Proportionality denotes a linear relationship between two quantities or variables.
A. Table is mentioned below.
B. Yes, it is a proportional relation.
C. y = 1/24 x
What is meant by proportional?A linear relationship between two quantities or variables is referred to as proportionality. If one quantity doubles in size, the other does as well; if one variable decreases to one-tenth of its previous value, the other does as well.If the ratio or relationship between y and x is the same or constant, the quantities are proportional: y/x = k, where k is the proportionality constant.When two quantities are proportional, it means that as one increases, so does the other, and the ratio of the quantities remains constant across all values.Consider a circle's circumference and diameter; the ratio of the two values equals pi.Therefore,
Part C : We know that,
1 day = 24 hours,
⇒ 1 hour = 1/24 day
As a result, the number of days in x hours (say y) = hours number of days in each hour
⇒ y = 1/24 x
Which is an equation of line.
Part A :
Hours 1 2 3 4 5
Days 1/24 1/12 1/8 1/6 5/24
Part B :
∵ a line passes through the origin always shows a proportional relation,
Since, for (0, 0),
0 = 1/24 (0) ( True )
i.e. there is a proportional relation between number of days and number of hours.
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What is the value of 5/x + 1.25x when x=10
a manufacturer wants to increase the absorption capacity of a sponge. based on past data, the average sponge could absorb 3.5 ounces. after the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. what is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
Reject a null hypothesis because computed t is higher than 2.821 is the decision rule.
Define the term hypothesis?The hypothesis is a succinct statement of the researcher's estimate of the findings of the study, that may or may not be confirmed by the results, in such a scientific experiment or survey. The scientific method's fundamental step is hypothesis testing.A statistical hypothesis known as a null hypothesis asserts because no statistical significance can be found in a collection of provided observations.For the given question;
Test hypothesis:
H₀; μ = 3.5
Upper tailed test:
Hₐ; μ > 3.5
Significance value; α = 10.
Then, degree of freedom.
Df = α - 1
Df = 10 - 1
Df = 9
The critical value;
t(₀.₀₁, ₉) = 2.821
Rejection region;
Rejected H₀ for t > 2.821
Thus, reject a null hypothesis because computed t is higher than 2.821 is the decision rule for the absorption amount of the sponge.
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What fraction is equivalent to the decimal and percent below? Enter your
answer in simplest form, using the slash (/) as the fraction bar.
Fraction Decimal Percent
?
0.33
33.3%
Answer:
Step-by-step explanation:
1 / 3
Reason being: 100 / 3 = 33.333333333
h(x)=x²+3x-2; 12-h(7)
How would I input 12-h(7) in place of x to solve this function?
Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
Compare the governments of Germany and Russia. Make three lists pointing out similarities and differences. In the first list, point out the unique traits of the German government. In the second list, point out the unique traits of the Russian government. In the third list, point out the traits both governments have in common.
DON'T write an entire essay i just need a paragraph
Answer: During the Russian war, The Russians and Germans were at war with each other, Beating them brutally.
Step-by-step explanation:
Solve the equation: 4 - 2y + 3 = - 9. What is y equal to?
Answer:
b
Step-by-step explanation:
In the given equation 4 - 2y + 3 = - 9, y is equal to 8.
The equation is a statement in which the values of two mathematical expressions are equal (indicated by the sign =).
To find the value of y from the given equation
∴ 4 - 2y + 3 = - 9
=> 4+3 -2y = -9
=> 7 - 2y = -9
=> 7 + 9 = 2y
=> 16 = 2y
=> 16/2 = y
=> 8 = y
=> y = 8
So, the value of y in the above equation 4 - 2y + 3 = -9 is 8.
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Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?
Answer:
Corinna will have to run at 7 meters per second to get there at the same time as Deanna.
