Answer: y/x = k, where k is the constant of proportionality.
Step-by-step explanation:
The proportional connection is represented by the linear equation y equals two-thirds times x.
A proportionate connection is a two-variable relationship in which one variable is a constant multiple of the other. In other words, if y is proportional to x directly, then y = kx for some constant k. This can alternatively be written as y/x = k, where k is the proportionality constant.
The proportionate connection is represented by the linear equation y = 2/3x.
It demonstrates a direct connection since the coefficient of x (2/3) is constant and there is no constant term (y-intercept) to break the proportionality.
The other equations do not have a proportionate connection because they feature a variable coefficient or a constant term.
Answer:
y/x = k, where k is the constant of proportionality.
Step-by-step explanation:
Find the average value of the following list of numbers.
20, 25, 7, 27, 18, 17
The average value is
Answer:
19
Step-by-step explanation:
First we need to add all these numbers together
20+25+7+27+18+17=114
Next, we have to divide all these numbers by the number of values there are.
If we count, there are 6 values that we added together.
After that, we divide 114 by 6 to get the answer
114/6=19.
Step-by-step explanation:
this is a college question ???
and you don't know how to do this ?
remember middle school and high school ? besides math classes themselves, did you never track your class scores and such ?
the average or mean value is always the sum of all data points divided by the number of data points.
here we have 6 data points.
the average is
(20+25+7+27+18+17)/6 = 114/6 = 19
The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3 . At the instant when dp/dt = 41 and c = 15 , what is the value of dc/dt ？
The value of dc/dt when dp/dt = 41 and c = 15 is -41/75.
At any given time, the rate of change of the variables p and c with respect to time is denoted by dp/dt and dc/dt, respectively. The equation given to us is p^2 = (20-c)^3. We are given the values of dp/dt = 41 and c = 15. Thus, we are required to calculate the value of dc/dt.
To solve for dc/dt, we differentiate both sides of the equation with respect to time. On the left side, we get 2p*dp/dt, and on the right side, we get -3(20-c)^2*dc/dt. Equating both sides and solving for dc/dt, we get dc/dt = -41/(3(20-15)^2) = -41/75.
Hence, the value of dc/dt when dp/dt = 41 and c = 15 is -41/75.
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Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant, how many ways can this be done?
If the order of the choices is relevant ,72 times can this be done.
What is nPr in permutation formula?Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant
The permutation of arranging 'r' things from a collection of 'n' objects into an order or sequence is known as nPr in mathematics. Permutation is calculated using the formula nPr = (n!) / (n-r)! N permutations = nPr = n!/ (n-r)! Combination, nCr, is the selection of r items from a collection of n objects such that the order of the objects does not matter.
N permutations are as follows: 9P6 = 8!/(8-6)! = 8*7*6*5*4 = 6,720.
N combinations = nCr = n!/((n-r)!r!) is the response to b.
N combinations = = 8C6 = = 8!/((8-6)!6!) = (8*7*6)/(2*1) = 72
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HELP FAST WILL MARK BRAINLYIST! You are a housekeeper in a hotel. It takes you 15 minutes to clean 1 room. In the floor you are assigned, there are 26 rooms. At that rate, how many hours will it take you to clean all 26 rooms?
3.75
3.9
6.5
9.0
15.6
Answer:360 minutes
Step-by-step explanation: 15 x 26 = 360
360 minutes = to 6 HOURS
Answer: 390 minutes
Step-by-step explanation:
The largest angle of a triangle is four times the middle angle. The smallest angle measures 24° less than the middle angle. Find the measure of each angle.
