Answer:
Step-by-step explanation:kk
The constant of proportionality that relates the number of milliliters of coffee made y to the number of teaspoons of sugar used x is 12.
Why is that, therefore, if K is the proportionality constant?When two variables are directly or indirectly proportional to one another, their relationship can be represented as y = kx or y = k/x, where k denotes the direction of the relationship between the two variables. It is known as the proportionality constant, or k.
We must determine the ratio of the two amounts in order to determine the constant of proportionality that connects the number of teaspoons of sugar used x to the number of millilitres of coffee brewed y.
Considering the information provided, we understand that:
168 millilitres of coffee require 14 tablespoons of sugar.
As a result, the following is the relationship between the quantity of coffee prepared and the quantity of sugar used in teaspoons:
y/x = 168/14
Reducing the ratio:
y/x = 12
This indicates that 1 teaspoon of sugar is needed to make every 12 millilitres of coffee.
As a result, 12 is the constant of proportionality that links the quantity of coffee created (y) to the quantity of sugar utilised (x).
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Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
8 + (10 - 7)
Convert 9kilograms=____milligrams
Answer:
9000000 Milligrams
Step-by-step explanation:
We know that,
1 kilogram = 10^6 Miligram
So, 9 Kilpgrams = 9×10^6 = 9000000 Milligrams
I need help with some math questions
17. Number of hours, h 10 + 2h Total Cost
1 10 + 2 x 1 12
2 10 + 2 x 2 14
3 10 + 2 x 3 16
4 10 + 2 x 4 18
This is true because as shown in the first example, you have to sub in the number of hours into the "h" value, and multiply it times two. After that, you add ten.
Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6 A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9. A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
The shaded area to the right of 4 indicates all values larger than 4 being inequality included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.
What is inequality?A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.
The graph below shows the set of solutions to the inequality where x + 2 is larger than or equal to 6:
From negative 9 to positive 9 is a number line. At positive 4, a closed circle appears. Positive numbers four through nine are shaded on the number line.
This means that the inequality will be satisfied by any value of x larger than or equal to 4. The graph includes the value 4 in the solution set since it has a closed circle there, and because it is shaded to the right of 4, it also includes all values higher than 4.
Here is an illustration of the graph:
|----|----|----|----|----|----|----|----|----|
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
o
---->
4
----]
>
|----|----|----|----|----|----|----|----|----|
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
The shaded area to the right of 4 indicates all values larger than 4 being included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.
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the distance between (8, 0) and (8, -8)
Answer:
Step-by-step explanation:
The two given points are (8, 0) and (8, -8).
Using the distance formula, the distance between the two points can be calculated as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where x1 = 8, y1 = 0, x2 = 8, and y2 = -8
d = sqrt((8 - 8)^2 + (-8 - 0)^2)
d = sqrt(0 + 64)
d = sqrt(64)
d = 8
Therefore, the distance between the two points is 8 units.
Jill bought 8 pounds of potatoes at a local wholesaler for $18. Her friend Jack bought 6 pounds of potatoes at the supermarket for $15. Jack thinks he got the better deal because $15 is less than $18. Is Jack correct? Why or why not.
Answerer Latoya got a better deal because she paid less than Herman by 25 cents
Step-by-step explanation:
Latoya 18 divided by 8= $2.25
Herman 15 divided by 6= $2.50
So Latoya saves $0.25 cents
In a right triangle, sin ( x − 3 ) ∘ (x−3) ∘= cos ( 6 x + 9 ) ∘ (6x+9) ∘ . Find the smaller of the triangle’s two acute angles.
The smaller acute angle of the right triangle is x-3 = 12.6 degrees.
What is Right Triangle?
A triangle in which one angle is 90 degree is called a Right Angled Triangle.
In a right triangle, if one acute angle is x-3 degrees, then the other acute angle is 90-(x-3) = 93-x degrees.