Step-by-step explanation:
So to find the distance of Deanna's route, you can use the Pythagorean theorem.
a^2 + b^2 = c^2
60^2 + 80^2 = 10000
c^2 = 10000
Take the square root of both sides.
c = 100
So Deanna runs 100 meters at 5 meters per second.
100/5 = 20
She runs for 20 seconds.
To find Corinne's distance, we add 60 and 80, which is 140.
To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7
Solve for c. You must show ALL of your work.
6c + 14 = -5c + 4 + 9c
Answer:
c = -5
Step-by-step explanation:
6c + 14 = -5c + 4 + 9c
1) We want to first combine the c values on the right side. This would give us 6c + 14 = 4c + 4.
2) Next, we want to move the c value to one side of the equation. This means we would subtract 4c from the right side. This gives us 2c + 14 = 4.
3) We can then subtract 14 from the left side to isolate the c value. This gives us 2c = -10.
3) We can then divide both sides by 2 and get the answer for c.
This gives us c = -5.
What is the area of the shaded portion of the parallelogram? Dimensions are in centimeters.
The area of the shaded portion of the parallelogram is 35.43 centimeter square
The base of the parallelogram = 8 centimeter
The height of the parallelogram = 6 centimeter
The area of the parallelogram = Base × Height
= 8 × 6
= 48 centimeter square
The radius of the circle = 2 centimeter
The area of the circle = π × [tex]r^2[/tex]
= π × [tex]2^2[/tex]
= 12.57 centimeter square
The area of the shaded region = The area of the parallelogram - The area of the circle
Substitute the values in the equation
= 48 - 12.57
= 35.43 centimeter square
Hence, the area of the shaded portion of the parallelogram is 35.43 centimeter square
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pls solve all the question as er the questions given below
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence Postulate that is used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;
∠AOB ≅ ∠BOD
1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;
∠Q = ∠B
∠R = ∠C.
Therefore, the additional information is BC ≅ QR
2a) The symbolic form of the given congruent triangles is expressed as;
ΔABC ≅ ΔADC
2b) The congruence postulate that was used here is SAS Congruency postulate.
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the function when x = 3: b(x) = -2x-4
Answer: b(3)=-10
Step-by-step explanation:
Is this what you meant?
If a $900 plasma screen TV
is reduced by 25%, what is
the discount?
Answer: $225
Step-by-step explanation: 900 * .25 = 225
Answer:
$225
Step-by-step explanation:
25 : 100 = x : 900
x = 25 * 900 / 100
x = 25 * 9
x = 225
Work out the 3rd term.
in the
geometric sequence
generated by 5n
The third term in the sequence generated by 5n is 15.
According to the question,
We have the following information:
The sequence is given by the formula 5n.
In this case, n represents the number of the term.
(Note that the sequence generated by this formula can not be a geometric sequence because the common ratio of these terms is not the same.)
So, we have to find the 3rd term of this sequence. Then, we will find the value of this sequence by putting the value of n as 3.
So, we have the following expression:
5*3
15
Hence, the third term in the sequence generated by 5n is 15.
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x-1
3
If-
A) 2
B) 4
C) 9
D) 10
F.
= k and k = 3, what is the value of x ?
Answer:
D
Step-by-step explanation:
Multiply both sides by 3
x − 1 = 9
Add 1 to both sides
x = 10
Rewrite in simplest terms: 6(8v-7)-10v
Step-by-step explanation:
[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]
Which equation represents the sentence, "The sum of twenty-four and p minus fifteen is q"?
A. 24 + p + 15 = q
B. 24 + p – 15 = q
C. p + q – 15 = 24
D. 15 + p = q – 24
Answer:
B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.
Step-by-step explanation:
What is the slope of the line created by this equation?
