Therefore, Thabo will get R18, Patrick will get R24, and Lucas will get R30.
What is ratio?In mathematics, a ratio is a comparison between two quantities or numbers, indicating how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, with the first quantity as the numerator and the second quantity as the denominator. Ratios can also be simplified by dividing both the numerator and denominator by their greatest common factor. Ratios are used in many areas of mathematics, science, and everyday life, such as in finance, cooking, and sports. They are particularly useful for comparing two quantities of different units or scales, as they provide a standardized way to express the relationship between them.
Here,
To determine how much each person will get, we first need to find the total of the ratios which is:
3 + 4 + 5 = 12
This means that the total amount of money is divided into 12 equal parts.
To find out how much each person gets, we need to multiply their share of the ratio by the total amount of money:
Thabo's share = 3/12 x R72 = R18
Patrick's share = 4/12 x R72 = R24
Lucas's share = 5/12 x R72 = R30
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If G is a group with subgroups A, B of orders m, n, respectively, where m and n are relatively prime, prove that the subset of G, AB = {abla E Ab E B}, has mn distinct elements.
The number of distinct elements of AB = m n.
Given that G is a group with subgroups A and B of orders m and n, respectively, where m and n are prime, we need to prove that the subset of G, AB = {abla E Ab E B}, has m n distinct elements. Step-by-step. Let, G is a group with subgroups A and B of orders m and n, respectively. Since, m and n are relatively prime, then we have gcd(m, n) = 1.By Lagrange's Theorem, the order of any subgroup of G divides the order of G.
Hence, the order of G is equal to the product of the orders of A and B, i.e. |G| = |A| * |B| = m * n Let, a and a' be two distinct elements of A and b and b' be two distinct elements of B. Thus, a and a' generate distinct subgroups of G, i.e. ≠ and b and b' generate distinct subgroups of G, i.e. ≠ .Now, the number of distinct elements of AB = {abla E Ab E B} is equal to |A||B| since any two elements ab and a'b' of AB will be distinct if either a and a' are distinct or b and b' are distinct or both are distinct. Hence, the number of distinct elements of AB = m n.
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Which box plot represents data that contains an outlier?
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 10, and the box ranges from 6 to 8. 5. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 3 to 9, and the box ranges from 5 to 7. A line divides the box at 6,
The box plot represents the data set 2, 4, 6, 8, 10, 12 is option (a) A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot is a graphical representation of a data set that displays the distribution of the data, as well as its quartiles and any outliers. The plot is made up of a rectangular box, which represents the middle 50% of the data, with a line in the box representing the median. Two lines, called whiskers, extend from the box to represent the range of the data outside of the box, excluding any outliers. Outliers are any values that fall outside of the whiskers.
In the given options, the box-and-whisker plot that represents the data set 2, 4, 6, 8, 10, 12 is the one that has a box ranging from 4 to 10, with a median line dividing the box at 7. This means that 50% of the data falls between 4 and 10, with the median value being 7. The whiskers range from 2 to 12, indicating that the data set has a minimum value of 2 and a maximum value of 12.
Therefore, the correct option is (a) A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
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The given question is incomplete, the complete question is:
Which box plot represents the data set 2, 4, 6, 8, 10, 12?
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 8. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 9. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 6 to 10. A line divides the box at 8.
Answer: (B)
Correct Answer 100%! Pls, give me brainliest. Thank You!
In the above video lecture, we verified the following result: Computing the gradient of n
Rn (θ) = 1/n Σ (y^(t) - θ.x^(t)^2 / 2
t=1
we get ΔRn (θ) = Aθ-b (=0) where A= n n
A = 1/n Σ x^(t) (x^(t))^T , b = 1/n Σ y^(t) x^(t)
t=1 t=1
Now, what is the necessary and sufficient condition that Aθ - b = 0 has a unique solution?
- None of A's entries is 0. - A is invertible.
- A's dimension is the same as that of θ's
The direction of the steepest descent, which is used to find the minimum value of a function.
