Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. ... Describe situations in which opposite quantities combine to make 0.
Proportional quantities are described by equivalent ratios as shown below
[tex]\frac{p_1}{q_1} = \frac{p_2}{q_2}[/tex]
Let the two proportional quantities be p and q
If p and q are proportional, then [tex]p \alpha q[/tex]
Introducing a proportionality constant (k)
[tex]p = kq\\\\k = \frac{p}{q}[/tex]
Since the two quantities are proportional, the ratio of initial values will be equal to the ratio of their final values.
That is [tex]\frac{p_1}{q_1} = \frac{p_2}{q_2}[/tex]
Therefore, proportional quantities are described by equivalent ratios as shown below
[tex]\frac{p_1}{q_1} = \frac{p_2}{q_2}[/tex]
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Which expression is equivalent to 3/5 divided by 7/9
Answer:
Step-by-step explanation:
its 27/35, so 27/1 * 1/35
The equivalent expression is obtained by changing the division sign to multiplication and taking the reciprocal of the denominator. Hence, we have 3/5 × 9/7 = 27/35
Denominator = 7/9Numerator = 3/5Reciprocal of denominator = 1 ÷ 7/9 = 9/7
Therefore, change the division operator to multiplication and use the reciprocal of the denominator.
3/5 ÷ 7/9 = 3/5 × 9/7
Hence, we have 3/5 × 9/7 = 27/35.
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Match the graph of the function with the function rule
What is the value of the expression 6.5 - (-7.25)?
Answer:
13.75
Step-by-step explanation:
Slash and dash. turn the both minuses into positives and add like normal. 6.5 plus 7.25 equals 13.75.
I’m just not getting it! I need step by step.
Answer:
[tex]7x + 10 + x + 20 + 2x \\ 7x + x + 2x + 10 + 20 \\ 10 x + 30 \\ x = \frac{30 }{10} \\ x = 3 \\ (7x + 10) = 7 \times 3 + 10 = 31 \\ (x + 20) = 3 + 20 = 23 \\ (2 \times 3) = 6[/tex]
Step-by-step explanation:
Please mark as brainliest
You are a glass cutter, and a customer needs glass tops cut for two tables. One tabletop is a rectangle that is 36
inches long by 48 inches wide. The other tabletop is circular and has a diameter of 72 inches. You have a sheet of
glass that covers an area of 32 square feet. Do you have enough glass to make both tabletops?
Why or why not?
Answer:
Step-by-step explanation:
No, because you need 40.26 square feet of glass to make both tabletops.
when she home all alone all she do is twerk
Answer:
LOL WHAT
Step-by-step explanation:
Answer:
Yes, this is true
Step-by-step explanation:
Cardi B be twerking when she get home bc she knows that she got her weave snatched and her nails, and eyebrows got snatched. Her hubby broke up with her bc Cardi b wanted to be islam but he didn't. So she b twerking while she eating ice-cream. She sometimes does the WAP
A carnival charges $6 for admission and $2.50 per ride. You have $50 to spend at the carnival. What is the greatest number of rides you can go on at the carnival?
Answer:
17
Step-by-step explanation:
the answer above me is wrong and silly how are you supposed to get a 17.6 rides makes no sense
The greatest number of rides you can go on at the carnival will be 17.6.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A carnival charges $6 for admission and $2.50 per ride. You have $50 to spend at the carnival.
Let x be the number of rides.
Then the equation is given as,
2.50x + 6 = 50
Simplify the equation, then we have
2.5x + 6 = 50
2.5x = 44
x = 17.6
Thus, the greatest number of rides you can go on at the carnival will be 17.6.
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the difference of a number squared a
6
Answer:
36
Step-by-step explanation:
The given statement can be modelled to a equation as -
f(x) = x² - 6.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is the statement - the difference of a number squared and six.
The given statement can be modelled as a equation as follows. Assume the number to be [x]. Then, we can write -
f(x) = x² - 6
Therefore, the given statement can be modelled to a equation as -
f(x) = x² - 6.
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A car is driving at 65 kilometers per hour. How far, in meters, does it travel in 5 seconds?