Round your answer out to two decimal places
6x + 7y = 5
Answer:
-0.86
Step-by-step explanation:
What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5
_____________________________________________
Slope intercept form solves for y:
y = mx + b when m = slope and b = y-intercept
First, solve for y:
6x + 7y = 5
subtract 6x from both sides:
6x + 7y - 6x = 5 - 6x
7y = 5 - 6x
divide both sides by 7:
7y/7 = (5 - 6x)/7
y = 5/7 - 6/7x
rearrange right side:
y = - 6/7x + 5/7
Back to the equation: y = mx + b when m = slope and b = y-intercept
your slope is -6/7
in decimal form, rounded to two digits: -0.86
help meeeeeeeeeeeeeeeeee please
Answer:
x + x + 2 = x + 3
2x + 2 = x + 3
x = 1
x + 2 = 3
x + 3 = 4
PLEASE EXPLAIN……………………..
The range of the function is y ≥ -2 so , correct option is option c
What is range of a function ?Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.
CalculationThe graph of the range of the given function is attached below .
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A community hall is in the shape of a cuboid.
The hall is 40 m long, 15m wide and
3 m high.
The community hall needs re-decorating
with new paint for the walls and ceiling,
and new tiles on the floor.
A 10 litre tin of paint covers 25 m² and costs £10.
Work out the total cost of paint needed
to re-decorate the community hall.
The total cost of painting is $564.
What is surface area of cuboid ?
A cuboid is a three-dimensional figure enclosed by six rectangular planes, each of which has a different size in terms of length, breadth, and height. Anything in the shape of a rectangle, such as a box, brick, or other object, may be a cuboid if you look about. When viewed from any of the ends, a cuboid (3-dimensional) can be seen to be made up of different-sized rectangles (2-dimensional). A cuboid's area is its surface because it is a solid with three dimensions. Since a cuboid's faces are rectangular, its area may be determined using the formula for the area of a rectangle.
Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units
We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.
The paint will be required for 4 walls and ceiling.
Let us find area of walls and ceiling.
Area of walls and ceiling = 2( 40*15) + 2(3*15) + (40*3)
=> Area of walls and ceiling = 2(600)+2(45)+120
=> Area of walls and ceiling = 1200+90+120
=> Area of walls and ceiling = 1410 [tex]m^2[/tex]
Therefore, the area of walls and ceiling is 1410 square meters.
Here Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter.
Then total cost of paint = 10*[tex]\frac{1410}{25}[/tex] = 10*56.4 = $564.
Hence cost of paint is $564.
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Lat week, Lia old 20 hand-engraved watch band, earning a total profit of $105. 0. She plan to make 50 engraved watch band to ell at the community art fair. If he ell all 50 watch band, how much profit can Lia expect to earn?
$
If Lisa sells 50 watch bands, she gets a profit of $262.50.
A unitary method is defined.
Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.
We must first ascertain the cost of one watch band.
To determine this, we simply divide $105 by 20, which equals $5.25.
We can divide $5.25 by 50 because she sells all 50 watchbands.
50 multiplied by $5.25 equals $262.50.
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a department store chain is expanding into a new market, and is considering 24 different sites on which to locate 6 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected? a) 144 b) 96,909,120 c) 168 d) 134,596 e) 30 f) none of the above.
Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways
We can find the number of ways by multiplying the number of possibilities each store can have.
Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites
Therefore the number of ways is:
C = 24 * 23 * 22 * 21 * 20 * 19
C = 9,69,09,120 possibilities
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Would the reaction rate on graph B of Model 2 ever reach a maximum level? Justify your answer.
By applying the concept of rate of a reaction, The graph B never saturates because the enzyme is always in excess.
What is the enzyme substrate reaction?
The enzyme is called a catalyst as it has an active site where the substrate can bind and convert into the product. Here in the graph the enzyme is amylase, and its substrate is starch. When there is an excess of enzymes in the solution, they can convert it into a product till substrates are available. If the substrate runs out, the reaction will come stop.
As per the concept of rate of a reaction, The graph B never saturates as the enzyme in the reaction is always in excess. These excess enzymes present will convert the starch into simple glucose molecules. Hence, there will be no upper limit, as both are in abundance.
