Answer:
\(⚪ \: \: 16.5u + 9.8\)
Step-by-step explanation:
\(7.9u + 8.5 + 8.6u + 1.3 \\ = (7.9 + 8.6)u + 8.5 + 1.3 \\ = 16.5u + 9.8\)
Three friends were playing a game of marbles.
At the end of the game, Marcy had 25% of the
marbles, Roger had
2
1
of the marbles, and Ann
had the rest of the marbles. If there were 100
marbles altogether, how many marbles did Ann
have at the end of the game?
The number of marbles Ann had at the end is 54.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total marbles = 100
The number of marbles:
Marcy:
= 25% of 100
= 1/4 x 100
= 25
Roger:
= 21
Now,
The number of marbles:
Ann = 100 - (25 + 21) = 100 - 46 = 54
Thus,
Ann has 54 marbles at the end.
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Choose the correct exponential form for the expression. 0.3 × 0.3 × 0.3 × 0.3 (0.3)3 (0.3)4 40.3 43
Answer:
It is B. (0.3)4
Step-by-step explanation:
(0.3)4
0.3 × 0.3 × 0.3 × 0.3
Answer:
(0.3)4 or B
can i has brainlyiest
Step-by-step explanation:
A characteristic or measure obtained by using all the data values for a specific population is called a _____.
A characteristic or measure obtained by using all the data values for a specific population is called a parameter.
What is a parameter in data?A parameter in statistics is a number that identifies a population trait. The average height of all adult males in the population, for instance, may be a criterion if we were interested in researching the heights of all adult men in the United States. The standard deviation, variance, median, mode, and range of a population are other examples of parameters.
In most cases, parameters must be calculated using statistical techniques from a sample of the population. Statistics are the values derived from the sample and are used to predict the values of the related parameters.
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5/8 - 5/24
I am doing some homework my brain isnt working right now can someone help me out?
Answer:
5/12
Step-by-step explanation:
i just looked it up...
====================================================
Explanation:
Multiply top and bottom of 5/8 by 3 to get 15/24
This means 5/8-5/24 is the same as 15/24-5/24
The denominators are the same, so we can subtract the numerators to have them placed over the common denominator
15/24 - 5/24 = (15-5)/24 = 10/24
Then we reduce by dividing each part of the fraction by the GCF 2
10/2 = 5
24/2 = 12
Meaning that 10/24 = 5/12
Note how multiplying top and bottom of 5/12 by 2 leads to 10/24 again.
So overall,
5/8 - 5/24 = 5/12
Mr. Jones has 160 animals on his farm. Of these animals, 20% are cows, 30% are goats, 10% are horses, and the rest are chickens how many chickens are on Mr. Jones's farm
Answer:
64 chickens (40%)
Step-by-step explanation:
16 horses(10%), 32 cows(20%), 48 goats(30%),
Answer:
b
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
ALSO 50 POINTS!
Answer:
h = 12 m
\( v_{cylinder}= 235.5 \: {m}^{3} \)
Step-by-step explanation:
Radius of cylinder (r) = 5/2 = 2.5 m
\( {h}^{2} = {13}^{2} - {5}^{2} \\ h = \sqrt{ {13}^{2} - {5}^{2} } \\ h = \sqrt{169 - 25} \\ h = \sqrt{144} \\ h = 12 \\ \\ v_{cylinder} = \pi {r}^{2} h \\ v_{cylinder}= 3.14(2.5) ^{2} (12) \\ v_{cylinder}= 235.5 \: {m}^{3} \)
The volumes of two similar figures are given. The surface area of the smaller figure is given. find the surface area of the larger figure
V=2875 m^3
V = 1472 m^3
S.A. = 928 m^2
The surface area of the larger figure is [blank] m^2
Step-by-step explanation:
the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).
and the volume of 3 dimensions (side lengths).
"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).
so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.
in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.
let's call the scaling factor f.
1472 × f³ = 2875
and then
928 × f² = large S.A.
let's use the first to get f :
1472 × f³ = 2875
f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64
f = 5/4
f² = (5/4)² = 5²/4² = 25/16
large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²
Can some plz help me!
Answer:
a=9+6
p=-30+20
z=15+(-12)
x=-10+(-7)
Step-by-step explanation:
A six-sided die is rolled 25 times and the results are recorded as follows: 4 ones, 5 twos, 5 threes, 3 fours, 4 fives, 4 sixes. What is the experimental probability of rolling a number greater than four? Express your answer in fraction, decimal, and % forms.
