are the adjacent angles in a parallelogram congruent always, sometimes, or never
Answers
Answer:
always
Step-by-step explanation:
if something parallel then it never touch each other and are opposite of each other
Related Questions
4 Unit Roots 1. Consider a series that changes deterministically: AYt = a. Given initial value of Yo, write the general solution of the difference equa- tion. (4 points) 2. Explain whether the process above is trend stationary or stochastic trend. (6 points) 3. Explain the method that you would use to remove the trend in point 1 & 2. (4 points) 4. Consider now a series with the following motion: AY₁ = a + et. Given initial value of Yo, write the general solution of the difference equa- tion. (6 points) 5. Explain whether the process above is trend stationary or stochastic trend. (6 points) 6. Explain the method that you would use to remove the trend in point 4 & 5. (4 points) 7. Write the hypothesis for a unit roots test. Write the specification to test for unit roots using the Dickey-Fuller Test. (5 points) 8. Write the specification to test for unit roots using the Augmented Dickey- Fuller Test. (5 points)
Answers
1. Consider a series that changes deterministically: AYt = a. Given initial value of Yo, write the general solution of the difference equation. A difference equation of the form Ay(t) = a has a general solution of y(t) = A + at, where A is a constant of integration. Therefore, the general solution for the difference equation in question is y(t) = Yo + at.
2. In a trend stationary process, the trend is deterministic. Therefore, it is stationary after removing the trend. In a stochastic trend, the trend is stochastic, and the process is non-stationary even after the trend is removed. Since the process above has a deterministic trend, it is a trend stationary process.
3. The first difference of the series should be taken to remove the trend from the series. The first difference is calculated as y(t) - y(t-1).
4. Consider now a series with the following motion: AY₁ = a + et. Given the initial value of Yo, write the general solution of the difference equation. The difference equation Ay(t) = a + et has a general solution of y(t) = (a/e) + A + Bt + ut, where u(t) is a stationary noise term with zero mean and constant variance. Therefore, the general solution to the difference equation in question is y(t) = a/e + Yo + Bt + ut.
5. Explain whether the process above is trend stationary or stochastic trend. Since the process above has a stochastic trend, it is a non-stationary process.
6. The first difference of the series should be taken to remove the trend from the series. The first difference is calculated as y(t) - y(t-1).
7. The hypothesis for a unit root test is that a series has a unit root, meaning it is non-stationary. The Dickey-Fuller test can be used to test for unit roots by regressing the first difference of the series on the lagged level of the series and testing whether the coefficient on the lagged level is significantly different from zero
8. The Augmented Dickey-Fuller test can be used to test for unit roots by regressing the first difference of the series on the lagged level of the series and the lagged first difference of the series and testing whether the coefficient on the lagged level is significantly different from zero.
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Find the value of x.
Answers
Answer:
x = 9
Step-by-step explanation:
Triangle BCD is a right triangle, so the inscribed angle at C is the complement of the given angle:
angle C = 90° -45° = 45°
The measure of arc BE is twice that angle value, so we have ...
arc BE = 2·angle C
10x° = 2(45°)
x = 9 . . . . . . . . . divide by 10°
Jane's school is due west of her house and due south of her friend Norma's house. The distance between the school and Norma's house is 8 kilometers and the straight-line distance between Jane's house and Norma's house is 9 kilometers. How far is Jane's house from school? If necessary, round to the nearest tenth.
Answers
Answer
Distance = 4.1 km
Explanation
Let the distance between Jane's house from school be x
The distance can be calculated using pythagora's theorem
\(\begin{gathered} \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = 9km, opposite = 8km and adjacent = x km} \\ 9^2=8^2+x^2 \\ \text{Isolate x}^2 \\ 81=64+x^2 \\ \text{Collect the like terms} \\ 81-64=x^2 \\ 17=x^2 \\ \text{Take the square roots of both sides} \\ \text{x = }\sqrt[]{17} \\ \text{x = 4.1 km} \end{gathered}\)Therefore, the distance between Jane's house from school is 4.1 km
a section is bounded by the x-axis, y-axis, y = 9x − x3, and x = 3. where is the centroid of this section in (x, y) coordinates?
