The percent tip Ruby left was 27%.
What is percent?
A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
Calculate the tip amount:
The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:
Tip = Total cost - Cost of meal
Tip = $34.29 - $27
Tip = $7.29
Calculate the percent tip:
The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:
Percent tip = (Tip / Cost of meal) x 100%
Percent tip = ($7.29 / $27) x 100%
Percent tip = 27%
Therefore, the percent tip Ruby left was 27%.
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6.3 A truck is carrying mango juice, tomato juice, and passion fruit juice bottles in a ratio of
4: 4:3. If there are 1020 passion fruit juice bottles, then how many juice bottles in total
are there?
The total number of juice bottles is given by the equation J = 3400 bottles
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as a : b : c
Now , the ratio of mango juices to tomato juice to passion fruit be 4 : 4 : 3
The total number of mango juice = 4x
The total number of tomato juice = 4x
The total number of passion fruit juice = 3x
The total number of passion fruit juice = 1020
Substituting the values in the equation , we get
3x = 1020
Divide by 3 on both sides of the equation , we get
x = 340 bottles
Now , the total number of bottles = 4x + 3x + 3x = 10x bottles
So , substituting the value of x in the equation , we get
The total number of juice bottles = 340 ( 10 ) = 3400 bottles
Hence , the proportion is 40 : 40 : 30
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get it right ok PLS!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The number in standard form is 304.014.
Answer:
The Standard form of the number is 44,410.
What is Multiplication?
To multiply means to add a number to itself a particular number of times.
Multiplication can be viewed as a process of repeated addition.
Here, given number(3 X 100) + (1 X 110) + (4 X 11000)(300) + (110) + (44000)300 + 110 + 44000410 + 4400044410
Thus, the Standard form of the number is 44,410.
Which equation represents f(x)?
O f(x) = 3√x+6+1
Of(x) = 3√x-6 +1.
O f(x)=3√x+6-1
O f(x)=3√x-6-1
The equation of the straight line would be -
y = 2x.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a straight line passes through the points (2, 4) and (3, 6).
Refer to the graph of the function attached. We can see that the function that represents the graph is -
[tex]$y=\sqrt[3]{x+6} \;+1[/tex]
Therefore, the function representing the graph is -
[tex]$y=\sqrt[3]{x+6} \;+1[/tex]
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Help if you know how to do it
First we multiply 9 and 15, which is 135cm. 100cm = 1m so the plant will grow 1.35m, so the plant is now 9.35m
What is the slope of this line?
-8
5
8
6
4
0
15
내
-8
ㅇ
6
8
Based on the graph, the slope of this line is equal to 2.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided in the graph, we can logically deduce the following data points on the line:
Points on x-axis = (-2, 5).Points on y-axis = (-8, 6).Substituting the given data points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (6 + 8)/(5 + 2)
Slope, m = 14/7.
Slope, m = 2.
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Jake ran 145 meters before lunch and 389 meters after lunch.
How many kilometers did Jake run in all?
Responses
0.00534 km
0.0534 km
0.534 km
5.34 km
Answer:
.534
Step-by-step explanation:
add, then convert meters to kilometers
problem 1.7 each of the four vertical links has an 8x36 mm uniform rectangular cross section and eash of the four pins has a 16mm diameter. determine the maximum calue of the average normal stress in the links connecting (a) points b and d, (b) points c and e.
The average normal stress in the links connecting:
(a) points B and D is:
|σ_max| = 13.7 MPa
(b) points C and E is:
|σ_max| = 13.0 MPa
The value of the average normal stressTo determine the maximum value of the average normal stress in the links connecting points B and D, we need to calculate the bending moment and the axial force in the link. Assuming the links are in pure bending, we can use the bending stress formula to calculate the maximum normal stress:
σ_max = Mc / I
where M is the bending moment, c is the distance from the neutral axis to the outer fiber, and I is the moment of inertia of the cross-sectional area.
The bending moment in the link BD can be calculated as the sum of the moments due to the applied loads and the reactions at the pins. The axial force can be calculated as the sum of the forces in the link due to the applied loads.