Answer:
8/25, 0.16, 16%
Step-by-step explanation:
P(#>4) = P(5)+P(6) = 4/25+4/25 = 8/25
Charles and Wilma have different internet providers. Charles pays $0.25 per gigabyte of data. Wilma pays a flat fee of $20 and $0.05 per gigabyte. How many gigabytes of data must each use for Charles' internet bill to equal Wilma's internet bill?
Answer:
We want to find the point where these two lines intersect:
Equation for Charles: y=0.25x
Equation for Wilma: y=0.05x+20
0.25x=0.05x+20
0.2x=20
x=100
So, Charles must use 100 gigabytes of data to equal Wilma's internet bill.
Let me know if this helps!
The number of gigabytes of data that must be used for Charles' internet bill to equal Wilma's internet bill is; 100 gigabytes
What is the Intercept of the equations?Let the amount of gigabyte of data be x.
Since Charles pays $0.25 per gigabyte of data, then the equation for Charles is; y = 0.25x
Wilma pays a flat fee of $20 and $0.05 per gigabyte and as such the equation for Wilma is; y = 0.05x + 20
For Charles' internet bill to equal Wilma's internet bill, Thus;
0.25x = 0.05x + 20
0.2x = 20
x = 20/0.2
x = 100
Thus, Charles must use 100 gigabytes of data to equal Wilma's internet bill.
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please answer B and C for me, i already know A.
Use the information below to answer 1–3.
Three students are playing a video game. Each player is randomly
assigned a character from a collection of characters that includes
5 blue, 6 green, and 3 red characters. After each character is picked,
it is not replaced in the collection.
A. What is the probability that the first player does not get a blue character?
B. The first player gets a blue character. What is the probability that the
second player also gets a blue character?
C. Both the first and second players get blue characters. What is the
probability that the third player does not get a blue character?
Answer: B: 4/13, C: 3/4
B:
There were originally a total of 14 characters (including 5 blue characters) from the collection. Since the first player got a blue character, there are now 13 characters to choose from and 4 of them are blue. Therefore, the probability is 4/13.
C: If both the first and second players get blue characters, then there will be 12 characters left, and 3 of them are blue. Now we know that there are 9 characters that are NOT blue. Therefore, the probability is 9/12, or 3/4.
Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
Maria is making a rectangular quilt. She starts with a square of fabric with side length x cm.
She adds some fabric to one side of the square and a different amount of fabric to an adiacent side of the square. Her final quilt has an area of x2 + 13x + 30 cm?. How much longer is the long dimension of the quilt than the short dimension?
Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.
What is area?Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.
Here,
The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:
(x + y)(x + z) = x^2 + xy + xz + yz
We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:
x² + xy + xz + yz = x² + 13x + 30
Simplifying this equation, we get:
xy + xz + yz = 13x + 30
We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:
xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)
Substituting this expression for yz in the equation above, we get:
(y - z)(x + y + z) = 13x + 30
We want to solve for y - z, so let's focus on the left side of the equation:
(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)
= xy + y² + yz - xz - z² - yz
= y² - z² + xy - xz
Substituting the expression we found earlier for xy - xz, we get:
(y - z)(x + y + z) = y² - z² + (y - z)(x + z)
(y - z)[x + y + z - (x + z)] = y² - z²
y - z = (y² - z²)/(y - z) = y + z
= (13x + 30)/(x + 6)
So the difference between the length and the width of the rectangle is:
y - z = (13x + 30)/(x + 6)
Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:
[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]
= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)
= (26x + 60)/(x + 6)
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help! last question
Question 1 (1 point)
Simplify the expression and rationalize the denominator.
16x4y8
5z
Answer:
\( = \frac{ {4x}^{2} {y}^{4} \sqrt{5z} }{5z} \)
Step-by-step explanation:
\( \sqrt{ \frac{16x {}^{4} y {}^{8} }{5z} } \\ = \sqrt{ \frac{16 {x}^{4} y {}^{8} }{ \sqrt{5z \\ } } } \\ = \frac{4 {x}^{2}y {}^{4} }{ \sqrt{5z} } \\ = \frac{ {4x}^{2} y {}^{4} \sqrt{5z} }{5z} \)
the larger the value of our obtained t: group of answer choices the less probable that our results are due to chance alone. the larger our critical t-value. the larger the probability of making a type 1 error. the more probable that our results are due to chance alone.
