The constant of proportionality is $0.50.
A mathematical constant is a significant integer whose value is determined by an explicit definition. It is frequently denoted by a symbol or by the names of mathematicians to make it easier to use in a variety of mathematical situations.
The amount paid by Rocko is $12.50 for 25 game tickets.
The amount paid by Rocko is $17.50 for 35 game tickets.
A proportional relation can be written as:
y = k × x
where k is a constant, y is the cost, and x represents the number of tickets purchased in this instance.
Substituting the values, for Rocko
$12.50 = k × 25
Therefore
k = $12.50 / 25
k = $0.50
For Louisa,
$17.50 = K × 35
K = $17.50 / 35
K = $0.50
Now, k = K
So we have the same value of the constant in both cases, which means that the constant of proportionality is k = $0.50.
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Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags. if all the bags were identical, what was the weight of each?
The weight of each bag is 23.25 pounds.
For given question,
Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.
If all the bags were identical, we need to find the weight of each bag.
Let 'm' be the weight of each bag.
As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.
8 × m = 187.6
now we solve above expression to find the value of m i.e., to find the weight of each bag.
⇒ 8 × m = 187.6
⇒ m = 187.6 / 8
⇒ m = 23.25 pounds
Therefore, the weight of each bag is 23.25 pounds.
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50 points plus brainliest please help
Answer:
x = 14Angle 1 = 6°Angle 2 = 84°Step-by-step explanation:
from the sign it's a right angle, so 90°
Find x90 = x - 8 + 6x
90 + 8 = 7x
98 = 7x
x = 98 : 7
x = 14
------------------
check
90 = 14 - 8 + 6 * 14 (remember pemdas)
90 = 14 - 8 + 84
90 = 90
the answer is good
Find angle 1
x - 8
14 - 8 =
6°
Find angle 2
6x
6 * 14 = 84°
--------------------
check
84 + 6 = 90°
the answer is good
Answer:
[tex]\textsf{a)} \quad \textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]
[tex]\begin{aligned}\textsf{b)} \quad m \angle 1 & =\boxed{6^{\circ}}\\ m \angle 2 & =\boxed{84^{\circ}}\end{aligned}[/tex]
Step-by-step explanation:
Part (a)From inspection of the given diagram, the sum of the two angles is 90° (indicated by the right angle sign):
[tex]\implies m \angle 1+m \angle 2=90^{\circ}[/tex]
[tex]\implies (x - 8)^{\circ} + (6x)^{\circ} = 90^{\circ}[/tex]
[tex]\implies x-8+6x=90[/tex]
[tex]\textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]
Part (b)To find the measure of each angle, solve the equation for x:
[tex]\implies x-8+6x=90[/tex]
[tex]\implies x+6x-8=90[/tex]
[tex]\implies 7x-8=90[/tex]
[tex]\implies 7x-8+8=90+8[/tex]
[tex]\implies 7x=98[/tex]
[tex]\implies \dfrac{7x}{7}=\dfrac{98}{7}[/tex]
[tex]\implies x=14[/tex]
Substitute the found value of x into the expression for each angle:
[tex]\implies m \angle 1=(x-8)^{\circ}[/tex]
[tex]\implies m \angle 1=(14-8)^{\circ}[/tex]
[tex]\implies m \angle 1=\boxed{6^{\circ}}[/tex]
[tex]\implies m \angle 2=(6x)^{\circ}[/tex]
[tex]\implies m \angle 2=(6 \cdot 14)^{\circ}[/tex]
[tex]\implies m \angle 2=\boxed{84^{\circ}}[/tex]
ms. justen had 250 students. every year after she had 100 students. calculate the amount of students she's had in 7 years
The students she's had in 7 years is 850.
How to calculate the value?It should be noted that we want to find the 7th term. This will be:
a + (n - 1)d
a = First term = 250
d = Difference = 100
n = Number = 7
Therefore, a + (n - 1)d
= 250 + (7 - 1)100
= 250 + 600
= 850
Therefore, the students she's had in 7 years is 850.
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Find the sum of the first 13 terms of the sequence 2, 5, 8, 11,....
The sum of the first 13 terms is 260
How to calculate the sum of the first 13 terms ?The first term(a) is 2
The common difference(d) is 3
n= 13
The formular is
n/2(2a + (n-1)d)
= 13/2 [ 2(2) + (13-1)3]
= 6.5 [4 + 12(3)]
= 6.5 [4 + 36]
= 6.5(40)
= 260
Hence the sum of the first 13 terms is 260
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Yo can anyone help me, you’ll get BRAINLY if you answer correctly
We get the translation rule as (x-4, y+5) for triangle ABC.