Assuming a sign convention where clockwise moments are positive and upward forces are positive, we have:M = 4kN * 80mm - 8kN * 120mm = -640 Nm
F = 4kN - 8kN = -4kN
The distance c for a rectangular cross section is half the height, so c = 4 mm. The moment of inertia can be calculated as:I = bh³ / 12
where b is the width and h is the height of the cross section. Therefore:I = (8mm) * (36mm)³ / 12 = 186624 mm⁴
Substituting these values into the bending stress formula, we get:σ_max = (-640 Nm) * (4mm) / 186624 mm⁴ = -13.7 MPa
Since the stress is negative, the maximum tensile stress occurs on the upper part of the link (above the neutral axis). Therefore, the maximum value of the average normal stress in the link connecting points B and D is:|σ_max| = 13.7 MPa
For the link connecting points C and E, the calculation is similar. The bending moment can be calculated as:M = 4kN * 40mm + 8kN * 80mm = 800 Nm
The axial force is:F = 4kN + 8kN = 12kN
The distance c is still 4 mm, but the moment of inertia is different due to the orientation of the cross section. The moment of inertia for a rectangular cross section rotated 90 degrees is:I = bh³ / 12 = (36mm) * (8mm)³ / 12 = 24576 mm⁴
Substituting these values into the bending stress formula, we get:σ_max = (800 Nm) * (4mm) / 24576 mm⁴ = 13.0 MPa
Since the stress is positive, the maximum compressive stress occurs on the lower part of the link (below the neutral axis). Therefore, the maximum value of the average normal stress in the link connecting points C and E is:|σ_max| = 13.0 MPa
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A recent survey found that 80% of IRSC students plan to go on a vacation after graduation. Suppose 5 IRSC
students are randomly selected and let z be the number of students that plan to go on a vacation after
graduation, out of the sample of 5. Use the binomial probability formula or the binomial probability table
to construct the probability distribution of x. Ao, use the binomial probability formula or the binomial
probability table to construct the cumulative probability distribution of .
The binomial distribution is solved as
a) The probability that no more than 2 students out of the random 5 plan to go out on vacation is P ( X ≤ 2 ) = 0.0579
b) The probability that more than 2 students out of the random 5 plan to go out on vacation is P ( X > 2 ) = 0.9421
What is a Binomial Distribution?The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the probability be represented as P
Now , the total number of trials = 5
The number of students going for vacation be represented as n
Now , the probability of success p = 0.8
So , the value of q = 0.2
a)
The probability that no more than 2 students out of the random 5 plan to go out on vacation is P ( X ≤ 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
Substituting the values , we get
The probability that no more than 2 students out of the random 5 plan to go out on vacation is P ( X ≤ 2 ) = 0.0579
The probability that no more than 2 students out of the random 5 plan to go out on vacation is P ( X ≤ 2 ) = 5.79 %
b)
The probability that more than 2 students out of the random 5 plan to go out on vacation is P ( X > 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
Substituting the values , we get
The probability that more than 2 students out of the random 5 plan to go out on vacation is P ( X > 2 ) = 0.9421
The probability that more than 2 students out of the random 5 plan to go out on vacation is P ( X > 2 ) = 94.21 %
Hence , the binomial distribution is solved
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LPQR is a right angle. Find m/PQS and mZSQR. Enter deg after any value that
is in degrees.
The required measures of the angles ∠PQS and ∠SQR are given as 51 and 49.
What is complementary angles?Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.
Here,
∠PQR is a right angle,
So ∠PQS and ∠SQR are supplementary angles, from the figure.
∠PQR = ∠PQS + ∠SQR
90 = 8x + 131 + 10x + 139
90 = 18x + 270
18x = -180
x = -10
Now,
∠PQS = 8x + 131 = -80 + 131 = 51°
Similarly,
∠SQR = 49°
Thus, the required measure of the angles ∠PQS and ∠SQR are given as 51 and 49.
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Find all possible fourth corners if the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2)
All possible fourth corners if the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2) is (2, 3, 5) and (3, 5/2, 9/2)
Let the corners be A(1,2,3);B(3,4,7);C(2,1,2)
Let the fourth vertex D =(x,y,z)
We know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the midpoint of BD.
Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2) is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).
So, midpoint of AC= Mid point of BD
⇒( 1+3/2, 2+4/2, 3+7/2) =(2, 3, 5)
Hence, D=(2, 3, 5).
Same if,
Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2) is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).
So, midpoint of AC= Mid point of BD
⇒( 3+2/2, 4+1/2, 7+2/2) = (3, 5/2, 9/2)
Hence, D= (3, 5/2, 9/2)
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write y=d^2-8d-10 in vertex form
The vertex form of the equation is,
⇒ y = (d - 4)² - 26
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ y = d² - 8d - 10
Now, We can change in vertex form as;
⇒ y = d² - 8d - 10
⇒ y = d² - 8d + 16 - 16 - 10
⇒ y = (d - 4)² - 16 - 10
⇒ y = (d - 4)² - 26
Thus, The vertex form of the equation is,
⇒ y = (d - 4)² - 26
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Mariene and her parents are baking a large batch of cookies for a fundraiser. There are 150 cookies and 62% of cookie and 62% of the cookies are chocolate chips.How many chocolate chip cookies did they make?