The necessary and sufficient condition that Aθ-b = 0 has a unique solution is: A is invertible.What is computing?Computing is a part of computer science that focuses on computer programs, including their software and hardware. It is concerned with designing algorithms to solve problems and creating software that will run these algorithms. As a result, computing is a field of study that is concerned with the process of creating algorithms and software.InvertibleAn invertible matrix is a matrix in which the determinant is not zero. An invertible matrix is also referred to as a non-singular matrix. An invertible matrix has a unique inverse. The rank of an invertible matrix is equal to its dimension. An invertible matrix can be used to solve a system of linear equations.GradientA gradient is a vector field in which the direction of the vector points to the steepest increase in a function, and the magnitude of the vector is the rate of increase in that direction. The gradient of a function is a vector field that is a derivative of the function. The gradient is used in multivariable calculus to solve optimization problems. The gradient is used to find the direction of the steepest ascent, which is used to find a maximum value of a function. It is used to find the direction of the steepest descent, which is used to find the minimum value of a function.
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Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 12. What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
A. -3
B. -1.5
C. 1.5
D. 3
2. The point (3,w) is on the graph of the line y = 2x + 7. What is the
value of w?
Answer:
We are given that the point (3,w) lies on the line y = 2x + 7. This means that if we substitute x = 3 into the equation y = 2x + 7, we will get the value of y at x = 3, which is equal to w.
Substituting x = 3 into the equation y = 2x + 7, we have:
y = 2(3) + 7
y = 6 + 7
y = 13
Therefore, the value of w is 13.
Step-by-step explanation:
Difference between 6z and z to the power of 6
Answer:
[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]
The mathematical statement in the form of expression can be written as 15625z⁶.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is to find the mathematical statement -
"Difference between 6z and z to the power of 6"
We can write the given mathematical statement in the form of expression as -
(6z - z)⁶
(5z)⁶
5⁶ x z⁶
125 x 125 x z⁶
15625z⁶
Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.
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PLEASE HELP !!!! QUICK
the wholesale price for a pair of shoes is $4.50 a certain department store marks up the wholesale price by 40%. find the price of the pair of shoes in the department store.
round your answer to the nearest cent, as necessary
Using percentages we know that the markup price of the pair of shoes will be $6.3.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A% is a number that has neither dimensions nor a defined unit of measurement.
When expressing a proportionate share of a total, percentages are frequently utilized.
(Similarly, the term "per mille" or the sign "%" can be used to denote a number as a fraction of 1,000.)
So, the market price of the store would be:
= 4.50/100 * 40
= 0.045 * 40
= 1.8
Markup price: 1.8 + 4.5 = $6.3
Therefore, using percentages we know that the markup price of the pair of shoes will be $6.3.
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Find the area of the shaded region.
80°
5 cm
A=[?] cm2
Enter a decimal rounded to the nearest tenth.
From the given information provided, the area of the shaded region inside the circle is 22.58
The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.
The space enclosed by the sector of a circle is called the area of the sector.
the radius of the circle is 5cm.
area of arc = radius² × θ/2
area of the arc is = 5² × 4π/9 = 25 × 4/9 = 34.88
area of the triangle inside circle = a×b × sin(y)/2
area of triangle = 5×5 × sin(80°)/2 = 25 × 0.492
area = 12.3
area of the shaded region is = 34.88 - 12.3 = 22.58
Hence, the area of the shaded region is 22.58
Question - Find the area of the shaded region in the circle if the angle of the arc is 80 degree radius is 5cm.
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a) if lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, what is lisa's percentile rank? (round your answer to the nearest whole number.)
Lisa's percentile rank is approximately 88%.
Percentile rank is a statistical measure that indicates the percentage of scores that fall below a particular score in a given distribution of data. It is commonly used to describe the relative position of a particular score in a set of scores.
If Lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, then her percentile rank can be calculated using the following formula:
Percentile Rank = [(Number of scores below Lisa's score) ÷ (Total number of scores)] × 100
Percentile Rank = [(240 - 29) ÷ 240] × 100
Percentile Rank = (211 ÷ 240) × 100
Percentile Rank = 0.8792 × 100
Percentile Rank ≈ 88 (rounded to the nearest whole number)
Therefore, her percentile rank is approximately 88%.
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In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset.
What is data analytics?Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.
The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.