Using the given equation, we have:
sin(x-3) = cos(6x+9)
Taking the sine of both sides:
sin(x-3) = sin(90 - (6x+9)) = sin(81-6x)
Now we have:
sin(x-3) = sin(81-6x)
Since the two angles have the same sine, they must differ by a multiple of 360 degrees. Thus:
x-3 = 81-6x + 360n or x-3 = 6x-81 + 360n
where n is an integer.
Simplifying each equation:
7x = 84 + 360n or 5x = 78 + 360n
Dividing both sides by 7 or 5, respectively:
x = 12 + 51.43n or x = 15.6 + 72n
The first equation gives us values of x that are too large for an acute angle, so we use the second equation:
x = 15.6 + 72n
The smallest such x that satisfies 0 < x < 90 is when n=0, which gives:
x = 15.6 degrees
Therefore, the smaller acute angle of the right triangle is x-3 = 12.6 degrees.
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2. Now, discuss your possible financial goals for the future, that could be related to this career choice.
(Hint: For example: Would you like to purchase a laptop or a car? Do you plan to purchase a condo/house?)
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
What are Stοcks?Stοcks, alsο knοwn as the shares οr equities, represent οwnership in cοrpοratiοn. When yοu buy stοck, yοu are buying small piece οf οwnership in cοmpany. The value οf stοck is determined by supply and demand fοr shares in market, as well as by the cοmpany's financial perfοrmance, industry trends, and οther factοrs.
I can suggest sοme pοssible financial gοals that sοmeοne in a career related tο finance might have:
Saving fοr retirement: A financial prοfessiοnal might set a gοal οf saving a certain amοunt οf mοney each year fοr their retirement.
Investing in stοcks οr οther assets: A finance prοfessiοnal might set a gοal οf investing in stοcks οr οther assets in οrder tο grοw their wealth οver time.
Building an emergency fund: A finance prοfessiοnal might set a gοal οf building an emergency fund tο cοver unexpected expenses οr incοme disruptiοns.
Paying οff debt: A finance prοfessiοnal might set a gοal οf paying οff debt, such as student lοans οr credit card debt, in οrder tο imprοve their financial stability.
Saving fοr a dοwn payment οn a hοme: A finance prοfessiοnal might set a gοal οf saving fοr a dοwn payment οn a hοme in οrder tο purchase a prοperty and build equity.
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
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What is the rectangular form of the parametric equations?
x(t)=t+3,y(t)=2t2−4, where t is on the interval [−4,0].
Enter your answer, in standard form, by filling in the boxes.
y = __,__ where x is on the interval [ , ].
The rectangular form of the parametric equation is given as follows:
y = y = 2x² - 12x + 14, where x is in the interval [-1, 3].
How to obtain the rectangular form of the parametric equation?The parametric equation in the context of this problem is defined as follows:
x(t) = t + 3.y(t) = 2t² - 4.The interval for t is given as follows:
[-4,0].
Hence the bounds of the interval for x are given as follows:
Lower bound: t = -4 -> x = -4 + 3 = -1.Upper bound: t = 0 -> x = 0 + 3 = 3.From the first equation, we can write t as a function of x as follows:
t = x - 3.
Replacing into the second equation, the rectangular form of the equation is given as follows:
y = 2(x - 3)² - 4
y = 2(x² - 6x + 9) - 4
y = 2x² - 12x + 14.
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Answer: y = "2x^2 - 12x + 14", where x is on the interval ["-1, 3"].
Step-by-step explanation: I took the test.
5 times the quantity 4 plus a number c
Answer:
[tex]5(4+c)[/tex]
Triangles M and N are similar.the ratio of sides N:M is 4:3 .the lengths of triangle M are 12 inches ,18 inches and 24 inches
The perimeter of triangle N is 72 inches.
What is similar triangle?Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.