Answer:
Largest angle=136
middle angle=34
smallest angle=10
Step-by-step explanation:
largest angle= A, 4B
middle angle= B
smallest angle= C, B-24
A+B+C=180
4B+B+B-24=180
5B+B=204
6B=204
B=34
A=4(34), 136
B=34
C=34-24, 10
Write the equation of the line with a slope of 3/2 that contains the point ( − 2, – 4). A-y=3/2x-1 B-y=3/2x+4 C-y= 3/2x−7 D-y= 3/2x−4
Answer:
A) y = 3/2 x - 1
Step-by-step explanation:
y + 4 = 3/2 (x + 2) This is the point slope form of a line.
y + 4 = 3/2 x + 3 Subtract 4 from both sides
y = 3/2 x -1
Label the triangle using the information given, then find the cos(l)-
The following is true about AGHI:
mZH = 90°
GH = 4
HI=7
GI = 8.1
Find the expression for cos(1).
The triangle AGHI can be labeled by using the given information.
Find the expression for cos(1)?The triangle is labeled AGHI.cos(l) = (GH^2 + HI^2 - GI^2) / (2 * GH * HI) = (4^2 + 7^2 - 8.1^2) / (2 * 4 * 7) = 0.848048096156426.The triangle AGHI is an isosceles triangle, with two sides of equal length (GH and HI). The angle formed between GH and HI is mZH, which is a right angle. The length of the side GI is 8.1.To find the cos(l) of the triangle, we use the law of cosines, which states that c2 = a2 + b2 - 2abcos(l). In this case, c is 8.1, a is 4, and b is 7. Substituting these values into the equation yields cos(l) = (42 + 72 - 81.2) / (2(4)(7)) = -0.67.Therefore, the cos(l) of the triangle AGHI is -0.67.Label the triangle AGHI:The right-angle of the triangle is at the vertex of Z, so angle ZHG is 90°. The side opposite to angle ZHG is GH, which is equal to 4. The side adjacent to angle ZHG is HI, which is equal to 7. The side opposite to angle HGI is GI, which is equal to 8.1.To find the expression for cos(l), we can use the Cosine Law. Cos(l) = (GH^2 + HI^2 - GI^2)/2(GH)(HI). Substituting the given values, we get Cos(l) = (4^2 + 7^2 - 8.1^2)/2(4)(7). Hence, the expression for cos(l) is equal to -0.10205.To learn more about The triangle is labeled AGHI refer to:
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Select the correct answer. Consider these functions: Which statements, if any, are true about these functions? I. The function f(g(x)) = x for all real x. II. The function g(f(x)) = x for all real x. III. Functions f and g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.
Based on the functions, the statements that are true about these functions include the following: C. I, II, and III.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
x = 3y³ + 2
3y³ = x - 2
y³ = (x - 2)/3
y = ∛[(x - 2)/3]
Therefore, the function f(g(x)) is given by:
Function, f(g(x)) = 3[∛((x - 2)/3)]³ + 2
Function, f(g(x)) = 3[(x - 2)/3] + 2
Function, f(g(x)) = x
For the function g(f(x)), we have:
Function, g(f(x)) = ∛[(3x³ + 2 - 2)/3]
Function, g(f(x)) = ∛x³
g(f(x)) = x
In conclusion, the input value (x-value) and output value (y-value) of these functions are interchangeable.
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Which inequality is true when the value of p is -1
When the value of p is - 1, then p- 1 ≤ 0.5 is the required inequality.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the inequalities;
(A). p- 1 ≤ 0.5
When p = -1,
-2 ≤ 0.5.
(B). -p - 1 ≤ -0.5
When p = -1,
0 ≤ -0.5.
This is contradiction.
(C). p - 1 ≥ 0.5
When p = -1,
-2 ≥ 0.5.
This is contradiction.
(D). -p -1 ≥ 0.5
When p = -1,
0 ≥ 0.5.
This is contradiction.
Therefore, p- 1 ≤ 0.5 is the required inequality.
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The complete question:
Which inequality is true when the value of p is -1?
