The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.
What is a linear relation?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
The first and the second differences are:
x y first differences second differences
4 18 ----
5 28 10 ------
6 35 7 -3
7 39 4 -3
8 40 1 -3
9 38 -2 -3
The values of second differences are constant, therefore, the relation is linear.
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need help i dont understand
Answer:
Step-by-step explanation:
it would be "c" because the question asks for the number that makes the inequality true
4x≤ x+3
the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example
4 x -7=-28
-28+3=-25
-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5
5 is not greater than 8 so it doesnt work
-6
-4
-2
6
4
2
2
4 6
f(1) =
Answer:
f(1)= -4
Step-by-step explanation:
o_o. .............>|||✓✓✓✓✓
Solve the system of equation by the substitution method
y=5x+1
2y-6x=10
Answer:
x=2 and y=11
Step-by-step explanation:
Okay so subtitution method
y=5x+1
2y-6x=10
Plug in the y
2(5x+1
)-6x=10
10x+2-6x=10
4x+2=10
4x=8
x=2
now plug in for y
lets use first equation
y=5(2)+1
y=10+1
y=11
Brainliest please.
En un triatlón, Jenny nadó durante 1 hora, anduvo en bicicleta durante 1,75 horas y corrió durante 1 hora. Su velocidad promedio en bicicleta fue 2 veces su velocidad promedio para correr, y su velocidad promedio para correr fue 8 veces su velocidad promedio para nadar. La distancia total del triatlón fue de 55,5 kilómetros. Escribe una ecuación y resuélvela para encontrar la velocidad de nado promedio de Jenny en kilómetros por hora. Explique su ruta de solución y el razonamiento detrás de su trabajo.
Jenny's Average swimming speed is 1.5 km/h.
Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.
We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.
Thus, the distance she swam is S * 1 = S km.
Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.
Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.
Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.
She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.
The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.
Therefore, we can write the equation:
S + 8S + 28S = 55.5.
Simplifying the equation, we get:
37S = 55.5.
To solve for S, we divide both sides of the equation by 37:
S = 55.5 / 37 = 1.5.
Thus, Jenny's average swimming speed is 1.5 km/h.
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divide 200 between Sita and Geeta in the ratio 2:3
Answer: 80:120
Step-by-step explanation:
hi <3
2 + 3 = 5
200/5 = 40
2 x 40 = 80
3 x 40 = 120
sita gets 80 and geeta gets 120
hope this helps :)
a rocket is launched from the top of an 8-foot ladder. It’s initial velocity is 128 feet per second, and it is launched at an angle of 60* with respect to the ground, write parametric equations that describe the motion of the rocket as a function of timeX=(v cos ?)ty= (v sin ?)t+k -16^2?= beta sign
We know that:
- a rocket is launched from the top of an 8-foot ladder.
- It’s initial velocity is 128 feet per second, and it is launched at an angle of 60* with respect to the ground
And we must write parametric equations that describe the motion of the rocket as a function of time
To write the parametric equations we need to know that the parametric general equations for a Projectile Motion are:
\(\begin{gathered} x=\left(v_0cos\theta\right)t \\ y=h+\left(v_0sin\theta\right)t-16t^2 \end{gathered}\)Where,
v0 represents the initial velocity
h represents the initial height
θ represents the angle respect to the ground
In our case,
\(\begin{gathered} v_0=128\frac{feet}{sec} \\ h=8feet \end{gathered}\)Finally, replacing in the parametric equations:
\(\begin{gathered} x=\left(128cos60\degree\right)t \\ y=8+\left(128sin60\degree\right)t-16t^2 \end{gathered}\)ANSWER:
\(\begin{gathered} x=(128cos60\operatorname{\degree})t \\ y=8+(128s\imaginaryI n60\degree)t-16t^2 \end{gathered}\)
A train running between two stations 50 Km apart arrives on time if it travels at an
average speed of 60 km/h. How late will it be if travels at an average speed of 50 Km/h?
If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.
