By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long
What are basic arithmetic?Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.
The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.
Here we are discussing the four basic rules of arithmetic operations for all real numbers.
Addition (sum; ‘+’)Subtraction (difference; ‘-’)Multiplication (product; ‘×’ )Division (÷)12 × x + 2 × y = 90
6 × x + 2 × y = 60
To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.
B. Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5
Now we replace x in any of 2 equations to get y.
30 + 2y = 60
2y = 30
y=15
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a mail carrier randomly inspects every 20th letter being mailed. out of 600 letters in the sample, 3 were open. there were 18,000 letters being mailed. make an inference about the number of all the letters being mailed that were open
90 letters out of the inspected sample of 900 letters will be found to be open
Inspection is done by mail carrier for every 20th letter
Inspection rate = 1/20*100 = 5%
It is a form of inspection where a sample of the same unit's manufactured goods, produced using the same procedures, is taken and examined, as opposed to the entire unit being examined. In general, the unit relates to the lot, and the lot determines whether the things are acceptable or rejectable.
Number of letters found open in 600 letters = 3 letters
Rate of letter found open = 3/600*100 = 0.5%
The sample being mailed = 18000 letters
Number of letters that were inspected for being open = 5% of 18000 = 900
letters
The number of letters found open = 0.5% of 18000 = 90
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Ms. Juhal was making t-shirts. One of the designs had the instructions to make points at the following locations and then draw lines to connect the points in order: A (-5,5) ; B (-5,3) ; C (-5,1) ; and D (2,1) . ⦁ Use graph paper to plot the points. ⦁ Connect them in order: A to B, B to C, C to D, and then D back to A. What shape is created?
HELP PLS
Identify that the shape created is a Triangle.
For this exercise it is important to remember that, given a point P (x , y), "x" is the the x-coordinate of the point and "y" is the y-coordinate of the point.
In this case, Ms. Juhal has the following points:
1) Point A (-5 , 5)
x = -5 and y = 5
2) Point B (-5 , 3)
Where:
x = -5 band y = 3
3) Point C (-5 , 1)
x = -5 and y = 1
4) Point D (2,1)
Where:
x = 2 and y = 1
Therefore, knowing the coordinates of each point, you can plot them and connect them in order (Observe the picture attached).
Finally, you can identify that the shape created is a Triangle.
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Yvonne is training for the marathon. She calculates to see whether she can cover 9 miles in 10 minutes. But she completes the distance in 8 minutes. What is the percent error in Yvonne's calculation?
The relative error exists multiplied by 100 to estimate the percent error. The percent error in Yvonne's calculation exists 11% error.
What is meant by percent error?The difference between the estimated value and the actual value in relation to the actual value is known as the percent error. To calculate the percent error, the relative error is multiplied by 100.
Percent error calculates the difference between an estimate and a correct value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual value. It is also referred to as % error and percentage error.
%error = (calculated value - experimental value) / calculated × 100%
%error = (10 - 9)/9 × 100%
= 1/9 × 100%
= 11.11111 ≈ 11% error
Therefore, the percent error in Yvonne's calculation exists 11% error.
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I need help with this question
The proportional relationship modeled by Table A is graphed on the image given at the end of the answer.
Direct proportional relationshipA direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:
y = rx.
The meaning of this is that a proportional relationship is only represented when the division of y by x for all pairs of points (x,y) are the same.
Hence, the proportional relationship in this problem is represented by table A, as:
r = 10/5 = 8/4 = 6/3 = 2/1.
Hence the equation is:
y = 2x.
For table B, a proportional relationship is not shown, as:
3/1 is different of 4/2.
The graph containing the points listed on table A are given at the end of the answer.
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2x-6y=-3
Determine if the given ordered pair. (3, 7/2)
satisfies the given equation.
O YES O No
Answer:
No, it doesn't satisfy.
Step-by-step explanation:
2x - 6y = -3
let us post the ordered pair in the equation and solve it
2(3) - 6(7/2) = -3
6 - 21 = -3
-15 = -3 ...... which isn't equal
so we conclude that the given ordered pair doesn't satisfy the equation.