(A). p- 1 ≤ 0.5
(B). -p - 1 ≤ -0.5
(C). p - 1 ≥ 0.5
(D). -p -1 ≥ 0.5
Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.
x P(x) xP(x)
0 0.10
1 0.25
2 0.30
3
4 0.10
5 0.05
6 (or more) 0.05
(a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.)
(b) In words, what does the expected value in this example represent?
the number of children adults in the country have
the number of children married adults in the country have
the average number of children married adults in the country have
the average number of children adults in the country have
(c) Find the expected value. (Enter your answer to two decimal place.)
children
(d) Is it more likely that a married adult will have two to three children or four to six children? How do you know?
it is more likely to have four to six children, with p = 0.2
it is more likely to have two to three children, with p = 0.45
it is more likely to have four to six children, with p = 0.8
it is more likely to have two to three children, with p = 0.3
it is more likely to have four to six children, with p = 0.1
In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).
a) The probability that a married adult has three children is 0.30.
b) The expected value in this example represents the average number of children married adults in the country have.
c) The expected value is 1.90 children.
d) It is more likely that a married adult will have two to three children, with p = 0.55. This is because the probability of having two to three children (0.30 + 0.25 = 0.55) is greater than the probability of having four to six children (0.10 + 0.05 = 0.15).
In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).
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Noah opens a savings account which gives compound interest of 2.5% per
year. He puts £4000 into it.
a) How much money will Noah have in the account after 9 years?
b) How much interest will Noah have earned from this account after
9 years?
Give your answers in pounds (L) to the nearest 1p.
The answer of the given question based on the compound interest is (a) Noah will have £4995.45 in the account after 9 years. (b) Noah will have earned £995.45 in interest from this account after 9 years.
What is Compound interest?Compound interest is type of the interest that is calculated on the both principal (initial amount) and any accumulated interest from the previous periods. In other words, interest is earned not only on the initial investment, but also on the interest earned in previous periods.
a) The formula for compound interest is given by:
A = P(1 + r/n)^(n*t)
In this case, P = £4000, r = 0.025 (2.5% as a decimal), n = 1 (since the interest is compounded annually), and t = 9. Substituting the values into formula, we will get:
A = £4000(1 + 0.025/1)⁽¹*⁹⁾ = £4995.45
Therefore, Noah will have £4995.45 in the account after 9 years.
b) The amount of interest earned is simply the difference between the amount at the end of the time period and the initial deposit, i.e.,
Interest = A - P = £4995.45 - £4000 = £995.45
Therefore, Noah will have earned £995.45 in interest from this account after 9 years.
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A recent poll of 738 randomly selected customers of a major U.S. cell-phone carrier found that 170 of them had walked into something or someone while talking on a cell phone. Show that the conditions for calculating a confidence interval for a proportion are satisfied.
Yes, the conditions to calculate a confidence interval for a proportion are satisfied.
n = 738
p = 170/738 = 0.2297
np ≥ 10 and n(1-p) ≥ 10
np = 0.2297*738 = 169.686 ≥ 10
n(1-p) = 738(1-0.2297) = 568.314 ≥ 10
Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.
Yes, the conditions for calculating a confidence interval for a proportion are satisfied. The sample size of the poll was 738 randomly selected customers of a major U.S. cell-phone carrier. Out of these 738 customers, 170 had walked into something or someone while talking on a cell phone. This gives us a population proportion of 170/738 or 0.2297. We need to ensure that np ≥ 10 and n(1-p) ≥ 10. Calculating these values, np = 0.2297*738 = 169.686 which is greater than 10 and n(1-p) = 738(1-0.2297) = 568.314 which is also greater than 10. Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.
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11
What is the value of this expression?
3 1/6 + 8 2/9 - 1 1/2
Answer:[tex]\frac{89}{9}[/tex] or [tex]9 \frac{8}{9}[/tex] or 9.8
Put a line above the 8 after the decimal point signaling that it will always be 8 after the decimal point.