Answers
The centroid of the given section is located at the point (1.8, 4.05).
Find the x-coordinate of the centroid using the formula x = (1/A) * ∫(y dA), where A is the area of the section and y is the distance of each infinitesimal area dA from the x-axis.
Find the area of the section by integrating y = 9x - x^3 from x = 0 to x = 3 and subtracting the area under the x-axis.
A = ∫(y dx) from 0 to 3 - ∫(-y dx) from 0 to 3
= ∫(9x - x^3 dx) from 0 to 3 - ∫(-9x + x^3 dx) from 0 to 3
= [4.5x^2 - (1/4)x^4] from 0 to 3 + [4.5x^2 - (1/4)x^4] from 0 to 3
= 40.5
Using the formula for the x-coordinate of the centroid to get:
x = (1/40.5) * ∫((9x - x^3) dx) from 0 to 3
x = 1.8
Find the y-coordinate of the centroid using the formula: y = (1/A) * ∫(x dA)
where A is the area of the shape, x is the distance of each infinitesimal area dA from the y-axis, and the integral is taken over the entire area of the shape.
y = (1/A) * ∫(x * y dx) from 0 to 3
y = 4.05
Therefore, the centroid of the given section is located at the point (1.8, 4.05).
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Need helpppp ASAP!!!!!!!
Answers
John would like to go on a ski trip with his friends. In order to go on the trip, John needs to save more
than $350 dollars. Write an inequality that describes, M, the money that John needs to save.
Answers
Answer:
$350 < M
Step-by-step explanation:
Read the excerpt from The Fellowship of the Ring. Many people from other parts of the Shire were also asked; and there were even a few from outside the borders. Bilbo met the guests (and additions) at the new white gate in person. He gave away presents to all and sundry—the latter were those who went out again by a back way and came in again by the gate. Hobbits give presents to other people on their own birthdays. Not very expensive ones, as a rule, and not so lavishly as on this occasion; but it was not a bad system. Actually in Hobbiton and Bywater every day in the year it was somebody’s birthday, so that every hobbit in those parts had a fair chance of at least one present at least once a week. But they got tired of them. What do readers learn about the setting in this excerpt? Many people are invited to the party. Some hobbits came from faraway. Hobbiton is a community with deep traditions. Bilbo purchased gifts for everyone in town.
Answers
Readers learn that Hobbiton is a community with deep traditions, where celebrations, gift-giving, and regular birthday events play a significant role in their daily lives.
In this excerpt from The Fellowship of the Ring, readers learn about the setting, particularly Hobbiton, which is portrayed as a community with deep traditions.
The passage describes how many people from other parts of the Shire, and even a few from outside the borders, were invited to the party hosted by Bilbo.
This indicates that the party is a significant event that attracts attendees from various locations.
Additionally, the excerpt mentions Bilbo meeting the guests at the new white gate in person and giving away presents to all and sundry.
This suggests a sense of community and generosity within Hobbiton.
It is mentioned that hobbits give presents to other people on their own birthdays, although not as lavishly as on this particular occasion.
This highlights the tradition of exchanging gifts among hobbits and suggests that gift-giving is an integral part of their culture and celebrations.
Furthermore, it is mentioned that in Hobbiton and Bywater, every day of the year is somebody's birthday, implying that birthdays hold importance in the community and are celebrated regularly.
This further emphasizes the deep-rooted traditions and customs within Hobbiton.
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How do you calculate national income statistics?
Answers
Natiοnal Incοme statistics = Tοtal Rent + Tοtal Wages + Tοtal Interest + Tοtal Prοfit. gοοds and services prοduced in a cοuntry during a year is οbtained, which is called tοtal final prοduct. This represents Grοss Dοmestic Prοduct ( GDP ).