The correct answer is "the less probable that our results are due to chance alone."
In statistics, t-value measures the difference between the mean of two groups and the variation within the groups. A larger t-value indicates that the means of the two groups are further apart and less likely to have occurred due to chance. Therefore, the larger the value of the obtained t, the less probable that our results are due to chance alone.
what is statistics?
Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves methods for collecting, organizing, summarizing, analyzing, and interpreting data in order to make decisions or draw conclusions about a population or a sample of data. Statistics is widely used in various fields such as business, economics, social sciences, medicine, engineering, and more, to help understand and solve problems through data analysis.
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HELLLPP!!!!
Which series of transformations will move the triangle in quadrant 1 onto the similar triangle in quadrant three?
Answer:
Its D if you think about it
Step-by-step explanation:in your mind move the triangle on the top right down 6 units and then turn your triangle 90 degrees counter clockwise (quick maths)
The only transformation that will move the triangle in quadrant 1 onto the similar triangle in quadrant three is;
Option D; translation 6 units down and rotation 90° counterclockwise
The y-coordinate of the right angle vertex of the triangle in quadrant 1 is y = -2. Meanwhile the y-coordinate of the same right angle point of the triangle in quadrant 3 is y = -4.
Thus, for the triangle in quadrant 1 to be on the same level with that in quadrant 3, we need to translate the triangle in quadrant 1 downwards by 6 units.
Now, since we want to map this newly translated triangle to the one in quadrant 3 and as such we need to rotate it 90° counterclockwise
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The following steps are used to rewrite the polynomial expression, 3(x + 4y) + 5(2x - y).
Step 1: (3x + 12y) + (10x - 5y)
Step 2: (3x + 12y) + (-5y + 10x)
Step 3: 3x + (12y - 5y) + 10x
Step 4: 3x + 10x + (12y - 5y)
Step 5: 13x + 7y
Identify the property used in each of the steps:
Step 1:
Select a Value
i hope this helps! let me know if i got it wrong
the number of people p that are contracting a new disease can be modeled by the population virus p of t equals 3725 divided by quantity 1 plus 1 and 72 hundredths times e to the negative 52 hundredths times t power end quantity comma where t is measured in days. at approximately what rate is the disease spreading on day 4?
Using the given exponential function,
The rate of the disease spreading is approx. 140 peoples per day affected.
let P be the number of people's that are contacting a new disease.
given exponential function about the new disease modeled by population is
P(t) = 3725/(1 +1.72 e⁻⁰·⁵²ᵗ) ---(1)
where t is time measured in days
we want to calculate the rate of diseases spreading on day 4 i.e t = 4
putting the value t = 4 in above formula, we get
P(t=4) = 3725/(1 + 1.72 e⁻⁽⁰·⁵²⁾⁴)
=> P( t= 4) = 3725 / (1 + 1.72× e⁻⁰·²⁸)
=> P(t=4) = 3725/(1 + 1.72× 0.124)
=> P(t = 4) = 3725/(1+ 0.2148)
=> P(t=4) = 3725/1.2148
=> P(t = 4) = 3066.14
Hence, after 4 days of diseases spread , total 3066 people's are affected from it .
rate of diseases spreading per day is equal to (3725-3066)/4 = 659/4 = 139.75
so, rate of spreding diseases is 139.75 ~ 140 peoples per day .
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Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) √5r2/r + 3 dr
After evaluating the integral using integration for √(5r²/(r+3)) dr is √5 (2√(r+3) + 3ln|r+3| + C).
To evaluate the integral:
∫ √(5r²/(r+3)) dr
we can start by using the substitution:
u = r + 3
Then, we have:
du/dr = 1, so dr = du
and
r = u - 3
Substituting these expressions into the integral, we get:
∫ √(5(u-3)²/u) du
= ∫ √(5(u² - 6u + 9)/u) du
= ∫ √(5u²/u - 30u/u + 45/u) du
= ∫ √(5u - 30 + 45/u) du
= ∫ √5(u/u - 6/u + 9/u²) du
= √5 ∫ (√u/u - 6√u/u + 9√(1/u²)) du
= √5 ∫ (1/√u - 6/√u + 9|1/u|) du
= √5 (2√u - 6ln|u| + 9ln|u| + C)
= √5 (2√(r+3) - 6ln|r+3| + 9ln|r+3| + C)
= √5 (2√(r+3) + 3ln|r+3| + C)
So, the final answer is:
∫ √(5r²/(r+3)) dr = √5 (2√(r+3) + 3ln|r+3| + C)
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The population of a town increased from 3300 in 2006 to 4200 in 2009. Find the absolute and relative (percent) increase. Absolute increase:
The absolute increase is 900 people, and the relative (percent) increase is 27.27%.