Answer:
90 m
Step-by-step explanation:
65 km = 65000m
1 hour = 3600 secs
speed in meters = 65000/3600
= 18 m / sec
Distance traveled in 5 secs = 18*5
= 90 m
yooooo whats 6x3 i don't know but i'm in 7th grade
You learn multiplication in 3rd grade but ok buddy, kinda sad you are doing algebra not knowing that 6x3=18
Answer:
18 lollllllllllllllllllllllllllll
Help please!:) Soon as possible
Answer:
-7
_____
because
2x+30=-2x+2
is
4x+30=2
which is
4x=-28
then
x=-7
What is the correct definition of the word famine?
A. Severe scarcity of food within a region
B. Narrow body of water that has land on two sides
C.long heavy fishing line with multiple hooks attacked that goes across run region
D. A territory, or section of land found within the borders of a government run region
Please select the best answer from the choices provided
O A
O B
O C
O D
Answer:
A
Step-by-step explanation:
10x+y+2xy2 - 4x2 - 4x?y
[(-4,-2).(-4x+y)+10x?y]+ 20
O 10:2y + 2xy +[(-4x2)+(-4x+y)]
(-4x²) + 2xy² + (10x²y+ (-4x²y)]
[10y2xy*+(-4x+y)]+(-)
o
Answer:10x+y+2xy^2-4x^2-4x?y[(-4,-2).(-4x+y)+10
Step-by-step explanation:
Simplify. (3x−2y)+(5x−4y)
8x−6y
8x−2y
−2x+2y
15x+8y
Answer:
8x-6y
Step-by-step explanation:
(3x-2y)+(5x-4y)
put like terms together
(3x+5x)+(-2y-4y)
add together
8x -6y
put together
8x-6y
Find the value of x .
Answer:
[tex]x=18[/tex]
Step-by-step explanation:
[tex](4x-11)\\(2x+25)[/tex]
According to the Alternate Exterior Angles Theorem, "when two lines are cut by a transversal, the resulting alternate exterior angles are congruent."
This means that the two expressions above are to be set equal to each other because they are representative of two alternate exterior angles, which are congruent:
[tex]4x-11=2x+25[/tex]
Add [tex]11[/tex] to both sides of the equation:
[tex]4x=2x+36[/tex]
Subtract [tex]2x[/tex] from both sides of the equation:
[tex]2x=36[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]2[/tex]:
[tex]x=18[/tex]
~
Check your work by substituting [tex]18[/tex] for [tex]x[/tex] in the initial equation:
[tex]4(18)-11=2(18)+25[/tex]
[tex]61=61[/tex]
It's correct!
Answer:
18
Step-by-step explanation:
From the given figure, we can see that angle (4x - 11) will be equal to angle 1 since they are corresponding angles
We notice that angle 1 is vertically opposite to angle (2x + 25)
Hence,
angle (4x - 11) = angle 1 = angle (2x + 25)
So, we can say that angle (4x - 11) = angle (2x + 25)
Now, solving for x:
4x - 11 = 2x + 25
2x = 36
x = 18
A carpenter had a piece of wood that was 7.28 feet long. He cut 2.9 feet off the
end of that piece. How many feet of wood were left?
Answer Choices :
A : 4.18 feet
B : 5.38 feet
C : 5.78 feet
D : 4.38
Answer:
D
Step-by-step explanation:
7.28 - 2.9 = 4.38
What is the value of x? 69° and (6x+3)
What is the solution to -1-7? + 4 5 6 9 10 2 -10-9-8-7 6-5- 4 -3-2 1 -8 O 6 6 O8
Lynn has an investment account which compounds interest annually at a rate of 2.9%. After 7 years, she has $9800 in the account. How much money did she initially place in the account? Round your answer to the nearest whole number. Do not include a $ in your answer.
Answer:8023
Step-by-step explanation:
local bowling alley charges each person $5.25 per game bowled and $3.50 to rent a pair of bowling shoes. The bowling alley also offers food
specials. Currently, bowlers can purchase a super pizza deal, which includes a large pizza and a pitcher of soda, for only $15.50.
Five friends decide to go bowling. Each friend bowls two games and rents a pair of bowling shoes. They also buy one super pizza deal to
share.
• What is the total cost (in dollars) for the five friends to rent shoes, bowl two games, and purchase a super pizza deal? Explain or show
your work.
• If the five friends split the total cost so each one pays the same amount of money, how much does each friend pay (in dollars)?
Answer:
1. $85.50
2. $17.10
Step-by-step explanation:
1. 5.25 x 10=52.5:cost for all games total.
3.50 x 5=17.5: cost for all shoes total.
15.50: cost for super pizza deal.
Add it all together.