We are given a triangle:
ABC where
A = (3, -1)
B = (7, -5)
C = (-2, -2)
And, we are also given the translation of the triangle as A'B'C'
where
A' = (-1, 4)
B' = (3, 0)
C' = (-6, 3)
We need to tell the translation rule for it,
For the x coordinate, we can see that:
- 1 - 3 = - 4
3 - 7 = - 4
- 6 - (-2) = -4
So, the rule for x coordinate will be:
x - 4
Now for y coordinate:
4 - (-1) = 5
0 - (-5) = 5
3 - (-2) = 5
So, the rule for y coordinate will be:
y + 5
Translation rule then becomes:
(x-4, y+5)
Therefore, we get the translation rule as (x-4, y+5) for triangle ABC.
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The snallest flowering plant is the flowering aquatic duckweed found in australia. it is 0.0236 inch long and 0.0129 inch wide. write these dimensions as fractions in simplest form.
The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.
To convert Decimal into Fraction form:
Do the following Steps:
Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.
Step 2: Remove the decimal places by multiplication.
Step 3: Reduce the fraction.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.
Given,
The smallest flowering plant is the flowering aquatic duckweed found in Australia.
And it is 0.0236 inch long and 0.0129 inch wide.
Here we need to write these dimensions as fractions in simplest form.
Rewrite the decimal number as a fraction with 1 in the denominator
So,
=> 0.0236/1 and 0.0129/1
Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.
Then we get,
=> 236/10000 and 129/10000
Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,
=> 59/2500
But the fraction 129/10000 is not reducible.
Therefore, the fraction form is,
=> 59/2500 in. long and 129/10,000 in. wide.
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Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero.
Considering the images (a),(b),(c),(d),(e),(f) the oriented path is
(a) Negative
(b) Positive
(c) Positive
(d) Zero
(e) Zero
(f) Zero
calculating each quadrant's line integral and symmetry.
In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.
What does a Line integral mean?
A line integral makes it possible to figure out a surface's area in three dimensions. Numerous situations call for the use of line integrals. They can be used, for instance, in electromagnetics to determine the work done on a charged particle moving along a curve in a force field that is represented by a vector field.Path, curvilinear, and curve integrals are other terms for line integrals. There are several uses for line integrals, including electromagnetics, where it is used to calculate the force exerted on a charged particle moving along a curve in a force field created by a vector field.To learn more about Line integral, visit:
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PLEASEEE HELPPPPP ILL GIVE BRAINLIEST
60-100 bpm and that is the range of a 16 year old heart beat
Answer:
Step-by-step explanation:
Lower limit of range:
H = [tex]\frac{7}{10}[/tex](220-a)
a = 16 [given]
∴ H = [tex]\frac{7}{10}[/tex](220-16)
H = [tex]\frac{7}{10}[/tex](204)
H = [tex]\frac{7}{10}[/tex]×[tex]\frac{204}{1}[/tex]
H = [tex]\frac{1428}{10}[/tex]
H = 142.8
H = 143 beats per minute [as an integer]
Calculate the product below and give your
answer in scientific notation.
(5.2 × 10-2) × (8.0 × 10-4) = ?
Answer:
3800
Step-by-step explanation:
(52-2)×(8×10-4)
50(80-4)
50×76=3800
Solution in Scientific Notation:
[tex]3.8[/tex] × [tex]10^{3}[/tex]
Hope this helps!
Does one frequency distribution provide a better summary of the data than the other? explain.
Changing the class width from 4,000 to 3,000 increases the details of the frequency distribution, thereby providing a better summary of the data.
How can changing the class width affect the frequency distribution obtained?Based on a similar question, the possible part of the question appear left out includes.
To construct a second frequency distribution with a class width of 4,000, where the class width of the first frequency distribution is 3,000Construct a frequency histogram using the values in the frequency distribution constructed above.The correct response is; Yes, the value or magnitude categories of the data are increased using the smaller class width of 3,000 such that more details about the influence of the different classes on the results are seen, which provides a better summary of the information in the data than the frequency distribution that a 4,000 class width.
The overall shape of the frequency histogram remains almost the same for both class widths
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You start a savings account with $200 and save $30 each month. Let f(n) be the amount in the account before the nth month. How much money will you have invested at one year?