We will first find the absolute increase and then the relative (percent) increase.
Absolute increase:
Subtract the initial population from the final population: 4200 (2009 population) - 3300 (2006 population)
Calculate the absolute increase: 4200 - 3300 = 900
Absolute increase:
900 people
Relative (percent) increase:
Calculate the absolute increase (which we found earlier): 900 people.
Divide the absolute increase by the initial population: 900 / 3300
Multiply the result by 100 to find the percentage: (900 / 3300) * 100
Calculate the relative (percent) increase: (900 / 3300) * 100 = 27.27%
Relative (percent) increase: 27.27%.
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Classify the given beam based on: (i) type of support (ii) equilibrium conditions and find the reactions at the supports for the beams. 20 kN/m 10 kN 1 A 4m C 4m' D ** -2m- B
Based on the information provided, the given beam can be classified as follows:
(i) Type of support:
The beam has two supports, A and D. The support at A is not specified, so we cannot determine the exact type of support. However, support D appears to be a roller support.
(ii) Equilibrium conditions:
To determine the reactions at the supports, we need to consider the equilibrium conditions. For a beam in equilibrium, the sum of the vertical forces and the sum of the moments about any point must be zero.
Reactions at the supports:
Since the type of support at A is not specified, we cannot determine the reaction at that support. However, at support D (roller support), there will be a vertical reaction (Rd) to counterbalance the vertical load of 10 kN.
Please note that without additional information, such as the type of support at A or the distribution of the 20 kN/m load, we cannot determine the exact reactions at support A or the internal forces within the beam.
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why do we use the standard uncertainty in the mean to quantify the uncertainty in the mean of a data set, but we use the standard deviation to quantify the uncertainty in individual measurements?
We use standard uncertainty because it helps to make less error when finding out mean value of a given sets.
Uncertainty is the non-exact value derived by counting the number of points and subtracting their standard deviation. The result obtained should be an approximation rather than a precise value. The score of spread values from the provided set of data is known as standard deviation.
There could be several points in the uncertainty. Errors could occur if the days are rounded uncertainly. We use single data to view uncertainty in the situation of single data. Additionally, rounding uncertainty is appropriate if the level is the same as the measured uncertainty. We measure and compute the mean after taking the set of values into account multiple times. Finding the mean's uncertainty is important.
Therefore we use the relation,
σmean = σindividual/√(n-1)
Value is less than the value of reading-specific uncertainty. As a result of the additional number measurements caused by the rounding process, the uncertainty exceeds the standard deviation by a significant amount.
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y-2=-3(x-4) in slope intercept form
Answer:
y = -3x + 14
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write point-slope form
y - 2 = -3(x - 4)
Step 2: Solve into slope-intercept form
Distribute -3: y - 2 = -3x + 12Add 2 to both sides: y = -3x + 14HELP ASAP 60 points ACELLUS WILL MARK BRAINLEST Find the expected value of the
random variable with the
following probability distribution:
Х
0
1
2
3
4
5
6
7
8
Р
.03
.15
.27
.20
.13
.10
.07
.03
.02
[?]
HELP
Answer:
0 = .3
1 = .15
2=.27
3=.2
4=.13
5=.10
6=.07
7= .03
8= .02
Step-by-step explanation:
Answer: 3.1
Step-by-step explanation:
For this line of XML, what is the attribute name?
5
a. parts
b. dist
c. even
d. 5
There is no attribute name for this line of XML.
The given line of XML `5` is not a valid XML element, as it does not have a tag name and does not follow the basic syntax rules for an XML element. An attribute in XML is a name-value pair that is associated with an XML element, and is specified within the opening tag of the element using the syntax `name="value"`.
For example, the following is a valid XML element with an attribute named "dist" and a value of "10":
```
<distance dist="10"/>
```
In this case, the attribute name is "dist".
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Which expression is a difference of squares with a factor of 5x − 8?
The expression that is a difference of squares with a factor of 5x - 8 is \(25x^2 - 64.\)
To identify the expression that is a difference of squares with a factor of 5x - 8, we need to understand what a difference of squares is and how it relates to the given factor.