93 chocolate chip cookies
Let T: n rightarrow m be a linear transformation, with A its standard matrix. Complete the following statement to make it true: "T maps n onto m if and only if A has pivot columns." Find some theorems that explain why the statement is true. T maps n into m if and only if A has Let S : p rightarrow n and T : n rightarrow m be linear transformations. Show that the mapping x T(S(x)) is a Unear transformation (from to m). (Hint: Compute T(S(cu + dv)) for u, v in p and scalars c and d. Justify each step of the computation, and explain why this computation gives the desired conclusion.! [M]
So x → T(S(x)) satisfies homogeneity.
x → T(S(x)) is a linear transformation from P to M.
The completed statement is: "T maps n onto m if and only if A has pivot columns in every row."
One theorem that explains why this is true is the Rank-Nullity Theorem, which states that the rank of a matrix plus the nullity of the matrix (the dimension of the nullspace) equals the number of columns. If A has pivot columns in every row, then the rank of A is equal to the number of rows, which means that the nullity is 0, and therefore T is onto. Conversely, if T is onto, then the range of T has dimension equal to the number of rows, which means that the rank of A is equal to the number of rows, so A has pivot columns in every row.
To show that the mapping x → T(S(x)) is a linear transformation, we need to show that it satisfies the two properties of linearity: additivity and homogeneity.
Additivity: Let x and y be vectors in P. Then we have:
T(S(x + y)) = T(S(x) + S(y)) (by definition of + in P)
= T(S(x)) + T(S(y)) (since T is linear)
= (x → T(S(x))) + (y → T(S(y))) (by definition of the mapping)
= (x + y) → (T(S(x)) + T(S(y))) (by definition of + in M)
So x → T(S(x)) satisfies additivity.
Homogeneity: Let x be a vector in P and let c be a scalar. Then we have:
T(S(cx)) = T(cS(x)) (by definition of scalar multiplication in P)
= cT(S(x)) (since T is linear)
= c(x → T(S(x))) (by definition of the mapping)
So x → T(S(x)) satisfies homogeneity.
x → T(S(x)) is a linear transformation from P to M.
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You are shopping and find the same shirt at two different
stores. Store "A" is selling the shirt for $25 and Store
"B" is selling the shirt for 10% off the original price of
$28. Which is the better buy?
a. The shirt at Store "A".
b. The shirt at Store "B".
Answer:
A. The shirt at Store "A".
Step-by-step explanation:
How to find 10% of 28.
First, we need to convert 10% into a decimal.
To do that, we just divide the number by 100.
[tex]\frac{10}{100}[/tex] [tex]= 0.1[/tex]
Now, we take the original number (28) and multiply it by the decimal
[tex]28 x 0.1 = 2.8[/tex]
Finally, we subtract.
[tex]28.00 - 2.80 = 25.20[/tex]
[tex]25.20[/tex] > [tex]25.00[/tex]
Therefore, Store "A" Has the cheapest shirt
What is the area, in square units, of triangle DEF?
Triangle DEF, with vertices D(3,-9), E(9,-5), and F(6,-2), is drawn on the coordinate grid below.
Answer:
Below
Step-by-step explanation:
You COULD calculate the lengths of the three sides and then use Heron's Formula to calculate the area.....