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Find the first five terms of the sequence a(n)=3n-1
Answer:
-1, 2, 5 , 8 , 11 or 2, 5, 8, 11 , 14
Step-by-step explanation:
Assume n starts from 0
a(0) = 3 (0) -1 = -1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
notice If we Assume n starts from 1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
a(5)= 3 (5) -1 = 14
Notice a sequence can start from any N. But the most common ones are n=0 or n=1
there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3 rd row, and so on. if the price per ticket is $32, how much will be the total sales for a one-night concert if all seats are taken?
Answer:
Step-by-step explanation:
To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.
To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:
S = n/2 * (a + l)
where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, we have:
n = 20 (since there are 20 rows)
a = 25 (since there are 25 seats in the first row)
d = 2 (since the difference between each row is 2 seats, the common difference is 2)
We can use d to find the last term as well:
l = a + (n-1)*d
l = 25 + (20-1)*2
l = 25 + 38
l = 63
Now we can plug these values into the formula:
S = 20/2 * (25 + 63)
S = 10 * 88
S = 880
So there are 880 seats in total.
To find the total sales, we just need to multiply by the price per ticket:
total sales = 880 * $32
total sales = $28,160
Therefore, the total sales for a one-night concert with all seats taken would be $28,160.
Could you please answer b and d
I will mark brainliest for the first answer
Answer: 50 uk pounds
Step-by-step explanation:
Step-by-step explanation:
See image below
I need the answer to this question(PLEASE IM BEGGING YOU)
Answer:
B & D
Step-by-step explanation:
For future reference, you can just a site called desmos. It has a graphing tool where you can just write the function and then check where the lines meet.
Complimentary Event The compliment of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted E (read "E bar"). Rule for Complimentary Events P(E)=1-P(E) or P(E)=1-P(E) O P(E)+P(E)=1 Example # 12: The probability that Mary can work a problem is 70%. Find the probability that Mary cannot work the problem. Example # 13: In 2004, 57.2% of all enrolled college students were females. Choose one enrolled student at random. What is the probability that the student was a male?
The student is male, which is P(male).Using the rule of complementary events, P(male) = 1 - P(female)P(male) = 1 - 0.572 = 0.428Therefore, the probability that the student is male is 0.428 or 42.8%.
The complimentary event is a part of probability theory. It is the event that occurs when the event E does not occur. In other words, it is a set of outcomes in the sample space that are not included in the outcomes of event E. The notation for the complement of E is E'. Rule for Complimentary EventsThe rule for complementary events can be expressed in two ways:
P(E) = 1 - P(E)P(E) + P(E') = 1Example # 12:Let the probability that Mary can work a problem be P(E) = 0.70.We need to find the probability that Mary cannot work the problem, which is P(E').Using the rule of complementary events,P(E') = 1 - P(E)P(E') = 1 - 0.70 = 0.30Therefore, the probability that Mary cannot work the problem is 0.30 or 30%.Example # 13:Let P(female) be the probability that the student is female. We are given that P(female) = 0.572.
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firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75. Assuming that we draw the isoquant map with labor on the horizontal axis and capital on the vertical axis, what is the slope of this firm's isoquant when L = 100 and K = 50? Give your answer to two decimal places and remember that the sign matters when describing the slope of an isoquant.
The slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
When the firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75, the slope of this firm's isoquant when L = 100 and K = 50 is equal to -0.50.What is an isoquant?An isoquant, also known as an equal product curve, is a graph that shows the various combinations of two inputs, say labor and capital, that produce the same level of output. It's a contour map that shows the different levels of output that can be produced using various combinations of inputs at the same cost. The slope of an isoquant is known as the marginal rate of technical substitution (MRTS) and represents the rate at which one input can be substituted for another while holding the level of output constant.How to determine the slope of an isoquant?The slope of an isoquant can be calculated by taking the ratio of the marginal product of the two inputs, which is the change in output resulting from a unit change in one input when the other is held constant, and is given by the following formula:Slope of isoquant = MP_L / MP_Kwhere MP_L and MP_K are the marginal products of labor and capital, respectively.Now, to determine the slope of this firm's isoquant when L = 100 and K = 50, we must first compute the marginal products of labor and capital as follows:MP_L = ∂f / ∂L = 0MP_K = ∂f / ∂K = 0.75 * 0.25 * K^-0.25 = 0.0469Then we can plug these values into the slope of isoquant formula:Slope of isoquant = MP_L / MP_K = 0 / 0.0469 = 0The slope of the isoquant when L = 100 and K = 50 is zero, indicating that labor and capital cannot be substituted for one another to produce the same level of output. However, since the question asks for the sign of the slope, we must take into account the standard convention for labeling isoquants. When labor is measured on the horizontal axis and capital on the vertical axis, the slope of the isoquant is negative. Therefore, the slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
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a ladder leans against the side of a house. the top of the ladder 8ft is from the ground. the bottom of the ladder is from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.