52.5 + 17.5 +15.50= 85.5
2. 85.5 Divided by 5 = 17.1
Find each sum or difference -1/2+1/3 please help quickly
Answer:sum: -1/6
Step-by-step explanation:
In a population of 9500 subjects, 72% possess a certain characteristic. In a sample of subjects selected from this population, possess the same characteristic. How many subjects in the population and the sample, respectively, possess this characteristic
This question is Incomplete
Complete Question
In a population of 9500 subjects, 72% possess a certain characteristic. In a sample of 400 subjects selected from this population, 73% possess the same characteristic. How many subjects in the population and the sample, respectively, possess this characteristic?
Answer:
Population = 6840 subjects
Samples = 292 subjects
Step-by-step explanation:
In a population of 9500 subjects, 72% possess a certain characteristic.
The number of subjects in the population with this characteristics =
9500 × 72%
= 6840 subjects
In a sample of 400 subjects selected from this population, 73% possess the same characteristic.
The number of subjects in this sample with this characteristics is :
400 subjects × 73%
= 292 subjects
6840 subjects in the population posses this characteristic, while 288 subjects in the sample posses this characteristic
The given parameters are:
[tex]\mathbf{n = 9500}[/tex] --- population
[tex]\mathbf{x = 400}[/tex] -- sample size
[tex]\mathbf{p =72\%}[/tex] ---- the proportion
The number of subjects that posses the characteristics is simply the average of the sample or the population.
For the population, the average is calculated as:
[tex]\mathbf{\mu =np}[/tex]
So, we have:
[tex]\mathbf{\mu =9500 \times 72\%}[/tex]
[tex]\mathbf{\mu =6840}[/tex]
This means that:
6840 subjects in the population posses this characteristics
For the sample, the average is calculated as:
[tex]\mathbf{\bar x=px}[/tex]
So, we have:
[tex]\mathbf{\bar x=72\%\times 400}[/tex]
[tex]\mathbf{\bar x=288}[/tex]
This means that:
288 subjects in the sample posses this characteristics
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Xfinity claims that the performance package for the internet will get you a download speed of 100Mbps. In reality, each person who pays for that package has a slightly different internet speed. For a large data set of performance internet customers, the mean internet speed is 100Mbps, with extended deviation of 8Mbps. As soon as that the internet speeds in the data set can be modeled by a normal distribution.
What percent of Performance Package internet customers would be expected to have internet speeds between 84Mbps and 116Mbps? Be sure to also explain your process of getting the answer. Also, please show your work.
Answer: 95%
Step-by-step explanation:
mean = 100, standard deviation (sd) = 8
mean ± 1 sd = z-score of 1 which is 68%
100 ± 8 = 92 to 108
mean ± 2 sd = z-score of 2 which is 95%
100 ± 2(8) = 84 to 116
mean ± 3 sd = z-score of 3 which is 99.7%
100 ± 3(8) = 76 to 124
The internet speeds are between 84 and 118 which is 2 standard deviations from the mean, which is 95% of their internet customers.
Look back at the plans these students used to solve the word problem below.
Who found a correct solution?
EK BAKI
The entire school, 250 students, went to the soap box derby.
The Math Club went in 2 vans, and each van held 6 students.
How many students from the Math Club went to the soap box
derby?
Paul added vans to students. Eva multiplied students by vans
Since 2+ 6 + 8, eight Math Club Since 6x2 = 12, twelve Math Club
students went to the soap box students went to the soap box
derby
derby
A. Eva
B. Paul
Answer:
A. Eva
Step-by-step explanation:
Given that
The entire school, 250 students, went to the soap box derby.2 vans went to soap box derby and each van held 6 students.
To find the total number of students from the Math Club who went to the soap box derby, we need to add the number of students in each van, the number of times equal to the number of vans.
i.e. by adding 6 (i.e. number of students in each van) 2 (number of vans )number of times, we can get the number of students from Math Club who went to the soap box derby.
Number of Math Club students who went to the soap box derby = 6 + 6 = 12
OR
Simply, multiply number of students in each van with the number of vans .
6 [tex]\times[/tex] 2 = 12
Therefore, Eva is correct about the calculations.
What is the graph of 4x + 3y = -24?
Answer:
Step-by-step explanation:
Which graphs cannot represent a proportional relationship?
Answer:
B and C
Step-by-step explanation:
A linear graph, that is a graph showing a straight line connecting the points plotted, shows a proportional relationship between two variables quantities if it cuts across the point of origin at (0, 0).
