Answer:
V = 3261.16
Step-by-step explanation:
Given:
P = 1380
r = 8.6% or 0.086
t = 10
Work:
[tex]V=Pe^{rt}\\\\V=1380e^{0.086*10}\\\\V=1380e^{0.86}\\\\V=3261.16[/tex]
4. A rectangular plate has a perimeter of 28cm. determine the dimensions of the plate that give the maximum area
Answer:
Step-by-step explanation:
The perimeter of a rectangle is the sum of its 2 widths and 2 lengths.
Lets call the width ‘W’ and the length ‘L’. The perimeter (P) is equal to 2W + 2L. So 28 = 2W + 2L which simplifies to 14 = W + L.
28/2=14
The area of a rectangle is the width multiplied by the length so the formula is A = W x L. We want to get rid of the length. So, if we rearrange the first equation 14 = W + L to make L the subject we get L = 14 - W. We can now substitute this into the area equation so we get → A = W x (14 - W). That’s your answer!
Which of the following expressions are polynomials? Justify your answer:
(i) 8
(ii) sqrt 3x^2 −2x
(iii) 1− sqrt 5x
(iv) 1/5x −2 +5x+7
(v) (x−2)(x−4)/x
(vi) 1/x+1
(vii) 1/7 a^3 −1/sqrt 3a^2 +4a−7
(viii) 1/2x
(i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
What is polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Name three types of polynomial.Monomial, binomial and trinomial are the three types of polynomials.
A polynomial may contain exponents, constants, and variables, but it never divides by a variable.
There cannot be a negative exponent in a polynomial.
No variable at all, one variable, two variables, or more are all possible for polynomials.
Exponents can only be multiples of 0, 1, or 2, not fractions.
Based on above definitions (i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
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Julie wanted to match Lisa's obstacle course record of 74.6 seconds. She has already spent forty and one-fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
23.79 seconds
29.69 seconds
34.35 seconds
64.04 seconds
Julie has spent 40.25 + 10.56 = <<40.25+10.56=50.81>>50.81 seconds on wall climbing and the ropes.
She needs to complete the course in 74.6 - 50.81 = <<74.6-50.81=23.79>>23.79 seconds to match Lisa's record. Answer: \boxed{23.79}.
How do you find the algebraic value?
Bring the variable to the left side and bring all the remaining values to the right side.
Now, According to the question:
Let's know:
What is an algebraic value?
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1.
An algebraic formula is an equation or a rule written using mathematical and algebraic symbols and terms. It is an equation that involves algebraic expressions on both sides. The algebraic formula is a short quick formula to solve complex algebraic calculations.
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How do you solve area of the base?
Square Bases: A = s².
Rectangle-shaped bases: A = l x w.
Circular bases: A = pi x r².
Define the term base area?In geometry, a three-dimensional object's bottom is referred to as its base; if the solid's top is parallel to its bottom, it is also referred to as a base.
Square Bases:The bases of cubes as well as square pyramids are square. The length of one of a square's sides multiplied on its own, or squared, determines the area of a square: It goes like this: A = s².
Rectangle-shaped basesPyramids and several rectangular solids have rectangular bases. A rectangle's area is determined by multiplying its length, l, by it's own width, w: A = l x w.
Circular bases:Cones and cylinders have round bases. The radius of a circle, r, squared, plus the number pi, is equal to a area of the circle:
A = pi x r².
Pi is approximately 3.14.
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If I arrange my pawns in a square as large as possible, I have 7 left. If I had 6 more pawns, I could arrange all my pawns in a square without remainder would have one more pawn. How many pawns do I have?
Please give me an explanation!
Note that in the word problem above, the number of Pawns that you have is 14 pawns.
What is the rationale for the above answer?
To solve this problem, you can use the equation:
Number of pawns = (Number of pawns in the largest possible square) + (Number of pawns needed to fill in the square) + 1
Substituting the given information, we get:
Number of pawns = (7 pawns) + (6 pawns) + 1 pawn
Simplifying, we get:
Number of pawns = 14 pawns
Therefore, you have 14 pawns.
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Who invented [infinity]?
