^2-1) f(u) * du) = (1/2) * (6 + ∫0^8 f(u) * du) = (1/2) * (6 + 6) = 6
∫31xf(x^2-1)dx = 6.
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Find the length of X
How much is 50 ml in ozs?
50 milliliters (ml) is equivalent to 1.69 fluid ounces (oz). To convert milliliters to fluid ounces, you need to use the conversion factor of 0.03381402 fluid ounces per milliliter.
This means that you can multiply the number of milliliters by this conversion factor to get the equivalent volume in fluid ounces. The conversion between milliliters and fluid ounces is commonly used in the measurement of liquids, especially in cooking and baking recipes.
Some recipes may use milliliters as the standard unit of measurement, while others may use fluid ounces or other units. Being able to convert between different units of measurement is important to ensure accurate measurement and a successful outcome in the recipe.
It's worth noting that fluid ounces are a measure of volume, while ounces can also be a measure of weight. In the United States, fluid ounces are commonly used to measure the volume of liquids, while ounces are used to measure the weight of both solids and liquids.
In summary, 50 milliliters is equal to 1.69 fluid ounces, and understanding how to convert between different units of measurement is important in cooking, baking, and other applications that involve measuring liquids.
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Lamonte is going to invest $48,000 and leave it in an account for 17 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Lamonte to end up with $120,000?
The interest rate that would be required is 5.39%. The solution has been obtained by using concept of compound interest.
What is compound interest?
Both the principal and the interest that has accumulated over the preceding period are taken into account when interest is calculated. In contrast to simple interest, which does not take the principal into account when calculating the interest for the following month, compound interest does. Compound interest is usually represented in algebra by the letter C.I.
We are given that Lamonte is going to invest $48,000 and leave it in an account for 17 years. She wants to end up with $120,000.
So, from this we get the equation as
120,000 = 48000e¹⁷ⁿ ( n is the interest rate)
Solving this, we get
e¹⁷ⁿ = 2.5
n = 5.39%
Hence, the interest rate that would be required is 5.39%.
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QUESTION 1 1.1 Draw any AABC with B = 90° in your answer book and find the ratios of the following in terms of the sides. 1.1.1 sinc (1.1.2 sin A 1.1.3 cosc 1.1.4 cosA 1.1.5 tanc 1.1.6 tan (1) ЗЗЗЗЗЕ (1) (1) (1) [6]
Based on the drawing of AABC, the ratios wrt to the sides are given below:
1.1.1 Sin C= c/b1.1.2 Sin A = a/b1.1.3 Cos C= a/b1.1.4 Cos A = c/b1.1.5 Tan C= c/a1.1.6 Tan A = a/cHow to find ratios of sides in geometryThere are several ways to find the ratios of sides in geometry, depending on the specific situation. Here are a few common methods:
Similar triangles: If you have two triangles that are similar, that is, they have the same shape but possibly different sizes, then the corresponding sides are in proportion. That is, if the sides of one triangle are a, b, and c, and the sides of the other triangle are x, y, and z, and the triangles are similar, then:
a/x = b/y = c/z
You can use this property to find the ratio of any two sides of a triangle if you know the ratio of the corresponding sides of a similar triangle.
Proportions: In some cases, you can use proportions to find the ratio of sides. For example, if you have a rectangle with sides of length a and b, and you know that the ratio of a to b is 2:3, then you can set up the proportion:
a/b = 2/3
and solve for either a or b.
Trigonometry: If you know the angles of a right triangle, you can use trigonometric ratios to find the ratio of sides. For example, in a right triangle with angle A, the ratio of the side opposite A (which we'll call a) to the hypotenuse (which we'll call c) is given by the sine of A:
sin(A) = a/c
You can rearrange this formula to solve for a or c, depending on what you know.
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What is infinite algebra 1?
Infinite Algebra 1 is a software program developed by the company Kuta Software that provides an online resource for teaching and learning algebra 1.