Differentiate the function, f(x) = ln (2x + 4) with respect to x?
Answer:
f'(x) = [tex]\frac{1}{x+2}[/tex]
Step-by-step explanation:
using the chain rule to differentiate
f(x) = g(h(x)) , then
f'(x) = g'(x) × h'(x)
f(x) = ln(2x + 4) , then
f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)
= [tex]\frac{1}{2x+4}[/tex] × 2
= [tex]\frac{2}{2x+4}[/tex]
= [tex]\frac{1}{x+2}[/tex]
Find the circumference and area of the figure if each unit on the graph measures 1 centimeter Round answers to the nearest tenth, if necessary
A(2,3)
B(4,1)
Circumference of the circle = 17.8 units
Area of the circle = 25.1 square unit
What is circumference of circle ?An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."
Formula to get the circumference of a circle = 2πr
Where r = radius of the circle
Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)
r = [tex]\sqrt{(2-4)^{2} +(3-1)^{2} }[/tex]
r = 2√2units
Therefore, circumference = 2π(2√2)
= 17.77
≈ 17.8 units
Area of the circle = πr²
= π(2√2)²
= 8π
= 25.13
≈ 25.1 square unit
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Determine the unknown angle in the triangle pictured below:
can someone explain functions to me please I don't get it.
Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.
The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")
Using math operations one can relate x values with y values via an equation of the type:
y = 2 x - 5
where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.
For example, try the number x = 0
and see which y number connects with it:
y = 2 (0) - 5 = 0 - 5 = -5
Then you say that the number 0 in the Domain connects with the number -5 in the Range.
This relationship can also be given with coordinate pairs of the form:
(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.
The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.
I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.
alpha writes the infinite arithmetic sequence \[10, 8, 6, 4, 2, 0 ,\ldots.\]beta writes the infinite geometric sequence \[9, 6, 4, \frac{8}{3}, \frac{16}{9}, \ldots.\]gamma makes a sequence whose $n^{\text{th}}$ term is the product of the $n^{\text{th}}$ term of alpha's sequence and the $n^{\text{th}}$ term of beta's sequence: \[10\cdot 9 \quad,\quad 8\cdot 6\quad ,\quad 6\cdot 4\quad,\quad 4\cdot \frac83\quad,\quad 2\cdot \frac{16}{9}\quad,\quad \ldots.\]what is the sum of gamma's entire sequence?
Consecutive terms in the α sequence have a common difference of
8 - 10 = 6 - 8 = 4 - 6 = … = -2
so they are given recursively by
[tex]\begin{cases} \alpha_1 = 10 \\ \alpha_n = \alpha_{n-1} - 2 & \text{for } n\ge2 \end{cases}[/tex]
By substitution, we have
[tex]\alpha_n = \alpha_{n-1} - 2 \\\\ \alpha_n = \alpha_{n-2} - 2\cdot2 \\\\ \alpha_n = \alpha_{n-3} - 3\cdot2 \\\\ \vdots \\\\ \alpha_n = \alpha_{n-(n-1)} - (n-1)\cdot 2 = \alpha_1 - 2(n-1) = 12-2n[/tex]
Consecutive terms in the β sequence have a common ratio of
6/9 = 4/6 = (8/3)/4 = … = 2/3
so the recurrence for these terms is
[tex]\begin{cases} \beta_1 = 9 \\\\ \beta_n = \frac23 \beta_{n-1} & \text{for } n\ge2 \end{cases}[/tex]
We can solve for [tex]\beta_n[/tex] similarly:
[tex]\beta_n = \dfrac23 \beta_{n-1} \\\\ \beta_n = \left(\dfrac23\right)^2 \beta_{n-2} \\\\ \beta_n = \left(\dfrac23\right)^3 \beta_{n-3} \\\\ \vdots \\\\ \beta_n = \left(\dfrac23\right)^{n-1} \beta_{n-(n-1)} = \left(\dfrac23\right)^{n-1} \beta_1 = \dfrac{2^{n-1}}{3^{n-1}} \cdot 3^2 = \dfrac{2^{n-1}}{3^{n-3}}[/tex]
The γ sequence has [tex]n[/tex]-th term
[tex]\gamma_n = \alpha_n \beta_n = (12-2n) \dfrac{2^{n-1}}{3^{n-3}} = (108-18n) \left(\dfrac23\right)^{n-1}[/tex]
and we want to compute