Infinity is a concept that refers to something that is unbounded, limitless, and endless. Mathematician John Wallis invented the standard sign for infinity,∞, in 1655.
Given that,
We have to find who invented the infinity.
We know that,
Infinity is a concept that refers to something that is unbounded, infinite, and endless. English mathematician John Wallis created the standard sign for infinity,∞, in 1655.
There are three basic categories of infinity: mathematical, physical, and metaphysical.
Examples of mathematical infinities are the quantity of points on a continuous line or the length of the never-ending series of the numbers 1, 2, 3, etc.
When one inquires if there are infinitely many stars or whether the universe will exist forever, they are posing spatial and temporal ideas of infinity.
There are issues about whether an ultimate entity must be infinite and whether lower things could also be infinite in a metaphysical discussion about God or the Absolute.
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solve by substitution:
y = x
y=x+2
Answer:
Step-by-step explanation:
No solution.
y=x
-1(y=x)
-1y=-1x
+1y=1x+2
-1y and 1y cancel each other out. -1x and 1x cancel each other out.
Leaving +2..so it's a no solution. Solved using elimination it's easier..
please can u ans the question thank u
will mark brainliest
Answer:
( D ) x must be a number divisible by 3
Step-by-step explanation:
Rational numbers cannot be whole numbers.
( A ) x must be an odd number
if x is an odd number, Let's take x as 1 then the answer will be in rational number. So, Option A is wrong.
( B ) x must be an even number
If x is an even number, Let's take x as 2 then the answer will be in Rational number. So, Option B is wrong.
( C ) x must be a number greater than 3
Let's take x as 4, then the answer will be in Rational number. So, Option C is wrong.
( D ) x must be a number divisible by 3
Let's take x as 6 as 6 is divisible by 3, then
[tex] \frac{2}{3}x+ 1[/tex]
[tex] \frac{2}{3}(6)+ 1[/tex]
[tex]2(2) + 1[/tex]
[tex]4 + 1[/tex]
[tex]5[/tex]
Therefore, 5 is a Rational number.So, The correct option is D.What is the median of 1 to 50?
The median of 1 - 50 is 25.5.
The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.
The first fifty numbers are 1,2,3,4,5................50
The number of terms in the data, n=50.
As the number of terms is even thus the median will be (n/2 th term + n/2 +1 th term) / 2
Median = (50/2 +50/2+1)/2
The 25th term of the sequence is 25.
The 26th term of the sequence is 26.
Median = 25+26/2 = 25.5.
Thus, the median of 1-50 is 25.5.
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The first fifty numbers are 1,2,3,4,5................50
The number of terms in the data, n=50.
Median = (50/2 +50/2+1)/2
The 25th term of the sequence is 25.
The 26th term of the sequence is 26.
Median = 25+26/2 = 25.5.
Thus, the median of 1-50 is 25.5.
Please Help!! 25 points!!
Write the equation of the function in vertex form that has the vertex (1, 2) and the point (-3, 6). If necessary, use reduced fractions and not
decimals.
The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
What is vertex form?
A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.
Here, we have
Given
The vertex (1, 2) and the point (-3, 6).
we have to find the equation of the function in vertex form.
We know that
The vertex form of the equation is :
f(x) = a (x-h)² +k
Now, we put the value of x, h, and k and we get
6 = a(-3-1)² + 2
6 = 16a + 2
4 = 16a
a = 1/4
Now, we put the value of a in the vertex form equation and we get
f(x) = 1/4 (x-1)²+2.
Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
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What is the formula for a linear function?
Answer:
⭐ There are 3 ways you can write a linear function (⭐ = most common):
⭐[tex]y = mx + b[/tex] (slope-intercept form)⭐[tex]y-y_1 = m(x-x_1)[/tex] (point-slope form)[tex]Ax + By = C[/tex] (standard form)
Graph the line x = - 1.
Answer: see below
Step-by-step explanation:
x=-1 is a vertical line at x=-1
If a=b^2 c^3 and c=j^2 k^5 , which of the following is a correct expression for a in terms of b,j, and k?