Graph A represents a proportional relationship between x and y variables, because the line that connects the points on the graph is a straight line, and also intercepts at (0, 0).
Graph B is a straight line graph, however, it does not intercepts the point of origin (0, 0). Graph B cannot represent proportional relationship.
Graph C is not a linear graph. If you try connecting the points together by drawing a line, the line would not be a straight line. Also, the line of the graph does not intercept at (0, 0). Therefore, it is safe to conclude that graph C does not represent a proportional relationship.
Graph D is a straight line graph. The rate of change between any two points on the lines of both graphs would be constant and the same all through, as the line of the graph intercepts at the point of origin, (0, 0). This connotes a proportional relationship.
Find the product:
-
4
/
9
And
-
3
/
8
The answer to the problem is [tex]\frac{1}{6}[/tex]
First, you must set up the equation.
[tex]-\frac{4}{9}*-\frac{3}{8}[/tex]
Then, you must cross multiply.
[tex]\frac{-12}{-72}[/tex]
Finally, simplify the fraction.
[tex]\frac{1}{6}[/tex]
PLZ HELP URGENT WORTH 10 POINTS AND IF ITS 100% RIGHT WILL GIVE BRAINLIST!!!
Answer:
the scale dilation is 2 times
Step-by-step explanation:
the scale is 2 because the size of the original is 2X2 and the dotted square is 4X4.
On which number line do the points represent negative five and one over two and +2?
A. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 5th and 6th tick marks to the left of 0. A point labeled T is placed between the 3rd and 4th tick marks to the left of 0.
B. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 3rd and 4th tick marks to the right of 0. A point labeled T is placed between the 5th and 6th tick marks to the right of 0.
C. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 2nd tick mark to the left of 0. A point labeled T is placed between the 5th and 6th tick marks to the right of 0.
D. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed between the 5th and 6th tick marks to the left of 0. A point labeled T is placed on the 2nd tick mark to the right of 0.
The number line which the points representing negative five and one over two (-5 1/2) and +2 would be on is: D. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed between the 5th and 6th tick marks to the left of 0. A point labeled T is placed on the 2nd tick mark to the right of 0.
What is a number line?In Mathematics, a number line can be defined as a type of graph that has a graduated straight line and comprises both positive and negative numbers that are placed at equal intervals along its length.
Generally speaking, a number line primarily decreases in numerical value towards the left and increases in numerical value towards the left.
Note: Each interval on this number line represents 1 unit.
Next, we would add the given numbers together in order to determine the distance between these points:
Distance = -5 1/2 + 2
Distance = -11/2 + 2
Distance = -7/2 or -3.5 units.
In conclusion, a distance of -7/2 or -3.5 units is shown in the number line shown in the image attached below.
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This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 70 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically, 3% of the components are identified as defective, and the components can be assumed to be independent.
Required:
a. If the manufacturer stocks 70 components, what is the probability that the 70 orders can be filled without reordering components?
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
Answer:
Step-by-step explanation:
a) This is a binomial distribution.
p = probability it is defective = 3% = 0.03, q = 1 - p = 1 - 0.03 = 0.97
This is a binomial distribution is given by the formula:
[tex]P(x)=C(n,x)*p^xq^{n-x}[/tex]
But n = 70
[tex]P(x=0)=C(70,0)*0.03^0*(0.97)^{70}=0.1186[/tex]
b) n = 102. Hence there can be 2 defective components, hence:
[tex]P(X\leq2)=P(X=0)+P(X=1)+P(X=2)=C(102,0)*0.03^0*(0.97)^{102}+C(102,1)*0.03^1*(0.97)^{102-1}+C(102,2)*0.03^2*(0.97)^{102-2}=0.0447+0.1441+0.2204=0.4062[/tex]
c) n = 105, there can be 5 defective products:
[tex]P(X\leq2)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=C(102,0)*0.03^0*(0.97)^{102}+C(102,1)*0.03^1*(0.97)^{102-1}+C(102,2)*0.03^2*(0.97)^{102-2}+C(102,3)*0.03^3 *(0.97)^{102-3}+C(102,4)*0.03^4*(0.97)^{102-4}+C(102,5)*0.03^5*(0.97)^{102-5}=0.0447+0.1411+0.2204+0.2273+0.174+0.1054=0.913[/tex]