What is Natiοnal incοme?Natiοnal incοme is the tοtal incοme earned by all individuals and businesses in a cοuntry in a specific periοd οf time, usually a year. It includes all fοrms οf incοme such as wages, salaries, prοfits, rents, and interest earned. Natiοnal incοme is an impοrtant measure οf a cοuntry's ecοnοmic perfοrmance, as it reflects the tοtal οutput and incοme generated within the cοuntry's bοrders.
Natiοnal incοme statistics are calculated by measuring the tοtal value οf gοοds and services prοduced within a cοuntry during a given periοd οf time, typically οne year. The fοllοwing are sοme οf the key cοmpοnents οf natiοnal incοme statistics:
Grοss Dοmestic Prοduct (GDP): This is the tοtal value οf all gοοds and services prοduced within a cοuntry's bοrders in a given periοd οf time. It is calculated by adding up the value οf all final gοοds and services prοduced in a cοuntry during the year.
Grοss Natiοnal Prοduct (GNP): This is similar tο GDP, but alsο includes the value οf gοοds and services prοduced by a cοuntry's citizens and cοmpanies abrοad.
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If a system reliability of 0. 998 is required, what reliability of two components in series is required?
Answers
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. If the standard deviation for the salaries of both genders is approximately $5200 and the salaries are normally distributed, find the 80th percentile salary for male professors and for female professors.
Answers
The 80th percentile salary for male professors is $104,037.2 and The 80th percentile salary for female professors is $95,637.2. This can be answered by the concept of Standard deviation.
Given that the average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. Also, the standard deviation for the salaries of both genders is approximately $5200 and the salaries are normally distributed, find the 80th percentile salary for male professors and for female professors. To find the 80th percentile salary for male professors, we use the z-score formula. z = (x - μ) / σGiven that the male full professor's average salary is $99,685 and the standard deviation is approximately $5200.
The z-score for the 80th percentile is 0.84.Therefore, the 80th percentile salary for male professors is x = zσ + μx = 0.84(5200) + 99,685x = 104,037.2. The 80th percentile salary for male professors is $104,037.2. To find the 80th percentile salary for female professors, we use the z-score formula. z = (x - μ) / σGiven that the female full professor's average salary is $90,330 and the standard deviation is approximately $5200. The z-score for the 80th percentile is 0.84.
Therefore, the 80th percentile salary for female professors is x = zσ + μx = 0.84(5200) + 90,330x = 95,637.2The 80th percentile salary for female professors is $95,637.2.
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El Papa de blanca destino la tercera parte de su salario quincenal para comprar alimentos y la mitad para pagos diversos si le sobran 500 ¿que cantidad de su sueldo gasta en alimentos?
Answers
Answer:
El papá de Blanca gasta $1,000 de su sueldo en alimentos.
Step-by-step explanation:
En primer lugar, se designa a la letra S como la cantidad total del salario de la persona.
Sabiendo que el papá de Blanca destina la tercera parte de su salario para comprar alimentos, y que la tercera parte de un número es la división de ese número entre tres, entonces se tiene la expresión:
Alimentos: \(A=\frac{S}{3} =\frac{1}{3} *S\)
Ahora sabes que el papá de Blanca destina la mitad de su salario en diversos gastos, y siendo la mitad de un número es la división de ese número entre dos, se obtiene la expresión:
Gastos: \(G=\frac{S}{2} =\frac{1}{2} S\)
El papá de Blanca gasta su salario en alimentos y en otros gastos y le sobran $ 500. Esto es expresado mediante:
Alimentos + Gastos + 500 = Salario
Entonces:
A + G + 500 = S
Sustituyendo A y G:
\(\frac{1}{3} S+\frac{1}{2} S+500=S\)
Resolviendo:
\(\frac{5}{6} S+500=S\)
\(500=S- \frac{5}{6} S\)
\(500= \frac{1}{6} S\)
\(\frac{500}{\frac{1}{6} } =S\)
3,000= S
Entonces el salario del papá de Blanca es de $ 3,000
Reemplazando este valor para el cálculo de su gasto en alimentos es:
\(A=\frac{1}{3} *S= \frac{1}{3}* 3,000\)
A= 1,000
El papá de Blanca gasta $1,000 de su sueldo en alimentos.