Here given the triangles M and N are similar, the ratio of sides N:M is 4:3
We can say that M and N with constant term x is, (by ratio proportion rule)
M = 3x and N = 4x and
Given the lengths of triangle M are 12 inches, 18 inches and 24 inches
for triangle M = 3x, (Using above ratio proportion rule)
3x = 12 inches 3x = 18 inches 3x = 24 inches
x = 4 x = 6 x = 8
Similarly, for similar triangle N = 4x, (Using above ratio proportion rule) put all values of x = 4, 6, 8
for x =4 for x =6 for x =8
4x = 4×4 4x = 4×6 4x = 4×8
16 inches 24 inches 32 inches
Length of triangle N is 16 inches, 24 inches and 32 inches
Perimeter of triangle N = 16+24+32 = 72 inches
Therefore, the Perimeter of triangle N is 72 inches.
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The workers' union at a particular university is quite strong. About 96 of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?
The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
To solve this problem, we can use the binomial probability formula, which is:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]
where:
n is the sample size (number of workers being interviewed)
k is the number of successes we are interested in (in this case, 2 of the workers being union members)
p is the probability of success (in this case, the probability that a worker is a union member)
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))
Plugging in the values, we get:
[tex]P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)[/tex]
[tex]= (6) * (0.96)^2 * (0.04)^2[/tex]
= 0.04403136
Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
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a square whose side measures 2 centimeters is dilated by a scale factor of 3. what is the difference de tween the area of the dilated square and the original square?
After solving the given problem, we found that the difference between the area of the dilated square and the original square is 32 square centimeters.
The area of the original square with a side length of 2 centimeters can be calculated as:
A = s²
A = 2²
A = 4 square centimeters
When this square is dilated by a scale factor of 3, the new side length will be:
s' = 3s
s' = 3(2)
s' = 6 centimeters
The area of the dilated square can be calculated as:
A' = s'²
A' = 6²
A' = 36 square centimeters
The difference between the area of the dilated square and the original square is:
A' - A = 36 - 4
A' - A = 32 square centimeters
Therefore, the difference between the area of the dilated square and the original square is 32 square centimeters.
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the length of PR if PQ is 3x-2 and QR is 5x+6
The length of the line segment PR from the given parameters is: 8x - 8
How to find the length of the Line Segment?The line segment addition postulate is a postulate that states that if we are given two points on a line segment, X and Z, a third point Y lies on the line segment XZ if and only if the distances between the points meet the requirements of the equation XY + YZ = XZ
We are given the parameters:
PQ = 3x - 2
QR = 5x + 6
Thus:
PR = PQ + QR
PR = 3x - 2 + 5x - 6
PR = 8x - 8
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Males
Females
Total
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d).
Nursing majors
Non-nursing
majors
1016
1728
2744
94
700
794
Question 8 of 11 >
Total
1110
2428
3538
(a) u puudumy L Sharon a un mar
P(being male or being nursing major) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the student is female or not a nursing major.
P(being female or not being a nursing major) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the student is not female or a nursing major.
P(not being female or being a nursing major) =
(Round to the nearest thousandth as needed.)
(d) Are the events "being male" and "being a nursing major mutually exclusive? Explain.
OA. No, because one can't be male and a nursing major at the same time.
OB. Yes, because there are 94 males majoring in nursing.
OC. Yes, because one can't be male and a nursing major at the same time.
This quiz: 11 point(s) possible
This question: 1 point(s) possible
C...
Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):
P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)
From the table, we have:
P(male) = 1110/3538 ≈ 0.314
P(nursing major) = 1016/3538 ≈ 0.287
P(male and nursing major) = 94/3538 ≈ 0.027
Therefore:
P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574
Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.
(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:
P(being female or not being a nursing major) = P(female) + P(not nursing major)
From the table, we have:
P(female) = 2428/3538 ≈ 0.686
P(not nursing major) = 1728/3538 ≈ 0.489
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175
This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):
P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)
From the table, we have:
P(female and nursing major) = 700/3538 ≈ 0.198
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977
Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.