How late will the train be if it travels at an average speed of 50 Km/h?Speed is simply referred to as distance traveled per unit time.
It is expressed as:
Speed = distance / time
Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.
The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:
Speed = distance / time
time = distance / speed
time = 50 km / 60 km/h
time = 5/6 hour
Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:
Speed = distance / time
time = distance / speed
time = 50 km / 50 km/h
time = 1 hour
Now, the difference in time between the two scenarios would be:
time difference = 1 hour - 5/6 hour
time = 1/6 hour
Convert to minutes
time = 1/6 × 60
time = 10 minutes
Therefore, the train would be late by 10 minutes.
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15. A botanist collected data on the different elevations at which a certainplant grows. The data collected by the botanist are shown.275, 300, 370, 425, 425, 450, 500,500, 550, 600, 600, 650, 725, 725, 800Which box plot correctly represents the data collected by the botanist?200300400500600700800200300400500600700800HHHHH200 300 400 500600+++800700200300+400500600700800
In order to find the correct box plot, first let's calculate the median of the data set.
The set is already in crescent order, and it has 15 elements, so the median will be the 8th element, which is 500.
This value is represented by the middle line in the box plot. Since there are two options with the median = 500, let's calculate the first interquartile.
If we consider just the first 7 elements, the middle term will be the 4th element, so the first interquartile is 425.
Looking at the options, the one with first interquartile equal 425 is the first one (option A).
-1/3v = -7 how do i solve this equation?
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
pls help giving brainliest Question: a ÷ b when a = 10 and b = 4 a ÷ b = *hint its not 2.5*
Answer:
5 : 2 or 2.5Step-by-step explanation:
Given:
a = 10, b = 4Find a : b:
a : b = 10 : 4 = 5 : 2 or 2.5Factor the expression: 16a + 10
Answer:
2(8a + 5)
Step-by-step explanation:
Hi there!
16a + 10
The two terms here are 16a and 10. Both of them are divisible by 2. Factor 2 out of the terms:
= 2(8a + 5)
Now, there are no more common factors between 8a and 5. Therefore, this expression is now fully factored.
I hope this helps!
The residents of a city voted on whether to raise property taxes.
The ratio of yes votes to no votes was 7 to 5.
If there were 6251 yes votes,
what was the total
number of votes?
Answer=4465
7*6251=893
893*5=4465
Step-by-step explanation:
what does a discrete quantitative variable mean?
Answer:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval)
Step-by-step explanation:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation. Examples of discrete quantitative variables are number of needle punctures, number of pregnancies and number of hospitalizations.
Teri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long will it take for Teri's account to earn $5000?
It will take 54 days for Teri's account to earn an amount of $5000.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
It is given by formula
A = \(p*e^{r*t}\)
where:
A is final amount
p is principal amount
r is rate of interest and
t, is time period
Given: A= $5000, p=$1500, r=2.25% = 0.0225
To find: time period to get compounded amount
5000=1500×\(e^{0.0225*t}\)
\(e^{0.0225t}\) = \(\frac{10}{3}\)
0.0225t = ㏑ (\(\frac{10}{3}\))
t = 53.5099 ≈ 54 days
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compare these decimals 0.7______0.6999
1. >
2.<
3.=
What values of b satisfy 3(2b + 3)² = 36?
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
HELP PLSLSSSSSSSSSSSSS
Answer:
Step-by-step explanation:
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters, and a variance of 49. If a random sample of 34 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.8 millimeters
The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is approximately 0.0668.
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
The standard deviation of the population is \($\sqrt{49} = 7$\) millimeters. The standard error of the sample mean is then
\($\frac{7}{\sqrt{34}} = \frac{7}{5.874} \approx 1.2$\)millimeters.
The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is the probability that it falls outside of the interval \($(139 - 1.8, 139 + 1.8)$\). We can use the standard normal distribution to approximate this probability.
First, we need to convert the difference between the sample mean and the population means to standard units.