Here is perhaps an easier way (see image)
calculate the entire area of the rectangle then subtract the 3 smaller RIGHT triangles from the total
Area of rectangle = 6 x 7 = 42 units^2
triangles 1/2 ( 3 x 7 + 3 x 3 + 4 x 6 ) = 27 units^2
42 - 27 = 15 units^2 = area of given triangle
Answer:
15 square units
Step-by-step explanation:
i am using Heron's formula for this question
Firstly, lets calculate the lengths of the triangle. We can do this by using the formula:
[tex]length=\sqrt{(y_{2}\\-y_{1}\\)^{2}+(x_{2}\\-x_{1}\\)^{2} }[/tex]
Calculating the length between D (3,-9) and E (9,-5):
[tex]length(A)=\sqrt{(-9-(-5))^{2}+(3-9)^{2} } \\length(A)=2\sqrt{13}[/tex]
Calculating the length between F (6,-2) and E (9,-5):
[tex]length(B)=\sqrt{(-2-(-5))^{2}+(6-9)^{2} }\\length(B)=3\sqrt{2}[/tex]
Calculating the length between D (3,-9) and F (6,-2):
[tex]length(C)=\sqrt{(-9-(-2))^{2}+(3-6)^{2} }\\length(C)=\sqrt{58}[/tex]
Now, we can find the semi-perimeter with the formula:
[tex]s=\frac{A+B+C}{2}[/tex]
where A, B and C are the lengths
The semi-perimeter is:
[tex]s=\frac{2\sqrt{13}+3\sqrt{2}+\sqrt{58} }{2}\\s=9.534758... (store \, the \, full \, value \, in \, your \, calculator)[/tex]
The formula for the area of the triangle:
[tex]A=\sqrt{s(s-A)(s-B)(s-C)}\\A=\sqrt{9.534758...(9.534758...-2\sqrt{3})(9.534758...-3\sqrt{2})(9.534758...-\sqrt{58} ) }\\A=15[/tex]
If a dose of 100 milligrams is contained in 4 milliliters, how many milliliters are in 40 milligrams?
Evaluate: (f+g)(-1)
f(x) = 5x^2 +7 (This reads 5x to the 2nd power plus 7)
g(x) = 3x - 6
Hint: (f+g)(x) = f(x) + g(x)
7
-7
-3
3
The function (f+g)(-1) is equal to 3.
How to find the value of the function?We can evaluate (f+g)(-1) by first finding f(-1) and g(-1), and then adding them together.
To find f(-1), we substitute -1 for x in the expression for f(x):
f(-1) = 5(-1)^2 + 7 = 5 + 7 = 12
To find g(-1), we substitute -1 for x in the expression for g(x):
g(-1) = 3(-1) - 6 = -3 - 6 = -9
Now we can add f(-1) and g(-1) together:
(f+g)(-1) = f(-1) + g(-1) = 12 + (-9) = 3
Therefore, (f+g)(-1) is equal to 3.
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i need help please!!!
Yes, the given figure is a parallelogram.
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Given is a parallelogram as shown in the image.
We have -
S(0, 0), T(3, 0), U(4, 3), V(1, 3)
For the figure to be parallelogram, we will have to prove -
ST = VU & SV = TU
We can calculate -
ST = 3
VU = 3
SV = 3.1
TU = 3.1
So -
ST = VU & SV = TU
Hence, it is a parallelogram.
Therefore, yes, the given figure is a parallelogram.
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15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)
Despite its age, the 15 puzzle remains a popular game today, and it has been adapted into many different variations, including digital versions and physical puzzles with different grid sizes and configurations.
15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)
The 15 puzzle is a classic sliding puzzle game that has been popular for over a century. The game was invented in the late 1800s by Noyes Chapman, and it quickly became a favorite pastime of people all over the world. The puzzle is sometimes called the "Gem Puzzle" or the "Boss Puzzle," and it has also been used as a tool for studying permutation groups and artificial intelligence algorithms.
Solving the 15 puzzle requires a combination of strategy, planning, and spatial reasoning. While the game is relatively simple to learn, it can be quite challenging to master, especially if you're trying to solve it in the minimum number of moves. In fact, there are over 1 trillion possible configurations of the 15 puzzle, and only a fraction of those can actually be solved.
Despite its age, the 15 puzzle is still widely played today. It has been transformed into a variety of games, including digital and physical puzzles with various grid sizes and arrangements.
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100 days make how many months?
Answer:
There are 3.28542 months in 100 days.
Step-by-step explanation:
For every 100 days, there are approximately 3.28542 months. To solve for any given number of days, divide the time value by 30.417.
For example, to solve for 200 days:
200 ÷ 30.417 = 6.57534 monthTherefore, 100 days make approximately 3.28542 months.
Answer:
3.28542
Step-by-step explanation:
100 days make how many months?
Value in months = value in days × 0.0328542
Value in months = 100 × 0.0328542 = 3.28542 (months)
1, 2, 3, 4, 5? (b) If one of the children is randomly chosen, what is the probability that child comes from a family having i children, i = 1, 2, 3, 4, 5?
The probability of having i children, i = 1,2,3,4,5 is 0.2, 0.4, 0.25, 0.1, 0.05 respectively. The probability that a randomly chosen child comes from a family with i children are 0.0741, 0,2963, 0.2773, 0.1481, 0.0926.