Step-by-step explanation:
If a = b^2 c^3 and c = j^2 k^5, then we can substitute c = j^2 k^5 into the expression for a to get:
a = b^2 (j^2 k^5)^3
= b^2 j^6 k^15
This is a correct expression for a in terms of b, j, and k.
The correct expression for a in terms of b, j, and k is [tex]a = b^2 j^6 k^{15}[/tex].
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol be used to indicate the logical syntax's order of operations and other features.
We are given the terms as a = b^2 c^3 and c = j^2 k^5, then
we can substitute c = j^2 k^5 into the expression for a to get:
[tex]a = b^2 (j^2 k^5)^3\\= b^2 j^6 k^{15}[/tex]
Which is a correct expression for a in terms of b, j, and k.
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What is rational function and irrational function?
The ratio of polynomials with which the polynomial denominator should not be equal to zero is known as a rational function. A function with a radical sign is frequently thought of as being irrational.
The ratio of polynomials to which the polynomial denominator should not be 0 is known as a rational function. It is same as the rational number's definition.
It's common knowledge that functions with radical signs are irrational functions. Activities including square roots, cube roots, or other roots, for instance, are regarded as irrational functions. It is claimed that a function is irrational if it performs addition, subtraction, multiplication, division, and raising to power with rational, non-integral exponents on the right side of the equation y = f(x).
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Select all that apply.
Which of the following are proportions?
2/8 = 3/12
3/4 = 8/10
25/10 = 5/2
3/4 = 15/20
Answer:
3/4 = 15/20
3/4 = 8/10
Step-by-step explanation:
Charles spent 1/4 of his net salary on school fees,1/3 of the remainder on electricity and water bills.He then spent 1/9 of what was left on transport.If he finally had sh.3600,what was his net january salary
The net salary of Charles in the month of January is 8100.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, 'x' be the total salary of Charles in January.
Charles spent 1/4 of his net salary on school fees so the reaming amount is,
= {x - (1/4)x}
= (3/4)x.
(1/3)rd of the remainder on electricity and water bills which is,
= (1/3)×(3/4)x.
= (3/12)x.
= (1/4)x.
Now, The remaining amount is {(3/4)x - (1/4)x}.
= (2/4)x.
He then spent 1/9 of what was left on transport which is,
= (2/4)x×(1/9).
= (1/18)x.
Now, The remaining amount is {(2/4)x - (1/18)x}.
= [(18 - 2)/36]x.
= (16/36)x.
= (4/9)x.
So, as he left with 3600 it is equal to (4/9)x.
Therefore,
(4/9)x = 3600.
4x = 32400.
x = 8100.
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expand and simpfly (x-5)(x-4)
Answer:
x² -9x + 20
Step-by-step explanation:
x²-4x -5x + 20
x² - 9x + 20
The diameter of a circle is 6 cm. What is the area of the circle to the nearest square meter?
Answer:
0.002827 m^2
Step-by-step explanation:
A = pi * r^2
d = 2r
r = 3 cm = 0.03 m
A = pi * (0.03) ^ 2
A = 0.002827 m^2
The area of the circle is - 0.028 [tex]m^{2}[/tex]
The diameter (D) of a circle - 6cm
A diameter is a line that passes through the center of a circle and meets the circumference at the opposite site.The radius of a circle is the distance between the center point to any other point on the circle.The diameter is equal to half of the radius(r).D=[tex]\frac{r}{2}[/tex]
The radius of a circle is = [tex]\frac{6}{2}[/tex] cm
= 3 cm = 0.03 meter
Now,
The formula of the area of a circle = π[tex]r^{2}[/tex]
(the value of π = [tex]\frac{22}{7}[/tex] )
Area of a circle = [tex]\frac{22}{7}[/tex] * [tex](0.03)^{2}[/tex] [tex]m^{2}[/tex]
=[tex]\frac{22}{7}[/tex] * 0.0009 [tex]m^{2}[/tex]
= 0.028 [tex]m^{2}[/tex]
∴ The area of the circle is - 0.028 [tex]m^{2}[/tex]
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8. Amy throws a ball so that when it is at its highest point, it passes through the centre of a
hoop. The path of the ball is modelled by the equation y=h+kx-x², where y is the
height in metres of the ball above the ground and x is the horizontal distance in metres
from the point at which the ball was thrown. The centre of the hoop is at the point where
x=2 and y = 5.