It offers a comprehensive collection of algebra 1 problems and exercises that cover a wide range of topics such as linear equations, systems of equations, inequalities, polynomials, factoring, and graphing.
The program includes features such as an interactive equation editor, step-by-step solutions, and the ability to generate customized worksheets and assessments.
It is designed to provide students with a self-paced and adaptive learning experience that allows them to practice and reinforce their understanding of algebraic concepts. Infinite Algebra 1 is widely used in schools and educational institutions as a tool for teaching and practicing algebra 1.
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What is Find the output, k, when the input, t, is -7.
k = 10t-19k=10t−19
What is K
Answer:
when the input t is -7, the output k is -89.
Using the equation k = 10t - 19 and substituting t = -7, we have:
k = 10(-7) - 19
k = -70 - 19
k = -89
Therefore, when the input t is -7, the output k is -89.
The height (h) of an object thrown from the top of a ski lift 2308 feet high after (t) seconds is h= - 16t² +32t+2308.
For what times is the height of the object at least 1300 feet?
The height of the object is at least 1300 feet from _______ seconds to _______ seconds.
The height of the object is at least 1300 feet after 9 seconds. The solution has been obtained by solving the algebraic equation.
What is algebraic equation?
A mathematical expression is said to be "algebraic" if it includes variables, constants, and algebraic operations (addition, subtraction, etc.). The expression has to satisfy the algebraic equation and have the equals sign in it.
We are given an equation as h = - 16t² + 32t + 2308
Since, we need to find the times at which the height of the object at least 1300 feet so, we will substitute h = 1300 in the equation.
From this, we get
⇒1300 = - 16t² + 32t + 2308
⇒0 = - 16t² + 32t + 1008
⇒0 = -t² + 2t + 63 (On dividing both sides by 16)
⇒t² - 2t - 63 = 0
⇒t² - 9t + 7t - 63 = 0
⇒t(t - 9) + 7(t - 9) = 0
⇒(t - 9) (t + 7) = 0
⇒t = 9 , -7
Hence, the height of the object is at least 1300 feet after 9 seconds.
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The system of equations below represents the amount in dollars that Brianna paid for 5 paint brushes and 3 art canvases and Ahmed paid for 10 paint brushes and 6 art canvases. {5x+3y=4710x+6y=94 Did Brianna and Ahmed pay the same price for the items?
There is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
What is the system of equations?
A system of equations is a set of one or more equations that are to be solved simultaneously. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.
In this case, the system of equations represents the amount that Brianna and Ahmed paid for 5 paintbrushes and 3 art canvases, and 10 paintbrushes and 6 art canvases, respectively. The system of equations is:
5x + 3y = 47 (Brianna's purchase)
10x + 6y = 94 (Ahmed's purchase)
To determine whether Brianna and Ahmed paid the same price for the items, we can compare the value of x and y that satisfy both equations. To do this, we can solve the system of equations using any method we prefer, such as elimination or substitution. Here, we'll use the method of substitution:
From the first equation, we can solve for y in terms of x:
5x + 3y = 47
3y = 47 - 5x
y = (47 - 5x)/3
Substituting this expression for y into the second equation, we get:
10x + 6y = 94
10x + 6((47 - 5x)/3) = 94
Simplifying, we get:
10x + 94 - 10x = 94
94 = 94
This equation is always true, regardless of the value of x.
Therefore, there is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
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the amount of soda was entered as 8 fluid ounces. however, this is not reflective of a typical serving size of most sugar-sweetened beverages. most sodas are now sold in bottles that contain 20 fluid ounces, and many are even larger. on the spreadsheet report, find the column for calories (cals). if zander were to drink 20 fluid ounces of soda, how many calories would he consume from soda?
8 fluid ounces are in one serving is the required fluid ounces in one serving.
Given that,
There are 8 fluid ounces in a cup, how many fluid ounces are in one serving is to be determined.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
There are 8 fluid ounces in 1 cup and in a serving of one cup there will be 8 fluid ounces.
Thus, 8 fluid ounces are in one serving is the required fluid ounces in one serving.