The probability that a randomly chosen family has i children is given by the ratio of the number of families with i children to the total number of families. Therefore:
P(1 child) = 4/20 = 0.2
P(2 children) = 8/20 = 0.4
P(3 children) = 5/20 = 0.25
P(4 children) = 2/20 = 0.1
P(5 children) = 1/20 = 0.05
(b) To calculate the probability that a randomly chosen child comes from a family with i children, we need to take into account the different numbers of children in each family. There are a total of 4+8x2+5x3+2x4+1x5=54 children in the community organization. Therefore, the probabilities are:
P(child from 1-child family) = 4/54 ≈ 0.0741
P(child from 2-child family) = 2x8/54 ≈ 0.2963
P(child from 3-child family) = 3x5/54 ≈ 0.2778
P(child from 4-child family) = 4x2/54 ≈ 0.1481
P(child from 5-child family) = 5/54 ≈ 0.0926
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____The given question is incomplete, the complete question is given below:
A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children,2 have four children, and 1 has five children.
(a) If one of these families is chosen at random, what is the probability it has i children, i = 1,2,3,4,5?
(b) If one of the children is randomly chosen, what is the probability this child comes from a family having i children, i =1,2,3,4,5?
Find the area A of polygon MNOPQ with the given vertices.
M(0,0), N(2,3), O(2,0), P(1, − 1), Q(−1,−1)
A=
square units
The area of the given polygon will be 10 square units.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
here, we have,
In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
Given the polygon with vertices
N(-2,1), P(3, 1),\ Q(3,-1), R(-2,-1)
If we draw the points in coordinate then it will become a rectangle with side lengths 5 and 2.
Area of rectangle = length × width
Area of rectangle = 5 × 2 = 10 square units.
Hence "The area of the given polygon will be 10 square units".
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#14.
The table below shows the value in dollars of a car at
the end of x years.
The function which represents the value of the car is [tex]y = 11000(0.85)^x[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
From the table, we can conclude the function of the car as:-
[tex]y = 11000(0.85)^x[/tex]
At x = 0, the value of y is,
[tex]y = 11000(0.85)^0[/tex].
y = 11000
At x = 1 the value of y is,
[tex]y = 11000(0.85)^1[/tex]
y = 11000 x 0.85
y = 9350
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Solve the system of equations by the addition method. If a system contains decimals, you may want to first clear the equation of decimals.0.9x +0.7y = 16 -0.3x-3.5y = - 71.6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution is (Type an ordered pair. Type an integer or a decimal rounded to one decimal place as needed.)O B. There are infinitely many solutions: {(x,y)|0.9x+0.7y=16) or {(x,y)] -0.3x - 3.5y = -71.6) O C. There is no solution, or Ø
The solution of the system of equations by adding method is equal to :
option A. Solution is ordered pair (x ,y) = ( 2.00 , 20.3 ) representing decimal rounded to one decimal place.
System of equations are :
0.9x +0.7y = 16 ___(1)
-0.3x - 3.5y = - 71.6 ___(2)
To get the solution of the system of equations are:
Multiply (2) by 3 and add it to (1)
0.9x +0.7y = 16
-0.9x - 10.5y = -214.8
0x - 9.8y = - 198.8
⇒ y = 20.3
⇒ x = 1.9966
⇒ x = 2.00
Therefore, the value of (x, y ) in the system of equations is given by :
option A. Type of solution is written as ordered pair (x ,y) = ( 2.00 , 20.3 ) having decimal rounded to one decimal place.
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PRACTICE IT Use the worked example above to help you solve this problem. parallel-plate capacitor has an area A = 2.50 X 10 m2 and plate separation d 1.40 * 10- m. (a) Find its capacitance_ 1.58e-12 (b) How much charge is on the positive plate if the capacitor Is connected to 3.00 battery? 12000 Your response differs significantly from the correct answer: Rework vour solution from the beginning and check each step carefully: € (c) Calculate the charge density on the positive plate, assuming the density is uniform: Clm (d) Calculate the magnitude of the electric field between the plates. 3.92 Your response differs significantly from the correct answer: Rework vour solution from the beginning and check each step carefully: Vlm
The capacitance is [tex]1.58*10^{-12} F[/tex], the charge is 12000 e, the charge density is [tex]4.80*10^{7} C/m^{2}[/tex], and the electric field is [tex]3.92*10^{6} N/C[/tex].