(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:
P(not being female or being a nursing major) = 1 - P(being female or being nursing major)
From part (a), we have:
P(being male or being nursing major) ≈ 0.574
Therefore:
P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426
Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.
(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.
Step-by-step explanation:
Can anyone find the first and second derivative for #26?? I’m gonna go crazy pls help
The first derivative of y is: y' = [4tan(πt)sec(πt) - πsec²(πt)]/(π³) and
The second derivative of y is: y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)
What are first and second derivative?The first derivative of a function represents the rate of change or slope of the function. The second derivative represents the rate of change of the first derivative or the curvature of the function.
To find the first derivative of y, we use the quotient rule:
y = [tan(πt)/π²] + [4 sec(πt)/π²]
y' = [π²(sec²(πt)) - 2tan(πt)sec(πt)]/(π⁴) + [4πsec(πt)tan(πt)]/(π⁴)
Simplifying this expression, we get:
y' = [(πsec(πt))(4tan(πt) - πsec(πt))]/(π⁴)
y' = [4πtan(πt)sec(πt) - π²(sec²(πt))]/(π⁴)
To find the second derivative of y, we again use the quotient rule:
y'' = [(π³(sec³(πt)) - 12πtan(πt)sec²(πt)) - 2π(4tan(πt)sec(πt) - πsec²(πt))(πsec(πt))]/(π⁶)
Simplifying this expression, we get:
y'' = [(4πsec(πt))(π²(sec²(πt) - 3tan(πt)))]/(π⁶)
y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)
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find the balance in the account: $3,000 principal, earning 3% compounding annually, after 4 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53[/tex]
7. In the following diagram of AABC it is known that ZA = ZC. If BD bisects ZABC then which two reasons would be needed to show that AB = CB? (1) H.L. and CPCTC (2) A.A.S. and CPCTC (3) S.A.S. and H.L. (4) H.L. and A.S.A. A B D 2 4
Check the picture below.
I just need the table
1) The nth term if the sequences are (a) 9a-7 (b) 13-6a
How to determine the sequence?A sequence is a list of numbers or objects in a special order.1 It is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequences are
1) (a) 2,11,20,...
the first term a= 2, the common difference d = 11-2 =9
The nth term is given as
Tn = a + (n-1)d
Tn = 2 + (n-1)*9
Opening the brackets to get
2 + 9n -9
Rearrange to have
9n -7
(b) the sequence is 7,1,-5,...
a = 7 ,
d= 1-7 = -6
Tn = a + (n-1)d
Tn = 7 + (n - 1)-6
Tn = 7 + -6n +6
Tn = 7+6 -6n
Tn = 13 -6n
2) Remember for every Fibonacci sequence
1st+2nd=3rd
2nd+3rd=4th
3rd+4th=5th
4th+5th=6th
Remember for every arithmetic Progression
Tn = a + (n-1)d
For every Geometric Progression,
Tn = arⁿ⁻¹
First five terms Next three terms Name of sequence(A,G,F,Q)
10,6,2,-2,-6 -10,-14,-18 arithmetic
2,8,32,126512 2048, 8192,32768 Geometric
20,13,33,46,79 125,204,329 Fibonacci
200,100,50,25,12.5 6.25, 3.125, 1.5625 Geometric
46,39,32,25,18, 11,4 , -3 Arithmetic
-2,,2,0,2,2,4 6,10,16 Fibonacci
3,6,10,15, 21 28,35,42 Arithmetic
25,15,0,-20,-45, -80,-125,-175 Arithmetic
2,5,7,12,19 31,50,81 Fibonacci
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Consider the right triangle below:
The length of the missing leg, AC= meters
Round your answer to the nearest tenth.
Note: Figure not drawn to scale and all the measurements are in meters.