The length of the ladder is c = √(x^2 + 64) ft.
The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.
The Pythagorean Theorem states that a^2 + b^2 = c^2.
Therefore, x^2 + 8^2 = c^2
Solving for c: x^2 + 64 = c^2
Taking the square root of both sides: √(x^2 + 64) = c
Therefore, the length of the ladder is c = √(x^2 + 64).
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Using c use the best term to identify the following.
The correct definition for the lines drawn to circle with centre C are:
FA is an secant.CD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.Explain about the circle?A circle is a spherical shape without boundaries or edges.
A radius describes the distance radiating from the centre.The Diameter passes through the centre of the circle in a straight line.The distance travelled through a circle is its circumference.A line that precisely crosses a circle at one point is said to be tangent.The circular region is divided into two sections by a circle's chord. The term "circular segment" refers to each component.The major segment and minor segment are distinguished by the arcs they contain. The major segment contains the minor arc.Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:
FA is an secantCD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.know more about the circle,
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PLEASE Answer before 3/12/2023
6, 14, 22, 30, 38, … Use the expression below to determine the value of the 15th term. 6 + 8n, where n is equal to 0, 1, 2, 3, … answers: 112 118 120 126
Answer: 118
Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.
Answer: 118
Step-by-step explanation:
you just keep going up at the rate of 8
Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = -7 and B = 7.(a) Compute P(X < 0).(b) Compute P(-3.5 < X < 3.5).(c) Compute P(-5 ≤ X ≤ 6).(d) For k satisfying -7 < k < k + 4 < 7, compute P(k < X < k + 4).
(a) Probability that X < 0 is P(X<0) = 1/2
(b) Probability that -3.5 < X < 3.5 is given by = 1/2
(c) Probability that -5 ≤ X ≤ 6 is given by = 11/14.
(d) Let k be any number such that -7 < k < k+4 < 7 = 2/7
(a) Since the distribution is uniform, the probability of X being less than 0 is equal to the proportion of the interval (-7, 7) that lies to the left of 0. This proportion is (0 - (-7))/(7 - (-7)) ⇒ 7/14 ⇒ 1/2.
Therefore, P(X < 0) = 1/2.
(b) Following the same logic as above, the probability of X lying between -3.5 and 3.5 is equal to the proportion of the interval (-7, 7) that lies between -3.5 and 3.5. This proportion is (3.5 - (-3.5))/(7 - (-7)) ⇒ 7/14 ⇒ 1/2.
Therefore, P(-3.5 < X < 3.5) = 1/2.
(c) Similarly, the probability of X lying between -5 and 6 is equal to the proportion of the interval (-7, 7) that lies between -5 and 6. This proportion is (6 - (-5))/(7 - (-7)) ⇒ 11/14.
Therefore, P(-5 ≤ X ≤ 6) = 11/14.
(d) The interval (k, k+4) lies completely within the interval (-7, 7) if -3 < k < 3. If k satisfies this inequality, then the probability of X lying between k and k+4 is equal to the proportion of the interval (-7, 7) that lies between k and k+4, which is (k+4 - k)/(7 - (-7)) ⇒ 4/14 ⇒ 2/7.
Therefore, P(k < X < k+4) = 2/7.
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Solve the triangle PQR (find the measures of ∠P, ∠Q, and side PQ).
(I need help finding both angle measure and side measure, please and thank you!)
Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
What precisely is a triangle?A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.
Here,
The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:
=> PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)
=> PQ² = 9² + 12² - 2(9)(12)cos(62°)
=> PQ² ≈ 110.03
=> PQ ≈ 10.49
As a result, side PQ is roughly 10.49 units long.
The rule of sines can then be used to determine the dimensions of angles P and Q:
=> sin(∠P) / PQ = sin(62°) / PR
=> sin(∠P) / 10.49 = sin(62°) / 9
=> sin(∠P) ≈ 0.6322
=> ∠P ≈ 39.39°
=> sin(∠Q) / PQ = sin(77°) / QR
=> sin(∠Q) / 10.49 = sin(77°) / 12
=> sin(∠Q) ≈ 0.8559
=> ∠Q ≈ 58.10°
As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
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For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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Which equation is equivalent to pq=r?
Responses
A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r
The equation is equivalent to pq=r is option (C) q=logR p
To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get
log(pq) = log(r)
Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation
log(p) + log(q) = log(r)
Now, we can compare this expression to each of the answer choices
A) p = logR q
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This is not equivalent to our expression, so A is not the correct answer.
B) p = logQ r
Substituting this into the equation, we get
log(logQ r) + log(q) = log(r)
This is also not equivalent to our expression, so B is not the correct answer.
C) q = logR p
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This matches our expression, so C is the correct answer.
D) q = logP r
Substituting this into the equation, we get
log(p) + log(q) = log(logP r)
This is not equivalent to our expression, so D is not the correct answer.
Therefore, the correct option is (C) q=logR p
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.
How to use Chinese remainder theorem?We are looking for a number $x$ that satisfies the following conditions:
[tex]$\begin{align*}x &\equiv 0 \pmod{4} \x &\equiv 6 \pmod{7} \x &\equiv 3 \pmod{5}\end{align*}[/tex]
Since 4, 7, and 5 are pairwise co-prime, we can use the Chinese Remainder Theorem to solve this system of congruences.
Let [tex]$M = 4 \cdot 7 \cdot 5 = 140$[/tex], and
let [tex]$M_1 = 7 \cdot 5 = 35$[/tex], [tex]$M_2 = 4 \cdot 5 = 20$[/tex], and [tex]$M_3 = 4 \cdot 7 = 28$[/tex]. Then we need to find integers [tex]$a_1$[/tex], [tex]$a_2$[/tex], and [tex]$a_3$[/tex] such that
[tex]$a_1 M_1 \equiv 1 \pmod{4}$[/tex], [tex]$a_2 M_2 \equiv 1 \pmod{7}$[/tex], and [tex]$a_3 M_3 \equiv 1 \pmod{5}$[/tex].
We can easily verify that [tex]$a_1 = 3$[/tex], [tex]$a_2 = 5$[/tex], and [tex]$a_3 = 3$[/tex] satisfy these conditions.
Then the solution to the system of congruence is given by
[tex]$\begin{align*}x &\equiv 0 \cdot 7 \cdot 5 \cdot 3 + 6 \cdot 4 \cdot 5 \cdot 3 + 3 \cdot 4 \cdot 7 \cdot 3 \cdot 3 \pmod{140} \&\equiv 69 \pmod{140}\end{align*}[/tex]
Therefore, Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.
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The probability that a person in a certain town has brown eyes is 2 out of 5. A survey of 450 people from that same town was taken. How many people would be expected to have
brown eyes?
A. 45
B. 90
C. 180
D. 225
From the given information provided, the number of people having brown eyes in town is 180.
If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.
To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:
(2/5) = (x/450)
where x is the number of people expected to have brown eyes.
Solving for x, we can cross-multiply:
5x = 2 × 450
5x = 900
x = 180
Therefore, the expected number of people in the survey who would have brown eyes is 180.
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The points (-7,4) and (r,19) lie on a line with slope 3. Find the missing coordinate r.
Answer:
r = -2
Step-by-step explanation:
We can use the slope formula to find r.
m = ( y2-y1)/(x2-x1)
3 = ( 19-4)/(r- -7)
3 = 15/(r+7)
Multiply each side by (r+7).
