Principal $960 interest rate 9% time in nine months what is the simple interest
keeping in mind that a year has 12 months, thus 9 months is really 9/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$960\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (960)(0.09)(\frac{3}{4}) \implies I=64.8[/tex]
If Terrence jogged 4380 km how many meters did he jog
Expand each binomial.
(x²+2 y³)⁶
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x + y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ.
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (x² + 2y³)⁶
By using binomial expansion theorem, we get
(x² + 2y³)⁶ = x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸
(x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸
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Find each value without using a calculator. If the expression is undefined, write undefined.
sec (-π)
The value of the expression sec (-π) is equal to -1 if the given expression is undefined.
As given in the question,
Given expression: sec (-π)
Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)
Hypotenuse = √ (-1)² + 0²
= 1
Value of the expression is given by
sec α = Hypotenuse / Base (x-coordinate)
⇒sec(-π) = 1 / -1
⇒sec(-π) = -1
Therefore, the value of the expression sec (-π) is equal to -1.
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given ij = 3x +3 HI = 3x-1 hj=3x+8 determine the numerical length of hj
if the point I is between points H and J, then the numerical length of hj is 14 units
How to determine the numerical length of hj?The given parameters are
IJ= 3x + 3
HI = 3x - 1
HJ = 3x + 8
The above implies that the point I is between points H and J
So, we have
HJ = HI + IJ
Substitute the known values
3x + 8 = 3x + 3 + 3x - 1
Evaluate the like terms
3x = 6
Divide by 3
x = 2
Substitute x = 2 in HJ = 3x + 8
HJ = 3 x 2 + 8
Evaluate
HJ = 14
Hence, the numerical length of hj is 14 units
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0.625(x+10) -10 =x SOLVE
Write an inequality that represents
Answer: x ≤ 4.5
Step-by-step explanation:
Since there is a closed circle on 4.5 and the ray is going left we know that x is ≤ 4.5
you and a friend are making jewelry for your friends. Bracelets cost $2.25 to make and
you spent $21.50 on supplies for necklaces. You only have $45 total to spend on supplies. Can you make bracelets for at least 10 friends? Explain your reasoning and show your work.
The fact that $45 is enough to make bracelets for 10.44 persons means that the we can make bracelets for 10 friends
What is the total necklace cost function?
The total cost of necklaces that can be made within the total budget of $45 can be modeled using a straight-line equation, which considers the fixed cost of necklace supplies of $21.50 and the total variable cost of supplies, the cost per necklace multiplied by the total number of necklaces possible, defined as x
45=21.50+2.25x
let solve for x to determine whether we can make bracelets for 10 friends
45-21.50=2.25x
23.50=2.25x
x=23.50/2.25
x=10.44
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PLEASE ANSWER QUESTION IN THE SCREEN SHOT!<3
Based on the information, it should be noted that there's an increase in percentage of 30%.
How to illustrate the information?Based on the information, it should be noted that the following can be illustrated:
Original amount = 30
New amount = 39
Therefore, it should be noted that the change in percentage will be:
= Change in amount / Old amount × 100
= (39 - 30) / 30 × 100
= 9/30 × 100
= 30%
Therefore, there's a increase in percentage of 30%.
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If mWVY = 70, find mYVX.
Two or more expressions with equal sign is called as Equation. If mWVY = 70 is an angle then mYVX =165 we get by solving the equation x-13=70.
What is equation?Two or more expressions with equal sign is called as Equation.
mWVY = 70
From the figure we can observe that mWVY =x-13
By this we form an equation
x-13=70
x-13=70
x=70+13
x=83.
So value of x is 83.
Now mYVX=2x-1
2(83)-1
166-1
=165
Therefore mYVX is 165 degree when mWVY = 70.
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b. What are the expressions ⁴√x³} and (⁵√y⁴) in exponential form?
Exponential Form
We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.
So, we use the following method to write the given expression in exponential.
Expression 1 = ⁴√x³
Expression 2 = ⁵√y⁴
Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)
similarly, we can write the second equation as
Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)
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A savings account pays 4.62% annual interest, compounded continuously. After approximately how many years will a principal of $ 500 double?
After approximately 16 years, the principal amount of $500 double.