Here's how you can solve the above problems:
(a) To find the capacitance of a parallel-plate capacitor, we use the formula:
C = ε0A/d
where ε0 is the vacuum permittivity constant [tex](8.85*10^{-12}F/m )[/tex], A is the area of the plates, and d is the distance between the plates. Substituting the given values, we get:
C =[tex](8.85 * 10^{-12} F/m) (2.50* 10^{-4}m^{2} )/(1.40*10^{-7}m )[/tex]
= [tex]1.58*10^{-12} F[/tex]
(b) To find the amount of charge on the positive plate of the capacitor, we use the formula:
Q = CV
where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. Substituting the values from (a) and the given voltage, we get:
Q = [tex](1.58*10^{-12}F )(3.00 V)[/tex]
= [tex]4.74*10^{-11} C[/tex]
= 12000 e
(c) To find the charge density on the positive plate, assuming the density is uniform, we divide the charge on the plate by the area of the plate:
ρ = Q/A = [tex](12000e)/(2.50*10^{-4}m^{2} )[/tex]
= [tex]4.80*10^{7} C/m^{2}[/tex]
(d) To find the magnitude of the electric field between the plates, we use the formula:
E = V/d
where E is the electric field, V is the voltage across the capacitor, and d is the distance between the plates. Substituting the given values, we get:
E = [tex](3.00 V)/(1.40*10^{-7}m )[/tex]
= [tex]2.14*10^{-7} V/m[/tex]
= [tex]3.92*10^{6} N/C[/tex]
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Mallory's Border Collie had 18 puppies in 3 litters. Determine the rate for a ratio of the two different quantities.
18 over 3 puppies per litter
3 over 18 puppies per litter
18 over 21 puppies per litter
1 over 6 puppies per litter
Answer:
3 over 18 puppies per litter
Step-by-step explanation:
usually, you want to go with the smaller number first, it's like a fraction.
20 Points
A slice is made perpendicular to the base of a right rectangular prism, as shown.
What is the area of the resulting two-dimensional cross-section?
Drag and drop the answer into the box.
The area of the resulting two-dimensional cross-section is 480 inch².
What is Area?The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Given:
The Resulting Cross section will Have the Size
= 20 inch by 14 inch
So, Area of two dimensional Cross section
= 20 x 14
= 240 inch²
As prism is Sliced so this cross section will on the face of two prism.
Then, the Total cross section area
= 2 x 240
= 480 inch²
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the school band has 80 students and 35% play woodwind instruments. fill in the missing information and determine how many students play a woodwind instrument in the band.
By using the unitary method, 28 students in the school band play woodwind instruments.
Unitary method, which involves finding the value of a single unit and then using that value to find the value of multiple units. In this case, the single unit represents the percentage of students who play woodwind instruments.
Here we need to find the value of a single unit
To find the value of a single unit, we need to divide the given percentage by 100. So, 35% can be written as 0.35.
Therefore, the value of a single unit is 0.35.
Now use the unitary method to find the number of students who play woodwind instruments
Now, we can use the value of a single unit to find the number of students who play woodwind instruments. To do this, we multiply the value of a single unit by the total number of students in the band.
So, the number of students who play woodwind instruments is:
0.35 x 80 = 28
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Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4 Select each correct answer. Responses The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−4, 0) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the system because it makes both equations true.
The correct statement about the ordered pair (-4,0) and the system of equations is given as follows:
The ordered pair (-4,0) is a solution to the system because it makes both equations true.
How to interpret the ordered pair and the system of equations?The system of equations for this problem is defined as follows:
2x + y = -8.x - y = -4.The ordered pair (-4,0) means that when x = -4, y = 0.
Hence we verify if the first equation is satisfied, as follows:
2(-4) + 0 = -8
-8 = -8 -> Satisfied.
For the second equation, we have that:
-4 - 0 = -4
-4 = -4 -> Satisfied.
As both equations are satisfied, the ordered pair is a solution for the system of equations.
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Question 2(Multiple Choice Worth 2 points)
(02.05 MC)
The following tabl summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes
35%
10%
45%
Do not have diabetes 5%
50%
55%
What is the ratio of false positives to true positives?
O
O
10
7
10
O
117
Ratio of false positives to true positives is 1/7 .
What is False positive?In statistics, when performing multiple comparisons, the false positive rate is the probability of incorrectly rejecting the null hypothesis for a particular test.
Given In the table,
Number of patient test positive, but not have diabetes = 5%
Number of false positives = 5%
Number of patient test positive, and have diabetes = 35%
Number of true positive = 35%
Ratio of false positives to true positives
= 5%/35%
= 1/7
Hence, 1/7 is the ratio of false positives to true positives.
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