3 ( r+7) = 15
Divide each side by 3.
r+7 = 15/3
r+7 = 5
Subtract 7 from each side.
r+7-7 = 5-7
r = -2
A snow making machine priced at $1800 is on sale for 25% off. The sales tax rate is 6. 25%. What is the sale price including tax? If necessary, round your answer to the nearest cent
The sale price including tax is $ 2390.625.
Given that,
The price of the snow machine= $ 1800
Discount percentage= 25%
Sales tax rate = 6.25%
Hence, Sale price = Price + Discount percentage of price
= 1800 + 25/100 × 1800
= 1800 + 450
= 2250.
Sale price including tax = Sale price + Tax rate
= 2250 + 6.25/100
= 2250 + 140.625
= $ 2390.625.
Hence, the sale price including tax is $ 2390.625.
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
A truck driver pays for emergency repairs that cost $1,215.49 with a credit card that has an annual rate of 19.95%. If the truck driver pays $125 a month until the balance is paid off, how much interest will have been paid?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$83.82
$180.83
$121.52
$155.37
Answer: the answer is $83.82
Step-by-step explanation:
To calculate the total interest paid, we need to first calculate how long it will take to pay off the balance. We can use the formula for the present value of an annuity to find this:
PV = PMT x [(1 - (1 + r/n)^(-nt)) / (r/n)]
Where:
PV = present value (the amount borrowed)
PMT = payment amount
r = annual interest rate
n = number of times interest is compounded per year
t = time in years
In this case, PV = $1,215.49, PMT = $125, r = 19.95%, n = 12 (monthly compounding), and we want to solve for t.
1,215.49 = 125 x [(1 - (1 + 0.1995/12)^(-12t)) / (0.1995/12)]
Simplifying this equation, we get:
12t = 27.9275
t = 2.3273 years
So it will take about 2.33 years to pay off the balance.
Now, we can calculate the total amount paid by multiplying the monthly payment by the number of payments:
Total amount paid = $125 x 28 (2.33 years x 12 months/year) = $3,500
The total interest paid is the difference between the total amount paid and the amount borrowed:
Total interest paid = $3,500 - $1,215.49 = $2,284.51
Finally, we can calculate the average monthly interest paid by dividing the total interest paid by the number of payments:
Average monthly interest paid = $2,284.51 / 28 = $81.59
Rounding this to the nearest cent, we get $81.58, which is closest to $83.82. Therefore, the answer is $83.82.
Answer:
b
Step-by-step explanation:
To calculate the interest paid, we need to find out how many months it will take to pay off the balance and what the total payments will be.
Using the formula:
n = -log(1 - i/p) / log(1 + r)
where:
p = monthly payment ($125)
i = initial balance ($1,215.49)
r = monthly interest rate (19.95% / 12 = 0.016625)
n = number of months to pay off the balance
n = -log(1 - 125/1215.49) / log(1 + 0.016625) = 11.02 (rounded up to 12)
So it will take 12 months to pay off the balance. The total payments will be:
12 x $125 = $1,500
The total interest paid will be:
$1,500 - $1,215.49 = $284.51
Therefore, the answer is closest to option B, $180.83.
what is the area of the parallelogram
The area of the parallelogram is 324 square yards.
What is a parallelogram ?
A parallelogram is a four-sided geometric shape that has two pairs of parallel sides. It isdefined by its four vertices, four sides, and two diagonals that intersect at their midpoint. The opposite sides of a parallelogram are congruent, and the opposite angles are also congruent. The adjacent angles are supplementary and add up to 180 degrees.
To find the area of a parallelogram, we need to multiply the length of the base by the height, which is the perpendicular distance from the base to the opposite side. This formula is similar to finding the area of a rectangle, where the base is one side of the rectangle and the height is the distance from that side to the opposite side.
Calculating the area of the given parallelogram :
The area of a parallelogram is A = bh, where b is the base and h is the height.
Given the height of the parallelogram is 12 yards and the base is 27 yards. Using the formula for the area of a parallelogram, we can calculate the area as follows:
A = bh
A = 27 yards × 12 yards
A = 324 square yards
Therefore, the area of the parallelogram is 324 square yards.
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