What do we mean by compound interest?Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate multiplied by the number of compound periods multiplied by one. The total initial loan amount is then deducted from the resulting value. The amount of interest added in each compounding period is determined by the interest rate, compounding period, and account balance. The basic formula is as follows: added interest = (interest rate for one period) × (balance at the beginning of the period).So, to find out how many years will a principal of $ 500 double:
Let x be the principal amount.The formula for calculating compound interest is as follows:
A = P(1 + r)^tThe value of r is 0.0462. In the equation, substitute this and x:
2x = x(1 + 0.0462)^t2 = (1.0462)^t (1.0462)^16 = (1.0462)^t t = 16Therefore, after approximately 16 years, the principal amount of $500 double.
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Solve each equation.
log₇343=x
The value of x for the equation log₇343=x will be 3.
What are the basic properties of logarithmic function?Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties.
These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.
For log₇343=x
It can be expressed in the form of -
343 = 7ˣ
It can be further expressed as -
7³ = 7ˣ
As base is same,
x = 3
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What is the least common denominator (LCD) of 1/10 and 1/6?
Answer:
LCD = 30
Equivalent Fractions with the LCD
1/10 = 3/30
1/6 = 5/30
Step-by-step explanation:
Rewriting input as fractions if necessary:
1/10, 1/6
For the denominators (10, 6) the least common multiple (LCM) is 30.
LCM(10, 6)
Therefore, the least common denominator (LCD) is 30.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/10 = 1/10 × 3/3 = 3/30
1/6 = 1/6 × 5/5 = 5/30
When Mt. St. Helens erupted in 1980, it reduced the elevation of the summit from 9,677 ft to 8,363 ft. By what percentage was the volcano's height reduced?
Answer:1314 or 13.14%
Step-by-step explanation:yes
I NEED HELP ASAP
Which expressions are polynomials?
Select each correct answer.
(to make it easier j put A,B,C,D. u also have to picc more thn one.)
A scientist analyzed numerous samples of drinking water for the presence of lead and nickel. One sample is chosen at random. Let L be the event that the sample contains lead. Let N be the event that the sample contains nickel. Which Venn diagram is shaded to represent the event ? a. c, B. D.
Answer:
A
Step-by-step explanation:
if it is meant literally as stated (lead AND nickel), then the check was only for both to be present.
and then A is the correct answer (L n N : intersection of both sets).
if it would have the typical meaning (we say we check for L and A, but mean inclusive "or" : either L or N or both), then B would be correct.
please help me the question is in the picture
Answer: C, 21
Step-by-step explanation:
Add one pair of parentheses or square
brackets to the left side of each equation to
make a true statement.
a) 3.5 x 4.1 3.5 2.8 = -0.7
b) 2.5+ (-4.1) + (−2.3) × (-1.1) = 4.29
c) -5.5 (-6.5) ÷ 2.4+ (-1.1) = -0.5
a. 3.5 x 4.1 (3.5 ×2.8) = -0.7
b. 2.5+ (-4.1) + [(−2.3) × (-1.1)] = 4.29
c. [-5.5 (-6.5) ÷ 2.4]+ (-1.1) = -0.5
Hence the required parentheses are added to make the statement true.
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Please help im stuck
The slope of the line is 1 / 3
How to find the slope of a line?The slope of a line is a measure of its steepness.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
Mathematically, the slope of a line can be described as follows;
slope = change in y / change in x
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Let's take two points from the graph
(0, 2)(3, 3)
where
x₁ = 0
x₂ = 3
y₁ = 2
y₂ = 3
Hence,
slope = 3 - 2 / 3 - 0
slope = 1 / 3
Therefore, the slope of the line is 1 / 3
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What is the solution of each exponential equation? Check your answer.
b. 5.2³x=400
Solution of exponential equation is , x = 10
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a is the base of function
x defines expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponential :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
5.2³ x =400
=> 5.8 x =400
=> 40x = 400
=> x =10
Thus solution for this equation is x =10.
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The complete question is :
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
b. 5.2³x=400
A nursery owner buys 9 panes of glass to fix some damage to hes greenhouse. The 9 panes cost 25.65 $. Unfortunately, he breaks 2 more panes while repairing the damage. What is the cost of another panes of glass?
Question content area bottom
Part 1
Another 2 panes of glass cost x $
enter your response here.