What is the perimeter of triangle ABC
PLEASE HELP!! I NEED IT FOR TODAY!! GIVE A GOOD EXPLANATION PLEASE!!
Based on the information given in the histogram, option B. The distribution of the data is asymmetrical, so the mean and the median are likely outside the "1,000-1,099 photocopies" category is the correct statement.
What is histogram?
The histogram shows that the distribution of the data is asymmetrical, with a longer tail towards the right. This means that there are more schools that made a higher number of photocopies than those that made a lower number of photocopies. Therefore, the mean and median are likely to be higher than the midpoint of the "1,000-1,099 photocopies" category, which has the highest frequency.
In a skewed distribution, the mean is typically affected by the outliers, while the median is a better measure of central tendency. Therefore, the median is more likely to be within the "1,000-1,099 photocopies" category, while the mean is likely to be higher.
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The population in a certain town is increasing linearly each year. The population at time t=3 is 1285 and at time t=8 is 2460, where t is the number of years after 1990.
Answer:
Step-by-step explanation:
We can use the two given data points to find the slope of the line that represents the population growth over time.
The population at time t=3 is 1285, which means that the population has increased by P1 = 1285 - P0, where P0 is the initial population at time t=0 (which is not given). Similarly, the population at time t=8 is 2460, which means that the population has increased by P2 = 2460 - P0.
The time elapsed between t=3 and t=8 is 8-3 = 5 years.
The slope of the line that represents the population growth over time is given by:
slope = (P2 - P1) / (t2 - t1)
where t1 and t2 are the corresponding times.
Substituting the given values, we get:
slope = (2460 - 1285) / (8 - 3)
slope = 235
This means that the population is increasing by 235 people per year.
To find the initial population at time t=0, we can use either of the two given data points. Let's use the population at time t=3:
P1 = 1285 - P0
235 * 3 = 705
1285 - 705 = 580
Therefore, the initial population at time t=0 (i.e., in the year 1990) was 580 people.
We can now use the slope to find the population at any given time t after 1990.
Let P(t) be the population at time t after 1990.
Then, P(t) = P0 + slope * (t - 0)
P(t) = 580 + 235t
For example, the population in the year 2000 (i.e., when t=10) would be:
P(10) = 580 + 235(10) = 3330
Therefore, the population in the year 2000 would be 3330 people.
1) What are nonexample of base and exponent in math?
2) What are example and nonexample of coefficient and exponential form?
3)What are example and nonexample of expanded form and standarm form?
4) Lastly, what are example and nonexample of exponent laws?
Answer:
Nonexamples of base and exponent in math would be any mathematical expressions that do not involve raising a base to an exponent. For example, 2 + 3 or √4 do not involve base and exponent.
An example of coefficient and exponential form is 5x², where 5 is the coefficient and x² is the exponential form. A nonexample could be x²/5, which does not have a coefficient in front of the exponential form.
An example of expanded form is 5x + 2, where the expression is fully written out. The standard form of the same expression would be 2 + 5x. A nonexample of expanded form is 2(x + 3), where the expression is not fully written out.
Examples of exponent laws include the product rule (a^m * a^n = a^(m+n)), quotient rule (a^m / a^n = a^(m-n)), and power rule ((a^m)^n = a^(mn)). A nonexample of an exponent law could be the sum of powers rule, which does not exist in traditional exponent laws.
The solutions for all the parts are given below.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by 'a' times to itself.
So, a is the exponent of m.
1) Non-examples of a base and exponent in math would be: "2 + 3" or "5 - 7" as these are expressions and not a base raised to an exponent.
2) An example of a coefficient and exponential form would be "2x^3" where 2 is the coefficient and x^3 is the exponential form. A nonexample would be "3x + 2" as it is an expression and not in exponential form.
3) An example of an expanded form would be 235 = 2 x 100 + 3 x 10 + 5 x 1, where each digit is multiplied by its corresponding place value. An example of standard form would be 235 written as is, without being broken down into its place values. A nonexample of expanded form would be 235 written as 2 + 3 + 5, as this is not a multiplication of the digits with their place values.