The money you will have invested at one year is $560
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How much money will you have invested at one year?The given parameters are:
Initial = $200
Rate = $30
Let the number of months be n
So, we have
f(n) = Initial + Rate * n
This gives
f(n) = 200 + 30n
There are 12 months in a year
So, we have:
f(12) = 200 + 30 * 12
Evaluate
f(12) = 560
Hence, the money you will have invested at one year is $560
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for each part, compare distributions (1) and (2) based on their means and standard deviations. you do not need to calculate these statistics; simply state how the means and the standard deviations compare
(a) The mean of (2) will be greater than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)
(b) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the minimum of (2) is smaller but negative than the minimum of (1) which is also negative.
(c) The mean of (2) will be more than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)
(d) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have smaller variation as compared to the distribution of (1) because the range of (1) is greater than the range of (2)
Define mean and distribution?The mean is a measure of the central trend of a probability distribution along the median and the mode.
a distribution is the set of all possible values for terms representing defined events.
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Which is an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity?
0.2d14
negative 2 over quantity 9 times d raised to the fourth power end quantity
72 over d raised to the fourteenth power
2 over quantity 9 times d raised to the fourteenth power end quantity
The equivalent expression using laws of exponents gives us; 2 over quantity 9 times d raised to the negative fourteenth power end quantity
How to use laws of exponents?
We want to write an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity. This can be expressed as;
4d⁻⁵/18d⁹
Now, according to laws of exponents, we know that;
x²/x³ = x²⁻³ = x⁻¹
Applying that law to our question gives us;
4d⁻⁵/18d⁹ = (4/18)(d⁻⁵⁻⁹)
= (4/18)(d⁻¹⁴)
Now, the expression 4/18 can be broken down to 2/9. Thus, our final expression is; ²/₉d⁻¹⁴
Writing that in words gives;
2 over quantity 9 times d raised to the negative fourteenth power end quantity
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Answer: 2/9d^14 or 2 over 9 times d to the 14th power
Step-by-step explanation: AFOKE88 gave the same answer. this answer is correct you just have to understand how to write this equation in word form to understand them. they also gave a great explanation for those who need it.
PLEASE HElP 25 points math
Answer: 4q^2
Step-by-step explanation:
(-2q)^2=
(-2*q)^2=
(-2)^2 * q^2=
4 * q^2=4q^2
How is ahow is a linear relationship between two variables measured in statistics? explain. select all the true statements.
The following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.What is a linear relationship?A linear relation, or simply relation, among elements of a vector space or a module, is a linear equation with these elements as a solution in linear algebra. A linear relationship (or linear association) is a numerical term that describes a two-variable relationship that follows a straight line. Linear relationships can be represented graphically or mathematically as the equation y = mx + b.So,
The following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.Therefore, the following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.Know more about the linear relationships here:
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A square pyramid has a volume of 4320 cubic inches. What is the volume of this pyramid in cubic feet?
The volume of the given square pyramid in cubic feet is 2.5 cubic feet.
Given that, a square pyramid has a volume of 4320 cubic inches.
We need to find the volume of this pyramid in cubic feet.
What is the volume of a square pyramid?The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).
To convert from cubic inches to cubic feet, divide your cubic inches figure by 1728.
Now, 4320/1728 = 2.5 cubic feet
Therefore, the volume of the given square pyramid in cubic feet is 2.5 cubic feet.
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Solve for the value of q
Answer:
q = 20
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
180 - 78 = 102
so
5q+2 = 102
subtract 2 from both sides
5q = 100
100 / 5 = 20
5q / 5 = q
q = 20
Hope this makes sense.
-8|x/3+1|>-8
Please help me
Answer:
-6<x<0
Step-by-step explanation:
-8|x/3+1|>-8
-8|x/3+1|/(-8)>-8/(-8)
|x/3+1|<1
x/3+1<1
x/3<0
x<0
x/3+1>-1
x/3>-2
x>-6
-6<x<0
Explain why subtracting a positive number is the same as adding its inverse.
Explanation:
To add a negative number, we are basically subtracting it because of this:
Example:
10 - 5 = 5
10 + (-5) = 5
The negative sign cancels out the positive which makes it into a subtraction problem instead.