[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \sum_{n=1}^\infty \left(\frac23\right)^{n-1} - 18 \sum_{n=1}^\infty n \left(\frac23\right)^{n-1}[/tex]
Recall the sum of an infinite geometric series with common ratio [tex]|r|<1[/tex] converges to
[tex]\displaystyle \sum_{n=1}^\infty r^{n-1} = \frac1{1-r}[/tex]
so that
[tex]\displaystyle \sum_{n=1}^\infty \left(\frac23\right)^{n-1} = \frac1{1-\frac23} = 3[/tex]
For the remaining sum, we can use the method shown in question [24494877] to compute
[tex]\displaystyle \sum_{n=1}^\infty nr^{n-1} = \frac1{(1-r)^2}[/tex]
which gives
[tex]\displaystyle \sum_{n=1}^\infty n \left(\frac23\right)^{n-1} = \frac1{\left(1-\frac23\right)^2} = 9[/tex]
Then the infinite sum of the terms of γ converges to
[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \cdot 3 - 18 \cdot 9 = \boxed{162}[/tex]
Give the circumference of a circle with a radius of 17 m.
Answer:106.81
Step-by-step explanation:
To find the Circumference of a circle you have to do is 2×[tex]\pi[/tex]×17 which would give you 106.81.
The circumference is the outline of the circle, it is the edge; in other words it is the perimeter of the circle.
To calculate the circumference of the circle, we apply the following formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{C=2\pi r} \end{gathered}$}}[/tex]We have that the radius is 17 meters, and the value of pi is 3.14, we substitute these data in the formula and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{C=2\cdot(3.14)\cdot(17 \ m)} \end{gathered}$}}[/tex][tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{C=106.76 \ m} \end{gathered}$}}}[/tex] The circumference of the circle is: 106.76 meters.Cody biked a total of 22 kilometers
by making 11 trips to work. How
many trips will Cody have to make to
bike a total of 30 kilometers?
Answer: 15
Step-by-step explanation:
This is the answer because 22 divided by 11 equals 2 kilometer each trip to work so 30 kilometer divided by 2 is 15.
Eugene is deciding between two payment plans when purchasing a new car. If Eugene chooses payment plan A, he will pay $429.47 a month for 36 months for the car. If Eugene chooses payment plan B, he will pay $340.89 a month for 48 months for the car. How much money will Eugene save on the car overall if he chooses payment plan A?
Eugene will save $901.8 on the car overall if he chooses payment plan A.
Eugene has to buy a new car, and there are two payment plans from which he has to decide which to opt for.The two plans are, namely, plan A and plan B.In plan A, he has to pay an amount of $429.47 a month for 36 months for the car.In plan B, he has to pay an amount of $340.89 a month for 48 months for the car.The total amount to be paid if he chooses plan A is 36*429.47 = $15,460.92.The total amount to be paid if he chooses plan B is 48*340.89 = $16,362.72.We can see that plan A is better than plan B.The amount saved by Eugene by selecting plan A is represented in the equation below:$16,362.72 - $15,460.92 = $901.8To learn more about equations, visit :
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X-3 is a factor of x³+ax²–2x+3
Answer:X-3 is a factor of x³+ax²–2x+3
Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3
p(x)=x
3
−ax
2
+2x+a−1
⇒ p(a)=(a)
3
−a(a)
2
+2(a)+a−1
⇒ 0=a
+2a+a−1=0
⇒ 3a−1=0
⇒ 3a=1 a=
3
1
Point Q has coordinates (5,6). If you rotate Q 90° about the origin, (0,0), what are the coordinates of Q′
The coordinates of the image after 90° about the origin is (6, -5)
What is a 90 degrees rotation?A 90 degrees rotation denoted by R(90, 0) is a rotation that has the same effect as the 270 degrees counterclockwise of a figure.