(a) Find the values of h and k.
(b) Find the value of x at which the ball hits the ground.
The values of h and k would be =2 and 2 respectively.
The value of x would be = 5.2
What is a horizontal distance?A horizontal distance is the distance that is be covered by a moving object through a horizontal pathway.
y = h + kx - 0.5x^2
When X = 2 and y = 5 is the centre of the hoop.
To calculate for y;
X max = -k/2× (-0.5)
X max = k = 2
y max = 5
Substitute the given variables into the equation and make h the subject of formula.
5 = (h + 2×2) - (0.5x^2)
5= (h + 4)- 1
h +4 = 5+1
h +4 = 6
h = 6-4
h = 2
Also from the graph, the value for x as the ball hits the ground would be = 5.2
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What table does 64 come in?
The Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.
What do we mean by multiples?Multiples are numbers that are multiplied by another number to get a particular number.
In mathematics, multiples are the results of multiplying an integer by a given number.
Multiples of 5 include, for instance, 10, 15, 20, 25, 30, etc.
Numerous 7s include 14, 21, 28, 35, 42, 49, etc.
A multiple in mathematics refers to the outcome of multiplying two numbers together.
Here, the number 7 is multiple by 56.
Because the result of multiplying 0 by any number is 0, 0 is a multiple of all numbers.
So, in order to know what tables come in 64, we need to check that what numbers multiples ae 64:
64/1 = 64
64/2 = 32
64/4 = 16
64/8 = 8
64/16 = 4
64/32 = 2
64/64 = 1
Therefore, the Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.
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if l brought a computer for $1500.00 and used my 75% off coupon. How much was the computer originally?
Answer:
$6000
Step-by-step explanation:
So, we know that
$1500 = 25%
We find 1% by taking
1500 divided by 25% = $60
We have to find the 75% off by taking
60 times 75 = $4500
Then we have to find the original price by taking
4500 + 1500 = $6000
So, the original price is $6000
Answer:
$6000
Step-by-step explanation:
The total cost is 100%
The discount was 75%
then:
100% - 75% = 25%
The percentage paid was:
25%
then:
$1500 ⇒ 25%
$A ⇒ 100%
A = 1500*100/25 = 6000
A = $6000
"Who wrote the book 'Terrible Weather"?" Ag Perez Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke. B. 4 1. 5x - 7 = 4x +3 Y. No Solution X= to N. 10 2. 6 + 2x = 7x - 9 ... X = - 3 1. - 11 3. 8x + 1 = - 8 - x S. -2 X=1 4. -5+ 12x = 18x + 7 P. 3 X=-2 V . -7 5. -4x + 3 = 5x - 13 - x E. 1 6. -10 - 11x + 24 = 3x W. 5 F. - 6 7. 8 + 3x = x + 11 + 2x 0. 3 No sofmar 8. 5 +'17x +9 = 2x + 21x + 14 A. 1 R. 2 9. 6x + 8 - 13x + 10 = 4 - 6x - 11 + 4x W. 8 10. -14 + 5 - X - 3 =x+6+x+3x Y. -13 D. O AYN 9 3 7 1 6 S 8 5 2 10 4 e #20 Solving Equations: Variables on Both Sides and Collecting L
The book 'Terrible Weather' was written by WAYNE DROPS
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Solving the equations,
1) 5x-7 = 4x+3
x = 10 (N)
2) 6+2x = 7x-9
5x = 15
x = 3 (O)
3) 8x+1 = -8-x
-9x = 9
x = -1 (A)
4) -5+12x = 18x+7
6x = -12
x = -2 (S)
5) -4x+3 = 5x-13-x
8x = 16
x = 2 (R)
6) -10-11x+24 = 3x
14x = 14
x = 1 (E)
7) 8+3x = x+11+2x
3x-3x = 11-8
3 = 0
No solution (Y)
8) 5+17x+9 = 2x+21x+14
6x = 0
x = 0 (D)
9) 6x+8-13x+10 = 4-6x-11+4x
-7x+18 = -7-2x
5x = 25
x = 5 (W)
10) -14+5-x-3 = x+6+x+3x
-18 = 6x
x = -3 (P)
Now, the answer is coded as 93716 852104
Decoding with the help of the solutions of the given equations
WAYNE DROPS
Hence, the answer is WAYNE DROPS
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Find the sum of -6x^2 + 3 and 4x^2 - 2x
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
What is polynomial?An algebraic statement with variables, coefficients, and mathematical operations like addition, subtraction, multiplication, or division is referred to as a polynomial. Let's talk about the definition of polynomials in this article, along with their types, uses, and standard form.Similar terms are added while adding polynomials, and similar terms are deleted when subtracting polynomials. Keep in mind that in mathematics, the sign following addition or subtraction will always be that of the variable with larger value.(4x^2 - 2x )+ ( -6x^2 + 3)
[tex]4x^2 - 2x + 0[/tex] +
[tex]-6x^2 + 0x + 3[/tex]
[tex]-2x^2 -2x +3[/tex]
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
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Does anyone know the answer?