107 + 78 will mark briniest pls help
Answer:
185
Step-by-step explanation:
Answer:
185
Factor:
5×37
Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
10
6
2
13
Answer:
10
Step-by-step explanation:
|-2(2) + (-3)(2)|
2(2) + 3(2)
4 + 6
| | indicate absolute value, negative numbers are turned to positive numbers in absolute value, making B and C (negative values) into positive values.
Please help with problem 10
Answer: 13 ==> B
Step-by-step explanation:
x=-3, y=4, z=-1
|2x-3y|+5z=
|2(-3)-3(4)|+5(-1)=
|-6-12|-5=
|-18|-5=
18-5=13 ==> B
Rosa paid $107.40 for 12 audio books that were all the same price. Which is the best estimate of the cost of each audio book?
Answer:
$8.95
Step-by-step explanation:
Divide 107.4 by 12 and you end up with the price of each audio book.
The same can be said for each problem you want find the individual amount of
Answer:
Each audio book costs $8.95
Step-by-step explanation:
Since 12 audio books that are at all the same prize equal $107.4, therefore in order to find the total of each book we divide $107.4 by 12
➟ 107.4 ÷ 12
➟ 8.95
∴ $8.95 is the cost of each book
pls help! if the present value of an item is P and we experience an inflation rate of r for t years, blah blah blah I dont feel like writing the rest.
Answer: 89633.78
Step-by-step explanation: Hope this helps :)
-12=6+2/3y pls helpppp
Answer:
Y= (-27)
Step-by-step explanation:
Well, I am assuming your just looking for Y. So what I did was you'd want to get rid of the fraction first. I multiplied 3 to all the numbers. so -12(3) = 6(3) + 2y since the bottom 3 from the fraction cancelled out with the (3). so now it would be -36=18+2y. -54/2=2y/2 which leads to -27. So I think Y= -27.
pls help What is the sum? will mark brainiest
47+ 85⎯⎯⎯⎯⎯⎯⎯
Answer:
132
Step-by-step explanation:
Find the lengths of ABC and BD explain pls
Answer: The length of AB =4 units
The length of BD = 2.4 units.
Step-by-step explanation:
Given data,
AD = 3.2 unit
BC = 3 unit
CD = 1.8 units
Find : AB =? units
BD=? units
We can use the formula of Pythagorean theorem,
Define Pythagorean theorem :
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.
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
Let be a ΔABC,
[tex](AB)^{2} = (BC)^{2} +(AC)^{2}[/tex]
From the above formula now determined the value of AB and BD,
Firstly , find the value of BD
In ΔBDC, by applying Pythagorean theorem,
[tex](BC)^{2} = (BD)^{2} + (DC)^{2}[/tex] (Eq - 1)
Substitute BC and CD values in equation 1,
BC = 3 units and CD = 1.8 units
So,
We can write,
[tex]3^{2} = (BD)^{2} +(1.8)^{2}[/tex]
9 = [tex](BD)^{2}[/tex] + 3.24
[tex](BD)^{2}[/tex] = 9 - 3.24
[tex](BD)^{2}[/tex] = 5.76
[tex]BD = \sqrt{5.76}[/tex]
BD = 2.4 units (Eq - 2)
Now find the value of AB,
In ΔABD, by applying Pythagorean theorem,
[tex](AB)^{2} = (AD)^{2} +(BD)^{2}[/tex] (Eq - 3)
Substitute AD and BD values in equation 3,
AD = 3.2 units and BD = 3 units
So,
We can write,
[tex](AB)^{2} = (3.2)^{2} + 3^{2}[/tex]
[tex](AB)^{2}[/tex] = 10.24 + 5.76
[tex](AB)^{2}[/tex] = 16
AB = [tex]\sqrt{16}[/tex]
AB = 4 units
Therefore,
The length of AB =4 units
The length of BD = 2.4 units.
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very important please help due today please
Answer:
According to my the answer is 32
Step-by-step explanation:
cuz 4 ÷ 1/8 becomes 4×8/1
which is 32
if a figure is a rectangle, then it has four sides
Answer:
True
(If it has 4 sides it is also known as a Quadrilateral!)
Step-by-step explanation:
Answer:
yes
the reson for htis is b/c retangles are qudrilateral and quadtrialterals have four sides
05-x=13 solve for x
i need help ASAP
Answer: X= -8
Step-by-step explanation:
Rearrange your terms:
5-X=13
-x+5+13
Subtract 5 from both sides
Simplify those = -X = 8
Dive both sides by same factor, -1
Simplify again
Solution= X= -8