How to determine the image of the rotation?The coordinate of the point is given as
(5, 6)
The rotation is given as 90° about the origin
So, we have
(x, y) => (y, -x)
Substitute (5, 6) in (x, y) => (y, -x)
So, we have
(5, 6) => (6, -5)
Hence, the coordinates of the image is (6, -5)
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rewrite cos^4 2x in terms of the first power of cosine.
cos2x = (1+cos(2x))/2
What is meant by first power of cosine?The cosine power is odd (n odd): u = sin x and du = cos x dx should be used. d u = cos To create an even number of cosine powers, replace dx with (a), canceling one power of cos x by substituting du. The Power Factor is the sine of the angle formed by Current and Voltage.
P = VI Cosθ OR.Cosθ = P ÷ V I OR.Cosθ = kW ÷ kVA OR.Cosθ = True Power ÷ Apparent Power.The ratio of the length of the side next to the angle to the length of the hypotenuse is known as the cosine, sometimes abbreviated as "cos." The ratio of the length of the side across from the angle to the length of the side next to it is called the tangent, which is frequently abbreviated as "tan."
cos2(2x) = (1+cos(4x))/2
cos4(2x)= [(1+cos(4x))/2]²
[tex]cos^{4}[/tex](2x) = [(1+cos(4x))/2]²
[tex]cos^{4}[/tex] (2x) = (1/4) × [1 + cos(4x)]²
[tex]cos^{4}[/tex](2x) = (1/4) × (1 + 2cos(4x) + cos²(4x))
[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1 + cos(2x))/2]
[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1/2)*(1 + cos(2x))]
[tex]cos^{4}[/tex](2x) = (1/8)*[2 + 4cos(4x) + 1 + cos(2x)]
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10y-2y + 30 = 8y - 15 + 5
Answer:
No Solution
Step-by-step explanation:
-Determine the equation of the line that passes through the point (9, -42)and is parallel to the line y = -5x + 1.Enter your answer in slope-intercept form.Pls see picture
Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:
[tex]y=-5x+1[/tex]The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.
The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line:
[tex]\begin{gathered} y-(-42)=-5(x-9) \\ y+42=-5(x-9) \end{gathered}[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+42=(-5)\cdot x+(-5)\cdot(-9) \\ y+42=-5x+45 \end{gathered}[/tex]Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:
[tex]\begin{gathered} y+42-42=-5x+45-42 \\ y=-5x+3 \end{gathered}[/tex]The equation of the line is y= -5x + 3
can someone help me with this
Answer: Slope intercept from is y= 4/13x-5/13
Step-by-step explanation:
Do number 12 and 13 please thank you!!
12. The statement ' x+3 = 9' is true sometimes.
How is this explained?
Let x= 6,
6 + 3 = 9 (true)
Let x= 5 ,
5 + 3 = 8 (not true)
13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.
How is this explained?
Let us consider some numbers,
a) 1
The multiplicative inverse of 1 = 1
Thus, multiplicative inverse of this number is not less than the original number.
b) 2 (greater than 1)
The multiplicative inverse of 2 = 1/2
multiplicative inverse of this number is less than the original number.
c) 8/7 (greater than 1)
The multiplicative inverse of 8/7 = 7/8
Here, multiplicative inverse of this number is less than the original number.
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George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during the 51 blinks?
WILL GIVE BRAINLY IF WRITE PLS HEP ASAP
A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answer:
25 kg
Step-by-step explanation:
The sum of the weights of the small and large sacks is 65 kg. The larger sack weighs 15 kg more. You want the weight of the smaller sack.
SetupLet w represent the weight of the sand in the small sack. Then (w+15) is the weight of the sand in the larger sack. The total weight is 65 kg, so we have ...
w +(w+15) = 65
SolutionSubtracting 15 from both sides gives ...
2w = 50
w = 25
The weight of the sand in the small sack is 25 kg.