Answer:
For 2 more panes of glass it will cost $5.70.
Step-by-step explanation:
To find the price of each pane of glass you take the total price/ total panes of glass.
25.65/ 9 = $2.85.
If he wanted one more pane of glass it would be $2.85 but since you asked for two you multiply by 2 and get $5.70. Hope this helps!
The figure below is dilated by a factor of 33 centered at the origin. Plot the resulting image.
The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
How to determine the image of the transformation?The complete question is added as an attachment
The coordinates of the triangle are given as
R = (-4, 1)
S = (-4, 4)
T = (-2, 1)
The transformation is given as
Dilation by a scale factor of 3Centered at the originThe rule of the transformations is
(x, y) = 3(x, y)
So, we have
R' = 3 * (-4, 1) = (-12, 3)
S' = 3 * (-4, 4) = (-12, 12)
T' = 3 * (-2, 1)= (-6, 3)
Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
See attachment for the image of the transformation
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lowest common multiple of 18 and 42 x
Answer:
I'm assuming you inserting the variable x was a mistake.
Step-by-step explanation:
The least common multiple of 18 and 42 is 126.
[tex]\bold{Step-by-step}[/tex]
[tex]\mathrm{"LCM"}[/tex]
[tex]18 \times 7 = 126\\42 \times 3 = 126[/tex]
Any concerns, let me know, have a great day!
Solve each equation.
x²-13 x-30=0
After solving, the factors of the equation x²-13x-30=0 are:
(x-15) and (x+2)What exactly is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value for the variable x as x = 7.So,
Given equation: x²-13x-30=0
Then,
x²-13x-30x²-x( - )-30x²-x( 15 - 2 )-30x²-15x+2x-30x(x-15)+2(x-15)Factors are: (x-15) and (x+2)
Therefore, after solving, the factors of the equation x²-13x-30=0 are:
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Please help me! Brainliest to the person who answers this!
The area of the rectangular fenced area for dog run is given by:
A = 4x² + 34x + 18.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that:
The area is given by A = lw.The perimeter is given by P = 2(l + w).For this problem, the section enclosed by the fence is divided into two triangles, as follows:
One of dimensions 8 and 2x.Another with dimensions 6 + 2x and 2x + 3.Hence the total area is:
A = 8(2x) + (6 + 2x)(2x + 3)
A = 16x + 4x² + 18x + 18
A = 4x² + 34x + 18.
Hence the area of the rectangular fenced area for dog run is given by:
A = 4x² + 34x + 18.
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Simplify each expression. y¹/₂ . y³/₁₀
Simplify the expression by applying the index rule: a^mx a^n = a^m+n.
y¹/₂ . y³/₁₀
y¹/₂ . y³/₁₀ = y¹/₂ +³/₁₀
¹/₂ +³/₁₀ = 4/5
y¹/₂ +³/₁₀ = y^ 4/5
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Use natural logarithms to solve each equation.
e ²x=10
In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.
=> [tex]log_e(e^{2x})=log_e(10)[/tex]
By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]
=> [tex]2x(log_e(e))=ln(10)[/tex]
Also, as [tex]log_e(e)[/tex] = 1,
=> 2x (1) = ln(10)
=> 2x = 2.302 (approx)
=> x = 1.151
Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.
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I need to write the place value of a number. I know how to do that but I don't know how to write it as a fraction. Like "state the place value of 4 in the number 23.45. Write you answer as a fraction"
Answer:
the answer is 4 hundreds because starting from the decimal point is hundreds
Decide whether the following statements are always, sometimes, or never true.If a and b are rational numbers, then the product of (a+√b) and its conjugate is a rational number.
If a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.
The conjugate of ( a + [tex]\sqrt{b}[/tex] ) is ( a - [tex]\sqrt{b}[/tex] ) .
Product of ( a + [tex]\sqrt{b}[/tex] ) and ( a - [tex]\sqrt{b}[/tex] ) = ( a + [tex]\sqrt{b}[/tex] ) * ( a - [tex]\sqrt{b}[/tex] )
= ( [tex]a^{2}[/tex] ) - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] - [ [tex]\sqrt{b} ^{2}[/tex] ]
= ( [tex]a^{2}[/tex]) - b .
The expression ( [tex]a^{2}[/tex]) - b is rational .
Hence , if a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.
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