Step-by-step explanation:
6*3+1=19
9*8+2=74
1*2+1=3
[tex]\frac{19}{6} + \frac{74}{9} - \frac{3}{2} = \frac{89}{9}[/tex]
the tripple point is the set temperature and pressure where a substance occurs as a solid, liquid, and gas simultaneously at equilibrium.
The triple point of a substance, Tₜ, is the temperature and pressure at which the three phases of the substance, solid, liquid, and gas, can coexist in thermodynamic equilibrium.
The triple point can be calculated using the Clausius-Clapeyron equation, which states that the pressure and temperature of the triple point are related by the equation:
ln(Pₜ/P₀) = (ΔHₜ / R) (1/Tₜ - 1/T₀)
where Pₜ and Tₜ are the pressure and temperature of the triple point, P₀ and T₀ are the pressure and temperature of an arbitrary reference point, ΔHₜ is the enthalpy of vaporization, and R is the universal gas constant.
To calculate the triple point, values for P₀ and T₀ are selected and the enthalpy of vaporization is determined from tabulated data. Then, the equation is rearranged to solve for Tₜ, and the pressure and temperature of the triple point can be found.
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Raelyn has 33 red beads and 21 blue beads. She mixes the
beads together and uses 6 beads for each key chain she
makes. What multiplication equation and division equation can
help Raelyn determine how many key chains she can make?
The multiplication equation and division equation can
help Raelyn determine how many key chains she can make is 9
What is multiplication equation?When solving multiplication equations, these equations may have the form ax = c, bx = d, or cx = f
The question says that Raelyn has 33 red beads and 21 blue beads. She mixes the
beads together and uses 6 beads for each key chain she
makes.
Based on the given conditions, formulate:: (33+21) /6
Calculate the sum or difference: 54/6
Cross out the common factor: 9
Therefore, the multiplication equation and division equation gives 9
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(1.3) (2.5) (2,7) (4,9) does it represent a function
This doesn’t represent a function because the x value 2 repeats
Hope this helped =)
A machinist must cut 12 strips of metal that are each 2 ft 6 7/8 in. long. What is the total length needed in inches?
The total length needed in inches for the 12 strips of metal is 370¹/₂ inches.
How is the total length determined?The total length for the 12 strips of metal is determined using a combination of the mathematical operation of multiplication and unit conversion.
The 2 feet are converted to 24 inches (2 x 12) using unit conversion and multiplication.
The total length is determined by multiplication, involving the multiplicand and the multiplier, which results in a product called the result.
The number of strips of metal = 12
The length of each strip = 2 ft and 6⁷/₈ inches = 30⁷/₈ inches
1 foot = 12 inches
The total length = 370¹/₂ inches (30⁷/₈ inches x 12)
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Which graph represents the solution to the following inequality? | x | ≤ 7
Option D shows the correctly represents the solution to the given inequality: | x | ≤ 7
What is method to find the solution to inequality?A number is a solution to that of an inequality in x if it can be used to replace x with a statement that is true.
You may add the same amount to both sides of an inequality to make it equal.The same amount can be subtracted from each side.Each side may be multiplied or divided by a single positive number.You must flip the inequality sign if you multiply as well as divide every side by the a negative number.The inequality = x ≤ 7.
Due to the fact that this inequality shows that the x value is less than or equal to 7, This graph showsGiven that the graph indicates that x may be greater than 7 or equal to 7, Option D represents the inequality.Consequently, the fourth graph illustrates the inequality x ≤ 7.To know more about the inequality, here
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Please find k value
The value of k is -1 in the given matrix.
What is matrix?In mathematics, a matrix is a rectangular array or table of digits, characters, or expressions that is used to represent a mathematical object or a characteristic of one.
Matrixes represent linear maps and allow for explicit linear algebraic calculations in the absence of additional information.