A difference of squares is an algebraic expression of the form \(a^2 - b^2,\)where a and b are terms. It can be factored as (a - b)(a + b). In other words, it is the product of two conjugate binomials.
In this case, the given factor is 5x - 8. To determine the other factor, we can set it equal to (a - b) and look for the corresponding (a + b) factor.
Setting 5x - 8 equal to (a - b), we have:
5x - 8 = (a - b)
To find the corresponding (a + b) factor, we consider the signs. Since the given factor is 5x - 8, we can conclude that the signs in the factored expression will be (a - b)(a + b), where the signs alternate. This means the corresponding (a + b) factor will have a positive sign.
So, the (a + b) factor will be (5x + 8).
Now, we have both factors: (a - b) = (5x - 8) and (a + b) = (5x + 8).
To find the expression that is a difference of squares with a factor of 5x - 8, we multiply these two factors:
(5x - 8)(5x + 8)
Expanding this expression using the distributive property, we get:
\(25x^2 - 40x + 40x - 64\)
The middle terms, -40x and +40x, cancel each other out, resulting in:
\(25x^2 - 64\)
Therefore, the expression that is a difference of squares with a factor of \(5x - 8 is 25x^2 - 64.\)
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Find the surface area AND
volume of this figure.
We get the surface area as 202 inches² and volume as 168 inches³.
The surface area of a cuboid is given by:
Surface area = 2xy + 2xz + 2yz
Here length = x = 7 inches
Breadth = y = 3 inches
Height = z = 8 inches.
Substituting the values in the formula, we get that:
Surface area = A = 2(7)(3) + 2(7)(8) + 2(3)(8) inches²
A = 42 + 112 + 48 inches²
A = 42 + 160 inches²
A = 202 inches²
Volume of a cuboid is given by :
Volume = xyz
Substituting the values, we get that:
Volume = (7) (3) (8) inches³
Volume = 21 × 8 inches³
Volume = 168 inches³.
Therefore, we get the surface area as 202 inches² and volume as 168 inches³.
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Which table shows a proportional relationship between x and y?
x
1
2
3
6
O
у
1.5
:
3
6
9
.
x
2.
4
5
6
о
y
6
12
18
21
х
1
3
4
5
o
O
y
50
150
200
250
х
3
5
7
8
a
у
1.5
2.5
3
4.5
1
2
3
4
5
6
7
8
9
10
Next
The ratio of y:x should be constant for any value of x and y.
\( \frac{y}{x} = constant\)
If go over every table, you'll find that this is true for the third one and that the ratio is r=50
The table showing the proportional relationship between x and y is the third one.
What is proportional relationship?Two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.
Given are four tables, giving values of x and y, we need to identify the table giving the relation between x and y which is proportional.
Table 1)
x = 1, 2, 3, 6
y = 1.5, 3, 6, 9
y/x = 1.5, 1.5, 2, 1.5 [not proportional]
Table 2)
x = 2, 4, 5, 6
y = 6, 12, 18, 21
y/x = 3, 3, 3.6, 3.5 [not proportional]
Table 3)
x = 1, 3, 4, 5
y = 50, 150, 200, 250
y/x = 50, 50, 50, 50 [proportional]
Hence, the table showing the proportional relationship between x and y is the third one.
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Determine whether the given equation is separable, linear, or both. dxdt 9xt=ex group of answer choices
The given differential equation is not linear because it involves the product of x and t. However, it is separable, and we can integrate both sides to find the solution.
The given equation is 9xt(dx/dt) = e^x. To determine whether this equation is separable, linear, or both, we need to rearrange it into a standard form.
Dividing both sides by 9xt, we get:
(dx/dt) = e^x / 9xt
This equation is not linear because it involves the product of x and t in the denominator. However, it is separable because we can separate the variables x and t by writing the equation as:
9xt(dx/dt) = e^x
9x dx = e^x dt/t
Integrating both sides, we get:
4.5x^2 = ln|t| + C
where C is the constant of integration.
Therefore, the given equation is separable but not linear.
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The table below shows the number of each item sold at the concession stand. What might the ratio of 5:4 represent?
popcorn sold 20
nachos sold 15
hotdog sold 25
candy bar sold 30
The price of of the hotdog to the price of popcorn is in the ratio 5:4
25:20 is 5:4