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Graph y+3=5/2(x-5) on graph paper
The graph of the function [tex]y+3=\frac{5}{2}(x - 5)[/tex] is attached below.
What is graph of the function?
In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Consider the given function, [tex]y+3=\frac{5}{2}(x - 5)[/tex]
It is in the form [tex]y-y_1=m(x-x_1)[/tex]
Where, [tex](x_1, y_1)[/tex]is the point and m is the slope.
Graph passes through the point [tex](x_1, y_1)[/tex] and having slope m.
Here, [tex](x_1, y_1) = (5, -3), m = \frac{5}{2}[/tex]
Therefore, graph passes through the point (5, -3) and having slope 5/2.
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If the ratio of men to women in a movie theater is 3:2 and there are 45 men in the theater, how many total people are in the theater?
Answer:
113 people (112.5 if you don't round but you can't have half a person)
Step-by-step explanation:
45 men plus the number of women (x) is how many people there are
so you would do 3/x=2/45 since x is the number of women
do some basic algebra, and you get 67.5 women so round if you want to to 68 (i will round because you can't have half a person)
68+45=113 people
Find the diagonal of a rectangle with sides 7 in and 24 in
You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w², and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = √ (l² + w²).
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
2x + 8y = -3
3x + 6y = -4
We can multiply the top by 3 and the bottom by -2 which will result in:
6x + 24y = -9
-6x - 12y = 8
They are then added to each other to give:
6x - 6x + 24y - 12y = -9+8
12y = -1
y = -1/12
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
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five whole numbers are written in order
4 6 x y 10
median and mean of the five numbers are the same.
Workout the values of x and y
The values of x and y if the mean and median are equal are:
x = 7
y = 8.
What is the Mean and Median of a Data Set?The mean is the total sum of the values in a data set divided by the number of values of the data set.
The median of a data set is the center value when the data distribution is ordered.
Given the ordered data set as, 4, 6, x, y, and 10.
The center value is x. Therefore, the median of the data set is x.
The mean of the data = (4 + 6 + x + y + 10)/5
The mean of the data = (20 + x + y)/5
The mean and the median are equal, therefore:
(20 + x + y)/5 = x
20 + x + y = 5x
20 + y = 5x - x
20 + y = 4x
The value of x cannot be less than 6, if x = 7, we woud have:
20 + y = 4(7)
20 + y = 28
y = 28 - 20
y = 8
The values of x = 7, y = 8.
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Sorrel has 54 beads, and 16 of them are red. Of the remaining beads, half are yellow and half are green. How many yellow beads does she have?
Sorrel has 19 yellow beads.
What is fraction?Fraction is a ratio of two integers.
Fraction is divided into two section by a dividing line and these sections are numerator and denominator.
Fractions are of different types: proper fraction, improper fraction and mixed numbers.
Total number of beads =54
if 16 are red, the remaining beads would be ( 54 - 16) = 38
Half of the remaining are yellow = 1/2 x 38
Then number of yellow beads = 19
And number of green beads = 38 - 19
= 19
In conclusion, the total number of yellow beads is 19
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Rewrite in simplest terms: -5(-6k-6)-(-9k-10)−5(−6k−6)−(−9k−10)
help please n ty
The value of the expression -5(-6k-6)-(-9k-10) in simplest terms is 39k + 40
What is an algebraic expression?An algebraic expression can be described as an expression that is made up of terms, variables, coefficients, factors and constants.
These expressions are also known to be composed of certain mathematical operations, such as;
SubtractionDivisionMultiplicationBracketAdditionParenthesesWe have the expression;
-5(-6k-6)-(-9k-10)
expand the bracket
-5(-6k - 6) + 9k + 10
collect like terms
30k + 30 + 9k + 10
Add the like terms
39k + 40
Hence, the value is 39k + 40
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