Due to the fact that matrices can be used to express the majority of abstract linear algebra's properties and operations, a significant portion of linear algebra is devoted to their study. Matrix multiplication, for instance, can be used to represent how linear maps are put together.
the det(Y)=|Y| value is 0. Expanding through third column we get
[tex]0 - 7 \times \left[\begin{array}{ccc}2&-1\\k&2\\\end{array}\right] + 3 \times \left[\begin{array}{ccc}2&-1\\-1&4\\\end{array}\right][/tex]
0 - 7(4 -(-k)) + 3(8 -(1)) = 0
- 7(4 +k) + 3(8 -1) = 0
-28 - 7k + 24 -3 = 0
-7k -7 = 0
-7k = 7
k = -7/7
k = -1
Thus, The value of k is -1 in given matrix.
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One number is 6 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 780. Find the numbers
Answer: 156, 56, 336
Answer:
85,510 and 185.
Step-by-step explanation:
let the first number be "a"
let the second number be "b"
let the third number be "c"
we know that
b=6a
c=100+a and
a+b+c=780
If we substitute the first 2 equations on the third one we get:
a+6a+100+a=780
8a+100=780
8a=780-100
8a=680
8 8
a=85
b=6a
b=6×85
b=510
c=100+a
c=100+85
c=185
The sum of 11 and three-fourths of a number is less than 112
Answer:
81
Step-by-step explanation:
PLEASE HELP ME ASAP!!
Therefore, as a result, the answer to the given triangle issue is
ΔA"B"C "≅ ΔABC is congruent.
Describe the triangle.A triangle qualifies as a polygon because it has sides or vertices. It is a basic geometric form. Triangle ABC refers to a triangle well with sides A, B, and C. Whenever the edges are not collinear, a single plane and triangle are produced in Euclidean geometry. Any triangle with three sides & three corners is referred to as a polygon.
Here,
Triangle ABC is reflected across the y-axis to form triangle A'B'C.
After that, triangle A was created by dilation by a factor of 3 "B"C".
Again for triangles ABC and A"B"C, determine the correct response."
So,
We are conscious that reflection goes through a thorough alteration,
thus the original object's size and shape remain unchanged.
After consideration, figures always correspond to their pictures.
A'B'C, ABC, etc (i)
Dilation is a flexible technique. The shape remains the same even though the size has changed.
As a result, figures after dilation invariably resemble their photos.
ΔA'B'C' ≅ ΔA "B"C" ... (ii)
I and (ii) together give us
ΔA"B"C "≅ ΔABC
ABC and ABC are triangles that are similar.
Therefore, option A is the best decision.
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Bath towels sell for $13.25 each, while hand towels sell for $4.50 each. Theresa buys some of each type of towel for a total of $62.25. If she spends $17.25 more on bath towels than she spends on hand towels, how many of each type does she buy?
Theresa bought 5 bath towels and 2 hand towels for a total amount of $62.25.
Theresa buys 5 bath towels and 2 hand towels.
Bath towels: $13.25 x 5 = $66.25
Hand towels: $4.50 x 2 = $9.00
Total: $66.25 + $9.00 = $75.25
Since Theresa spent a total of $62.25, she saved $13.25. The difference between the amount she spent on bath towels and the amount she spent on hand towels should be equal to the amount she saved.
Bath towels: $66.25 - $17.25 = $49.00
Hand towels: $9.00 + $17.25 = $26.25
Total: $49.00 + $26.25 = $75.25
Therefore, Theresa bought 5 bath towels ($66.25) and 2 hand towels ($9.00).
Theresa bought 5 bath towels and 2 hand towels for a total of $62.25.