Question 5 (1 point)
(03.06 MC)
Use function notation to write a recursive formula to represent the sequence: 3, 6, 12, ...
The recursive formula is f(n - 1) . 3
The correct option is (c)
What are Recursive Formula ?
A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:
The first term of the sequenceThe pattern rule to get any term from its previous termGiven,
The sequence is:
3, 6 , 12 ....
To find the recursive formula of above sequence :
Now, The first term is 3.
Recursive formula is :
f(n - 1) . 3
Hence, The recursive formula is f(n - 1) . 3
The correct option is (c)
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For a certain airline, flight attendants need to be between 63 and 73 inches tall. Which of the following absolute value equations can be used to represent these minimum and maximum heights
Flight attendants for one carrier must be between 63 and 73 inches tall. The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.
Given that,
Flight attendants for one carrier must be between 63 and 73 inches tall.
We have to find what absolute value equations from the list below can be used to express these minimum and maximum heights.
In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is function of x = |x|, where x is a real number. The absolute value function is typically written as function of x = a |x - h| + k, where a denotes the vertical stretch of the graph, h denotes the horizontal shift, and k denotes the vertical shift from the graph of function of x = |x|.
Therefore, The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.
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Ian is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $1.25 per mile driven. How much would a taxi ride cost if Ian is riding for 2 miles? How much would a taxi ride cost that is mm miles long?
It would cost him $ 5 to cover a distance of 2 miles.
Amount charged by the taxi driver which is mandatory to be paid is $ 2.50
Additional amount charged by the driver is $1.25
Since Ian is driving 2 miles thus we can write it as follows :
2.50 + (1.25 × 2) = 2.50 + 2.5
= $5
The additional charges are basically the amount which is charged by the driver to cover a particular distance and thus this distance changes as the distance changes.
However the mandatory fees is constant and it never changes.
It would cost him $ 5 to cover a distance of 2 miles.
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Simplify the expression √9x^3/25y^2 and please be sure to explain your steps! Thank you!
The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
√9x^3/25y^2
Evaluate the square root of 9
So, we have the following equation
√9x^3/25y^2 = 3x^3/25y^2
The above expression cannot be further simplified
Hence, the solution to the expression is 3x^3/25y^2
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Pls help!
if you have to work it out pls work it out my teacher will be mad if no work!
Answer:
1st one: 50%, 0.5, 1/2
2nd one: 25%, 0.25, 1/4
3rd one: 18%, 0.18, 9/50
4th one: 10%, 0.1, 1/10
5th one: 20%, 0.2, 1/5
Step-by-step explanation:
Hope this helps!
Help please
I don’t understand
1) Let the value of yellow circles = x
Let the value of green butterflies = y
Consider the left string,
3x + y = 15 ----(1)
Consider the right string,
x + 2y = 15 ----(2)
Let us solve the linear equations
(1) *2 => 6x+ 2y = 30 ---(3)
(3) - (2) => 6x+ 2y = 30 - ( x + 2y = 15)
=> 5x = 15
=> x = 3
Substituting x in (1)
3(3) + y = 15
y = 15- 9
y = 6
The value of yellow circles = 3
The value of green butterflies = 6
2) Let the yellow circles = c
Let the green butterflies = b
The linear equations that could be formed are:
a) Left string equation:
3c+b = 15
b) Right string equation:
2b +c = 15
c) Equation of both strings:
4c +3b = 30
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a one way train ticket in the city costs $1.95. A monthly pass costs $50. For what numbers of rides should you buy the monthly pass?
For 26 rides in a month, a monthly pass should be made, while for rides less than 26 using a one-way ticket will be a cost-effective method
Cost of one way train ticket = $.195
Cost of monthly pass = $50
Monthly pass: It is a prepaid fare card good for one month of limitless travel. This saves cost and time in terms of commuting costs and time of getting the tickets issues
Let x represent the number of rides one takes
Formulating the equation we get:
Cost of one-way ticket*Number of rides = Cost of a monthly pass
= 1.95*x = 50
x = 25.64 or 26 rides
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