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What is the area of this figure?
Answer:
24
Step-by-step explanation:
Rect = 3*4 = 12
Rect 2 = 1*6 = 6
Triangle = (6-3)*1/2*4 = 6
6 + 6 + 12 = 24
If m∠11 = 118, what is the measure of ∠8?
The measure of ∠8 is also 118º because angles opposite the vertex are equal.
To explain further, when two lines intersect, they create four angles. The angles that are directly across from each other are called angles opposite the vertex. These angles are always equal. So, if one angle measures 118 degrees, the angle opposite the vertex will also measure 118 degrees.
In this case, ∠11 and ∠8 are angles opposite the vertex. Therefore, if m∠11 = 118, then m∠8 = 118 as well.
So, the measure of ∠8 is 118.
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Can someone help me?
Answer:
yeah sure, what you need?
realiza la inversa de la siguiente función f(x)=x+2/x-3
The inverse function {f⁻¹(x)} for the function f(x) is -
f⁻¹(x) = (3x + 2)/(x - 1)
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is the function f(x) as -
f(x) = (x + 2)/(x - 3)
We can write the function f(x) as -
f(x) = (x + 2)/(x - 3)
We can find the inverse function {f⁻¹(x)} as follows -
y = (x + 2)/(x - 3)
x = (y + 2)/(y - 3)
x(y - 3) = y + 2
xy - 3x = y + 2
xy - y = 3x + 2
y(x - 1) = 3x + 2
y = (3x + 2)/(x - 1)
f⁻¹(x) = (3x + 2)/(x - 1)
Therefore, the inverse function {f⁻¹(x)} for the function f(x) is -
f⁻¹(x) = (3x + 2)/(x - 1)
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{Question in english -
perform the inverse of the following function f(x)=x+2/x-3}
Find the smallest pair of 4 digit numbers such that the difference between them is 303 and
The smallest pair of 4 digit numbers such that the difference between them is 303 and HCF is 101 are found to be 1010 and 1313.
The HCF is the highest common factor or in other words, the largest number by which two numbers can be divided. List the four-digit numbers that could be the HCF for 101 to begin.
101 x 10 = 1010
101 x 11 = 1111
101 x 12 = 1212
101 x 13 = 1313
These numbers now reveal two further numbers whose difference is 303.
1313 - 1010 = 303
The two smallest 4 digit numbers are 1010 and 1313 as a result.
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Complete question - Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101.
what is big number calculator?
A big number calculator is a software application or program designed to perform arithmetic operations on large numbers that cannot be easily handled by standard computer hardware and software.
Big numbers are typically defined as numbers that are too large to be stored in the registers or memory of a typical computer processor.
In a big number calculator, arithmetic operations such as addition, subtraction, multiplication, and division are performed using algorithms that are specifically designed to handle large numbers. These algorithms may use techniques such as long division, long multiplication, and other mathematical strategies to perform the required computations.
Big number calculators are often used in scientific and engineering applications where very large numbers are encountered. They can also be useful in cryptography, where large prime numbers are used for encryption and decryption operations.
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The annual rate of growth in population of a certain city is 8%. If its present population is 1,96,830 then what was the population three years ago?
Answer: The population three years ago was 156250.
Step-by-step explanation:
Let 3 years ago, the population of a city = P
Rate of growth (R) = 8% p.a.
Present population (P) = 1,96,830.
Therefore,
[tex]A=P(1+R100)n[/tex]
P = A÷(1 + 8/100)³
196830 ÷ (1+2/25)³
=156250.
3 years ago, the population of the city = 156250.
pls help me solve this
The perimeter of the figure is 28 units
What is perimeter of a figureThe perimeter of a figure is the total length of its boundary or outer edge. It is the sum of the lengths of all the sides of the figure. The perimeter is usually measured in units such as centimeters, meters, inches, or feet, depending on the measurement system being used.
The perimeter of this figure is the sum total length of the boundaries.