Answer:
Step-by-step explanation:
if you move over from 2. 3 full lines you get to 2.6. draw the x in between 2.6 and 2.8.
each line is 0.2 so 3.5 lines is 2.7
I need help with this question.
Answer:
49
Step-by-step explanation:
Vertical angles are congruent.
8x-23=6x-5
8x-6x=23-5
2x=18
divide
x=9
8(9)-23
=49
What are the roots of 2x² 3x 5?
On solving the provided question we can say that, - the roots of the given equations are - x = -5/2 and x = 1
What are roots ?When referring to the values of a variable for which the supplied polynomial equals zero, we use the term "roots of a polynomial." The polynomial p(x) has zero roots if and only if an is its root. By setting each component to 0, you may solve for x to determine the roots, or solutions, of the polynomial equation P(x) = 0. Factoring is used to solve the polynomial equation. Set each component to a value of 0 (2x4), (x-6) or (x+1). Calculate x using the solution.
here,
[tex]2x^2 + 3x - 5[/tex]
(2x + 5)(x-1)
x = -5/2 and x = 1
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Is unique is an array formula?
Yes, the UNIQUE function is an array function. The results of this function just need to be written once, and the full array will be filled with the results (range of cells).
What is a formula for an array?A formula with numerous computations capabilities on one or more elements in an array is known as an array formula. An array can be thought of as a row, column, or mix of rows and columns of values. Array formulae may provide a single result or a number of outputs.
Can a formula for an array produce more than one result?Array formulae may provide a single result or a number of outputs. Any formula that can provide several outcomes will automatically spill them either down, starting with the Microsoft 365 September 2018 upgrade.
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A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=3. 5x+4 represents the cost y of bowling x games. Interpret the parameters of the function.
The function is in the form of linear equation in two variables where y is the cost and x are number of games played.
Linear equation in two variables is referred to a function that can be expressed in the form y = ax + b where a, b are constant values and x and y are variables. x is the independent variable and y is the dependent variable. Here we have the function y = 3.5x + 4 and the independent variable x is the number of games played and dependent variable y is the cost of the games that are played. Now in the equation the additional fee is represented by the constant value 3.5 and the fee for shoe is represented by the number 4 and is not dependent as the shoe rent fee is constant and not depends on number of games played.
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in what circumstances is the t statistic used instead of a z-score for a hypothesis test? the t-statistic is used when the population variance (or standard deviation) is known you use the z-test when the sample size is less than 30 the t-statistic is used when the population variance (or standard deviation) is unknown
A t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.
What do we mean by t-statistic?The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesized value relative to its standard error.
Through the Student's t-test, it is utilized in hypothesis testing.
In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.
When the variance and standard deviation of the population are unknown, a t-statistic is employed rather than a z-score.
The p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data.
The t-value is a way to measure the difference between population means.
Therefore, a t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.
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Correct question;
In what circumstances is the t-statistic used instead of a z-score for a hypothesis test?
(A) the t-statistic is used when the population variance (or standard deviation) is known
(B) you use the z-test when the sample size is less than 30
(C) the t-statistic is used when the population variance (or standard deviation) is unknown