4). Examples of exponent laws include:
Product law: aᵇ x aⁿ = a⁽ᵇ ⁺ⁿ⁾
Quotient law: [tex]a^m / a^n = a^{(m-n)}\\[/tex]
Power law: [tex](a^m)^n = a^{(m \times n)}[/tex]
Negative exponent law: [tex]a^{(-n)} = 1/a^n[/tex]
Zero exponent law: [tex]a^0 = 1[/tex].
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WILL GIVE THE BRAINLIEST PLEASE HURRYY!!!!!!!
Match the equation with the number of solutions for x that are possible.
Column A
1.
:
2.
y+5=12
:
y+5=12
3.
6a+1=9a:
6a+1=9a
4.
5x - 9 = 5x + 5:
5x - 9 = 5x + 5
5.
4(x - 7) +3x = 7x -28:
4(x - 7) +3x = 7x -28
Column B
a.Infinite solutions
b.Three solutions
c.Two solutions
d.One solution
e.There is no way to know
f.No solution
Answer:
1. One solution
2. No solution
3. Infinite solutions
4. Two solutions
5. Three solutions
Step-by-step explanation:
You're welcome ♡
I don't know the method to find the equations of the other 2 ides. Can someone please explain step by step how to do this.
The equations of the other two sides are AD: y = -3x + 3 and DC: y = 1/2x - 1/2.
What is point-slope form?
The point-slope form is a way to write the equation of a straight line in algebra. It is used when you know the coordinates of a point on the line and the slope of the line. The point-slope form of a linear equation is:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.
Since AB and BC are two sides of a parallelogram, they are parallel to each other. Thus, we can use the slope formula to find the slopes of these sides.
Slope of AB:
m = (y₂ - y₁)/(x₂ - x₁)
= (6 - 3)/(6 - 0)
= 3/6
= 1/2
Slope of BC:
m = (y₂ - y₁)/(x₂ - x₁)
= (3 - 6)/(7 - 6)
= -3/1
= -3
Now that we know the slopes of AB and BC, we can use the point-slope form to find the equations of the other two sides.
Equation of AD:
We know that AD is parallel to BC and passes through point A. So, we can use the point-slope form with the slope of BC and point A.
y - y₁ = m(x - x₁)
y - 3 = -3(x - 0)
y - 3 = -3x
y = -3x + 3
Equation of DC:
We know that DC is parallel to AB and passes through point C. So, we can use the point-slope form with the slope of AB and point C.
y - y₁ = m(x - x₁)
y - 3 = 1/2(x - 7)
y - 3 = 1/2x - 7/2
y = 1/2x - 1/2
Therefore, the equations of the other two sides are:
AD: y = -3x + 3
DC: y = 1/2x - 1/2
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A. When will the rock be 125 feet above the beach?
B. What is the maximum height reached by the rock and how many seconds did it take for the rock
to reach that height?
The quadratic equation for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The times at which the rock will be 125 feet above the beach are about; 3.66 seconds and 1.28 seconds
b. The maximum height reached is about 147.5 feet and it will take about 2.5 seconds for the rock to reach maximum height
What is a quadratic equation?A quadratic equation is an equation of the form, f(x) = a·x² + b·x + c, where; a ≠ 0, and a, b, and c are numbers.