This can be calculated as;
P = 2 + 4 + 5 + 3 + 7 + 7
P = 28 units
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Write the radical expression [tex]\frac{8}{\sqrt[7]{x^1^5} }[/tex] in exponential form.
The value of the exponential equation is A = ( 8 ) x ^ -105/2
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = 8 / ( 7√x¹⁵ ) be equation (1)
On simplifying the equation , we get
The value of √x¹⁵ = x ^ 15/2
Now , the 7th root of √x¹⁵ is = x ^ 105/2
Now , the equation will be
A = ( 8 ) x ^ -105/2
Hence , the exponential equation is A = ( 8 ) x ^ -105/2
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Picture attached !!! Help as fast as possible please!!!
Answer:
it would be -10x-15
Step-by-step explanation:
You're basically using distributive property
5(-2x-3)
5•-2x=-10x
5•-3=-15
-10x-15
It would stop there because you can't combine a number w/ a variable with a number without a variable, I hope that makes enough sense
how to convert 141 lbs to kg?
The conversion value of pounds to kilogram as per requirement is given by 141 pounds = ( 63.9576 ) kilograms.
Standard units pounds and kilograms are helpful in measuring the mass of the given object.One kilograms is equivalent to 2.20462 pounds.
This implies ,
⇒ 2.20462 pounds = 1 kilograms
Divide both the side by 2.20462 we get,
⇒( 2.20462 / 2.20462 ) pounds = ( 1 / 2.20462 ) kilograms
⇒ 1 pounds = ( 0.4536 ) kilograms
Now, Multiply both the side by 141 we get,
⇒ 141 pounds = ( 141 × 0.4536 ) kilograms
⇒ 141 pounds = ( 63.9576 ) kilograms
Therefore, the conversion factor of kilogram to pounds is 2.20462 this implies 141 pounds = ( 63.9576 ) kilograms .
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What does e to the pi mean?
The expression "e to the pi" refers to the mathematical constant e raised to the power of the mathematical constant pi (approximately 2.71828). (approximately 3.14159).
As, the exact value is an irrational number that cannot be expressed as a finite decimal or fraction, the value of e to the pi is approximately 23.14069.
The combination of e and pi is a well-known mathematical expression that can be seen in a variety of areas of mathematics, including calculus, number theory, and complex analysis.
Mathematicians are particularly interested in e to the pi because it is a transcendental number (a number that is not the root of any non-zero polynomial with rational coefficients).
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Is it possible to form a triangle with side lengths 8, 9, and 17? If not, explain why not.
This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.
What does a triangle actually mean?Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons.
Here,
No, it is not possible to form a triangle with side lengths 8, 9, and 17.
To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Symbolically, for sides a, b, and c, this can be written as:
a + b > c
a + c > b
b + c > a
Let's check if these inequalities are satisfied for the sides of 8, 9, and 17:
8 + 9 > 17 (true)
8 + 17 > 9 (true)
9 + 17 > 8 (true)
All three inequalities are true, which means that the given side lengths satisfy the triangle inequality and a triangle can be formed.
In this case, we see that 8 + 9 = 17, which is exactly the length of the third side.
This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.
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what us systems of equations solver
Systems of equations solver called Wolfram or Alphas can resolve systems of linear equations or nonlinear equations, and it can look for solutions that are only integers.
Systems of direct equations are a common and applicable subset of systems of equations. In the case of two variables, these systems can be allowed of as lines drawn in two- dimensional space. However, the system is said to be harmonious and has a result at this point of crossroad, If all lines meet to a common point. The system is said to be inconsistent else, having no results. Systems of direct equations involving further than two variables work also, having either one result, no results or horizonless results( the ultimate in the case that all element equations are original).
More general systems involving nonlinear functions are possible as well. These retain more complicated result sets involving one, zero, horizonless or any number of results, but work also to direct systems in that their results are the points satisfying all equations involved. Going further, more general systems of constraints are possible, similar as bones that involve inequalities or have conditions that certain variables be integers.
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