Given y1(t) = t^2 is a solution to: t^2y'' - 4ty' + 6y = 0, t > 0 find another solution using the method of reduction of order.
Answers
For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.
Given solution to t²y'' - 4ty' + 6y = 0 is
y₁(t) = t²
Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,
y₂ = vt²
y₂' = 2vt + t²v'
y₂'' = 2v + 2tv' + 2tv' + t²v''
y₂'' = 2v + 4tv' + t²v''
Substituting this
t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0
t⁴v'' = 0
v'' = 0
v' = c, c is a constant
v = ct
Therefore, y₂(t) = ct×t²
y₂ (t) = ct³
Therefore general solution will be y(t) = c₁t² + c₂t³
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The cost to rent a bike is $28 for the first day plus $2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting the bike for 8 days?
Answers
Answer:
42
Step-by-step explanation:
The explicit formula for the rental cost is =+. The cost of renting a bike for 2 days is $42.
The equation for the rental cost for n days will be 28 + 2n.
Based on the information given, the explicit formula for the rental cost for n days will be:
= 28 + (2 × n)
= 28 + 2n
Therefore, the cost of renting the bike for 8 days will be:
= 28 + 2n
= 28 + 2(8)
= 28 + 16 = 44
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A golf ball is hit from the ground with an initial speed of 192 feet per second. assume the starting height of the ball is 0 feet. how long will it take the golf ball to hit the ground?
Answers
It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.
To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:
\(h = ut + (1/2)gt^2\)
Where:
h is the height (0 feet, as the ball is on the ground)
u is the initial velocity (192 feet per second)
g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)
t is the time we want to find
Plugging in the given values, we get:
\(0 = (192)t + (1/2)(-32)t^2\)
Simplifying the equation, we have:
\(-16t^2 + 192t = 0\)
Factoring out t, we get:
t(-16t + 192) = 0
Setting each factor equal to zero, we have:
t = 0 (not applicable in this case)
-16t + 192 = 0
Solving for t, we get:
-16t = -192
t = 12
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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:
h0 = 0
v0 = 192
g = 32.2
a = 16.1
b = 192
t1 = 0
t2 = -b / a
t(-16t + 192) = 0
Setting each factor equal to zero, we have:
t = 0 (not applicable in this case)
-16t + 192 = 0
Solving for t, we get:
-16t = -192
t = 12
t2 >= 0:
time_to_hit_ground = t2
time_to_hit_ground = t1
The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.
The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
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Erik leans a 15 foot ladder up against his house in order to clean the gutters. The
base of the ladder is 9 feet from the base of the house. How far up the house does
the ladder reach?
Answers
So you have 9^2 + b^2 = 15^2
9^2 = 81
15^2 = 225
81+ b^2 = 225
225-81 = 144
Square root of 144 is 12
The answer is 12 foot
Answer:
12 Feet
Step-by-step explanation:
It's the same as Pythagoream Theroem, just backwards!
The equation I used was...
x^2 + 9^2 = 15^2 (Square the two numbers)
x^2+ 81 = 225 (Subtract 81 from both sides)
x^2 = 144 (Find the square root of 144)
x = 12
HELPP PLEASEEE
John's toy car is built on a scale of one
inch represents 12 inches on the actual
car. If john's toy car is 5 inches long,
how long is the actual car?
Answers
1 • x = 12 • 5
x = 60
John’s car is 60 inches long.