a. The function for the height of the rocket is presented as follows;
h(t) = -16·t² + 79·t + 50
The time at which the height is 125 feet can be found as follows;
h(t) = 125 feet
h(t) = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 125 - 125 = 0
-16·t² + 79·t - 75 = 0
The quadratic formula indicates that we get;
t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32
t = (79 ± √(1441))/32
t = (79 + √(1441))/32 ≈ 3.66
t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock is 125 feet above the beach are; t ≈ 3.66 seconds, and t ≈ 1.28 secondsb. The time at which the rock is at the maximum height can be obtained by using the formula for finding the input value at the maximum value of a quadratic function, which is; at the maximum height, x = -b/2·a
Therefore, at the maximum height, we get;
The time, t = -79/(2 × (-16)) = 2.46875
The time it takes the rock to reach the maximum height is 2.46875 seconds ≈ 2.5 seconds
The maximum height is therefore;
h(2.46875) = -16×2.46875² + 79×2.46875 + 50 = 147.515625 ≈ 147.5
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The table below displays the distances driven during each 1-hour interval of a 4 hour trip.
Which is closest to the total distance driven?
The closest option to the total distance driven is 270.
In one sentence, define distance.We kept an eye on them from afar. Compared to earlier, she perceives a distance between her and her brother. They had been close friends once, but now there was a great distance between them. He desires to disassociate himself from his old boss.
We must combine the distances for each hour in order to calculate the total distance travelled:
Distance total = 62 + 70 + 68 + 72
272 miles roundtrip.
Thus, option 270 comes the closest to the total mileage driven.
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If 5 x 6 = 20+ y,
0 5
0 6
O 10
0 30
what is the value of y?
Answer:
10
Step-by-step explanation:
5×6=20+y
30=20+y
30-20=y
10=y
therefore y=10
players per game 10 50 100
prizes awarded 2 6 18
A bag contains blue and yellow chips for a game at a carnival. To play, a person must select a chip from the bag. If the chip is blue, the person receives a prize. If the chip is yellow, the person does not receive a prize. The results after 10, 50, and 100 people played were recorded.
Which set of numbers from the table would give the best estimate of the probability of receiving a prize?
a
10 people and 2 prizes awarded
b
50 people and 6 prizes awarded
c
100 people and 18 prizes awarded
d
we cannot estimate the probability of receiving a prize
The best estimate of the probability of receiving a prize would be the ratio of the number of prizes awarded to the total number of people who played the game.
a) For 10 people, 2 prizes were awarded, so the estimate of the probability of receiving a prize is 2/10 or 0.2 (20%).
b) For 50 people, 6 prizes were awarded, so the estimate of the probability of receiving a prize is 6/50 or 0.12 (12%).
c) For 100 people, 18 prizes were awarded, so the estimate of the probability of receiving a prize is 18/100 or 0.18 (18%).
Therefore, the best estimate of the probability of receiving a prize would be c) 100 people and 18 prizes awarded, which gives an estimate of 0.18 or 18%.
[Economics, three part, 100 points]
The graph shows the average total cost (ATC) curve, the marginal cost (MC) curve, the average variable cost (AVC) curve, and the marginal revenue (MR) curve (which is also the market price) for a perfectly competitive firm that produces terrible towels. Answer the three accompanying questions, assuming that the firm is profit-maximizing and does not shut down in the short run.
1) What is the firm's total revenue?
2) What is the firm's total cost?
3) What is the firm's profit? (Enter a negative number for a loss.)
The three accοmpanying questiοns, assuming that the firm is prοfit-maximizing and dοes nοt shut dοwn in the shοrt run
1)Firm's Tοtal Revenue= $78000
2)Firm's Tοtal Cοst =$128700
3)Firm's Lοss = - $50700
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here in the given graph,
Cοst per unit = $300
Equilibrium quantity = $260 Then,
Firm's Tοtal Revenue = P * Q
=> $300*260 = $78000 (Equilibrium where, MR = MC)
Firm's Tοtal Cοst = Cοst per Unit * equilibrium quantity
=> $495*260 = $128,700
Firm's Lοss = TR - TC
=> $78000 - $128,700 = - $50700
Hence the answers are,
1)Firm's Tοtal Revenue= $78000
2)Firm's Tοtal Cοst =$128700
3)Firm's Lοss = - $50700
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