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Question 7, I am quite unsure
Answer: 137000 cm³
Step-by-step explanation:
formula to find the volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³
formula to find the volume of a cylinder= πr²×h
both the shapes will have the same radius therefore to get the radius you should divide the diameter by two *you probably already know abt it*
so 46/2= 23 (the radius of both the shapes)
In order to get the height of the cylinder you should subtract the radius of the hemisphere from the total height given as the radius is the same all around the hemisphere **but remember not to mistake the diameter as the radius when subtracting a hemisphere's height from a total height**
height of the cylinder= 90cm- 23cm= 67
Therefore now substitute the values into the formulas and find the volumes of the two shapes separately...
volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³
= [tex]\frac{2}{3}[/tex]× π × 23³
= 25482.5 cm³
volume of a cylinder= πr²×h
= π × 23² × 67 (including the height calculated above)
= 111347.5 cm³
Now add the volumes you found which will give you the volume of water that the tank holds when it if full.
volume of a cylinder + volume of a Hemisphere
111347.5 + 25482.5
136830
137000 cm³ (make sure to estimate the final answer to 3s.f or else you'll lose your accuracy mark)
Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
Answer:
44.57
Step-by-step explanation:
area of two semicircles = πr²
3.142×2×2= 12.568
area of rectangle=L×W2
4×8=32
32+12.568
44.568
=44.57
refer to exhibit 1-3. according to the data provided in this table, what is the approximate slope of the line between points c and d (if these data were graphed with x on the horizontal axis and y on the vertical axis)? a. -6.00 b. -1.00 c. -0.17 d. 6.00 e. 0.17
If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.
E. 0.17
The approximate slope between points C and D can be calculated by taking the difference in the y-values (9-15) and dividing it by the difference in the x-values (4-2). This yields a slope of -0.17.
The approximate slope between points C and D can be determined by first calculating the change in y-values (9-15) and the change in x-values (4-2). Then, the change in y-values is divided by the change in x-values to calculate the slope. In this case, the slope is -0.17. This means that for every unit of increase in x-values, the corresponding y-values decrease by 0.17. If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.
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If r = 2 units and h = 8 units, then what is the surface area of the cylinder
The surface area of the cylinder is 125.66
What is the area of a cylinder?The surface area of a cylinder is the area occupied by its surface in a three-dimensional space. A cylinder is a three-dimensional structure having circular bases which are parallel to each other. It does not have any vertices. Generally, the area of the three-dimensional shapes refers to the surface area.
The surface area of a cylinder is calculated with the formula:
= 2π × r × h + 2πr2= 2πr (h + r) Square units
A=2πrh+2πr2
With the following parameters from the question:
r = 2
h = 8
Substituting the parameters into the formula
A = 2πrh+2πr2=
A = 2·π·2·8+2·π·22
A = 125.66371
Hence, the surface area of the cylinder is 125.66371
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Identify the value of x that makes each pair of ratios equivalent.
5. x to 50 and 16 to25
32
34
41
The value of x that makes the given pair of ratios equivalent is: A. 32.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;
x/16 = 50/25
Cross-multiplying, we have the following:
25x = 16 × 50
25x = 800
x = 800/25
x = 32.
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21/24=7/8=49/x find x
Answer:
x is approximately 3.449.
Step-by-step explanation:
We are given the following proportion: 21/24 = 7/8 = 49/x
To find x, we can cross-multiply and simplify:
21/24 = 7/8 = 49/x
247= 218 = 49*x
168 = 168 = 49x
x = 168/49 = 3.44948979591836734693877551020408
x = 3.449489795918367
So, x is approximately 3.449.
the united states mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. if a jar contains exactly 100 cents worth of these coins, which of the following could be the total number of coins in the jar?
The total number of coins in the jar is 10.
The total number of coins in the jar can be determined using the following formula:
Number of Coins = (1-cent coins) + (5-cent coins) + (10-cent coins) + (25-cent coins) + (50-cent coins)
Since the jar contains a total of 100 cents, we can calculate the number of coins in the jar by solving the following equation:
1x + 5x + 10x + 25x + 50x = 100
The solution to this equation is x = 2. This means that the jar contains 2 coins of each denomination, for a total of 10 coins in the jar. Therefore, the total number of coins in the jar is 10.
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