Which of the following would be considered an example of a matched pair or paired data? a. the mean age of residents in Dayton compared to the mean age of residents in Miam b. the proportion of rainy days in Seattle compared to the proportion of rainy days in Phoenix c. the percestage of defective products produced by Company A compared to the percentage produced by Company B d. the math scores of current 9th-grade students compared with their 8th-grade math scores
Answers
Option D, the math scores of current 9th-grade students compared with their 8th-grade math scores, would be considered an example of a matched pair or paired data.
This is because the data is collected from the same group of individuals at two different points in time, allowing for a comparison of the change in math scores. The other options involve comparing different groups or populations, which would not be considered paired data. Additionally, the terms "mean" and "percentage" are not relevant in this context as the question is asking about the type of data comparison, not the specific used.
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For the given probability density function, over the stated interval, find the requested value. 1 f(x) = x, over the interval [0,5]. Find E (x²). ... O A. 625 32 313 B. 16 623 32 39 2
Answers
The given probability density function, over the stated interval, The correct option is: A. 625/32
To find the expected value of x², denoted as E(x²), we need to calculate the integral of x² multiplied by the probability density function (PDF) over the given interval [0, 5].
The probability density function (PDF) is defined as f(x) = x for x in the interval [0, 5].
The formula for calculating the expected value (E) is as follows:
E(x²) = ∫[a, b] x² × f(x) dx,
where [a, b] represents the interval [0, 5].
Substituting the given PDF f(x) = x, we have:
E(x²) = ∫[0, 5] x² × x dx.
Now, let's solve this integral:
E(x²) = ∫[0, 5] x³ dx.
Integrating x³ with respect to x gives:
E(x²) = (1/4) × x⁴| [0, 5]
= (1/4) × (5⁴ - 0⁴)
= (1/4) × 625
= 625/4.
Therefore, the value of E(x²) is 625/4.
In the provided options, this value is represented as:
A. 625/32
B. 16 623/32
The correct option is:
A. 625/32
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(-9) / *fill the blank* = 5
Answers
Answer:-1.8
Step-by-step explanation:
a system of equations is shown below what is the solution of the system of equation?
Answers
We will have the following:
*We will determine the solution by replacing the pairs of values and calculating, that is:
*a. (-10, 6.5):
\(\begin{cases}2(-10)+4(6.5)=6 \\ (-10)-2(6.5)=7\end{cases}\Rightarrow\begin{cases}6=6 \\ -23\ne7\end{cases}\)*b. (-2, 2.5):
\(\begin{cases}2(-2)+4(2.5)=6 \\ (-2)-2(2.5)=7\end{cases}\Rightarrow\begin{cases}6=6 \\ -7\ne7\end{cases}\)*c. (5, -1):
\(\begin{cases}2(5)+4(-1)=6 \\ (5)-2(-1)=7\end{cases}\Rightarrow\begin{cases}6=6 \\ 7=7\end{cases}\)So, the solution for the system is the point (5, -1).
a rectangle has perimeter 52 km, and its area is 165 sq-km. find the dimensions of this rectangle. (for purposes of this problem only, the width is shorter than the length.)
Answers
The dimensions of the rectangle: length = 15 km and width = 11 km
Let l be the length of rectangle and w be the width of the rectangle.
A rectangle has perimeter 52 km
Using the formula of the perimeter of rectangle we get an equation,
2(l + w) = 52 ............(1)
And its area is 165 sq-km.
Using the formula of the area of rectangle we get an equation,
l * w = 165 ............(2)
From equation (1),
l = 26 - w
Subatitute above value of l in equation (2),
(26 - w) * w = 165
26w - w² = 165
w² - 26w + 165 = 0
(w - 15)(w - 11) = 0
w = 15 or w = 11
For w = 15,
l = 26 - 15
l = 11
For w = 11,
l = 26 - 11
l = 15
But as we know, the length of rectangle is always greater than the width,
l = 15 and w = 11 is true .
Therefore, the length of rectangle = 15 km and width of rectangle = 11 km
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Define three equivalence relations on the set of buildings on a college campus. determine the equivalence classes for each of these equivalence relations.
Answers
If a relationship R fulfills the three conditions of being transitive, symmetric, and reflexive, then R is said to be an equivalence relation.
When (a, a) € R for any element a € A, we say that R is reflexive on A.
When (b, a) €R for every (a, b) €R, we say that the relation R on A is symmetric.
If (a.b) € R and (b, c) € R implies (a, c) € R, then R is transitive on A.
If you have an a, you may think of all the components that are equivalent to it as its equivalence class.
A=College buildings
We need to define three sets of things that are the same. For instance:
R1 = "(a, b) Both a and b have the same number of rooms."
R2=(a,b): Both a and b have the same number of floors.
R3=(a,b), which means that both a and b have the same number of windows.
Note: If the statement says that a and b have the same property, the relation is probably an equivalence relation.
The set of all elements that are related to an is its equivalence class.
[a]R1,= {b|b has the same number of rooms as a}
[a]R2 = {b|b has the same number of floors as a}
[a]R3= {b|b has the same number of windows as a}
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A certain type of novelty coin is manufac- tured so that 80% of the coins are fair while the rest have a .75 chance of landing heads. Let 0 denote the probability of heads for a novelty coin randomly selected from this population. a. Express the given information as a prior distribution for the parameter 0. b. Five tosses of the randomly selected coin result in the sequence HHHTH. Use this data to determine the posterior distribution of 0.
Answers
(a) a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .
(B) the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.
In this problem, we are dealing with a population of novelty coins, where 80% of the coins are fair (with a 50% chance of landing heads) and the remaining 20% of the coins have a 75% chance of landing heads. We need to determine the prior distribution for the parameter 0, which represents the probability of heads for a randomly selected coin. The prior distribution can be expressed as a weighted combination of a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .
Given the sequence of tosses HHHTH from a randomly selected coin, we can use this data to calculate the posterior distribution of 0. The posterior distribution represents the updated probabilities for the parameter 0 after taking into account the observed data. In this case, the posterior distribution will be a combination of the prior distribution and the likelihood of observing the given sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for 0 based on the data and the prior distribution.
To summarize, the prior distribution for the parameter 0 is a weighted combination of the probabilities of heads for fair coins and biased coins in the population. The posterior distribution is obtained by updating the prior distribution with the observed data, reflecting the updated probabilities for 0 based on the sequence of tosses HHHTH.
Now, let's explain the process of determining the posterior distribution of 0. We start with the prior distribution, which is a combination of 0.8 for fair coins and 0.75 for biased coins. After observing the sequence HHHTH, we calculate the likelihood of obtaining this sequence for each possible value of 0, considering the probabilities associated with fair and biased coins. For example, for a fair coin (0.5), the likelihood of observing HHHTH is (0.5)^4 * (1-0.5) = 0.03125, while for a biased coin (0.75), the likelihood is (0.75)^4 * (1-0.75) = 0.0703125.
To obtain the posterior distribution, we multiply the prior distribution by the corresponding likelihoods for each value of 0 and normalize the result to ensure it sums to 1. The normalized values represent the updated probabilities for 0, given the observed data. In this case, the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.
In conclusion, the process of determining the posterior distribution involves updating the prior distribution with the observed data, considering the likelihood of obtaining the sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for the parameter 0, reflecting our updated beliefs about the probability of heads for the randomly selected coin.
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what is the answer for this
Answers
The local newspaper has letters to the editor from 60 people. If this number represents 5% of all of
the newspaper's readers, how many readers does the newspaper have?
The newspaper has
readers
Answers
if you divide 95 by 5 it is 19. 19 times 60 equals 1140. 1140 plus 60 equals 1200. 5% of 1200 is 60.
Answer:
i believe the answer is 1200
Step-by-step explanation:
if you set up a proportion
60 over x equal to 5 over 100 and solve
you get the answer 1200.
if there are 12 eggs per carton, then how many eggs do we have in 5 catons
Answers
60
Step-by-step explanation:
Just multiply 12 and 5
The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = t2i + tj (4,2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) = a(t)
Answers
The velocity vector is v(t) = 2ti + j, the speed is s(t) = sqrt(4t^2 + 1), and the acceleration vector is a(t) = 2i.
To find the velocity vector, speed, and acceleration vector of the object, we differentiate the position vector with respect to time.
Given the position vector r(t) = t^2i + tj, we can differentiate it to find the velocity vector v(t) and acceleration vector a(t):
Velocity vector v(t):
Taking the derivative of r(t) with respect to t, we get:
v(t) = dr/dt = d/dt(t^2i + tj) = 2ti + j
Speed s(t):
The speed is the magnitude of the velocity vector. So, we calculate the magnitude of v(t):
s(t) = |v(t)| = |2ti + j| = sqrt((2t)^2 + 1) = sqrt(4t^2 + 1)
Acceleration vector a(t):
Taking the derivative of v(t) with respect to t, we get:
a(t) = dv/dt = d/dt(2ti + j) = 2i
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How long would it take R20000 invested today at a simple interest rate of 9% p.a. to reach an investment goal of R30000.
A Approximately 5.6 years
B Approximately 6.1 years
C Approximately 4.7 years
D Approximately 5.1 years
Answers
\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)
How many solutions does this system of equations have? y=3x+1 y=3x+7
Answers
Answer:
The following system of equation has no solution.
Step-by-step explanation:
since both of them are equal to y, set them equal to each other:
3x+1=3x+7
if you subtract both sides by 3x, you get 1=7. That is a contradiction, so this has no solutions.
This equation has no solution.
What is the inconsistent system?An inconsistent system is a system that has no solution in any case scenario.
Given this system of equations y=3x+1, y=3x+7.
on comparing both equations multiples of x and y are equal therefore, there will be no solution for a given equation.
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how can i solve this
Answers
Answer: Ill show you some not everything so u can try
Step-by-step explanation: for example 8+y=92
you can make a new problem...
move the 92...
92
subtract
92-
subtract the other number which isnt the variable
92-8
subtract and you get your answer!
Step-by-step explanation:
an equation means that whatever is on one side of the "=" sign is truly equal to whatever is on the other side.
it is like a balance.
you can change the content on one side of the balance, but then you have to make the same change on the other side of the balance. otherwise the balanced relation between both sides is destroyed. and it is no longer an equation.
for the same reason, you can perform any mathematical operation on an equation, as long as you do it simultaneously on both sides.
all these equations are equations with one variable.
so, if we find a way to bring all terms with the variable to one side, and everything else (typically constant numbers) to the other side, while still maintaining the equation relation, then we can solve this by saying "this is only an equation, if the variable has this is that value".
and that is the whole trick.
so, for e.g. t + 3 = 5, how can we get only the variable on one side ? well, the "+ 3" is disturbing, so we subtract 3.
and to keep the balance, we need to subtract 3 on both sides.
that gives us then
t + 3 - 3 = 5 - 3
t = 2
and boom ! the equation has solved itself right in front of our eyes.
and the same thing for all the other equations.
find what is the disturbing additional term on the side of the variable, then get rid of it (and repeat that exact action on the other side) and see what is left on the other side. and you have solved the equation.
that works in every direction like
n + 22 = 5
n + 22 - 22 = 5 - 22
n = -17
12.5 = 7.4 + z
12.5 - 7.4 = 7.4 - 7.4 + z
5.1 = z or
z = 5.1
remember, it is an equation like a balance. you can switch the balance bowls from left to right and right to left, and still they are in balance.