The difference of 1.8 millimeters is :
\($\frac{1.8}{1.2} = 1.5$\) standard units.
Then, we can use the standard normal distribution to find the probability that the sample mean falls outside of this interval.
This probability is equal to \($1 - 2\Phi(-1.5) \approx 0.0668$\),
where \($\Phi$\) is the standard normal cumulative distribution function.
Therefore, the required probability is approximately 0.0668.
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Here is a trapezium drawn on a centimetre grid (not drawn to scale) work out the area of the trapezium, stating the units of your answer
Answer: the answer is 21 squared
Answer:
21cm²,22cm (write both of them. they give you the total marks.)
Step-by-step explanation:
Select the graph of the solution. Click until the correct graph appears.
Answer:
convert the 27 degree into grades
each function
f(x)=-4x-5;
ion for
Find ƒ(1)
for the given
When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.
The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.
Replacing x with 1, we have:
ƒ(1) = -4(1) - 5
Simplifying further:
ƒ(1) = -4 - 5
ƒ(1) = -9
Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.
Let's break down the steps taken to arrive at the solution:
1. Start with the function f(x) = -4x - 5.
2. Replace x with 1 in the function.
3. Evaluate the expression by performing the necessary operations.
4. Simplify the expression to obtain the final result.
In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.
It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.
Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.
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20. You may already use algebra in your daily life. How do you imagine that you will use basic algebraic equations in your healthcare career? Explain.
Depending on the path that we decide to take, the algebra can help us in many forms.
As an example in the pharmaceutical/medical area, the nurses and doctors use basic algebra formulas to calculate dosages on different drugs depending on variables such as the weigh of each patient (commonly expressed as X or Y).
They used to have some paper sheets with formulas for different drug preparations (liquid ones particularly) within hospitals to avoid errors in medication.
As a healthcare provider, it is important to be able to read vital signs. Many of these are expressed as algebraic equations. Such equations can also be important when it comes to administering the right doses of medicine or converting different units of measurement.
what does this mean?
Answer:
That means you finished.
Step-by-step explanation:
Is there any variable or constant that you could add to or subtract from both sides of 2=2
Yes, you could add to or subtract from both sides of 2=2.
What is a variable?
A characteristic that can be measured and given different values is known as a variable. Variables include things like height, age, income, province of birth, school grades, and type of housing. There are two main types of variables: categorical and numeric.
Equivalent equations are those that have the same sets of solutions. According to the equations' multiplication/division rule, all terms on both sides of an equation can be multiplied or divided by the same term, with the exception of zero, without changing the equation's solution set.
The equation is 2 = 2
Add x with both sides:
2 + x = 2 + x
The equation remains the same.
Add 3 with both sides:
2 + 3 = 2 + 3
5 = 5
The equation remains the same.
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A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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If | x | = 5 Explain why the expression: x+ 7 has two different solutions
Answer:
Step-by-step explanation:
When a number is taken by the square root, it will always come out positive. Looking at |x| = 5, there are two solutions for this that being 5 and -5.
|5| = 5
|-5| = 5
So if we plug those solutions into the expression x + 7, we get two different answers.
5 + 7 = 12
-5 + 7 = 2
Simplify 3 (5x-2y) +2 (4X-37)
Answer:
3x - 6y - 74
Step-by-step explanation:
Given
3(5x - 2y) + 2(4x - 37) ← distribute parenthesis
= 15x - 6y + 8x - 74 ← collect like terms
= 23x - 6y - 74
Answer:
Distribute
3
(
5
−
2
)
+
2
(
4
−
3
7
)
{\color{#c92786}{3(5x-2y)}}+2(4x-37)
3(5x−2y)+2(4x−37)
1
5
−
6
+
2
(
4
−
3
7
)
{\color{#c92786}{15x-6y}}+2(4x-37)
15x−6y+2(4x−37)
2
Distribute
1
5
−
6
+
2
(
4
−
3
7
)
15x-6y+{\color{#c92786}{2(4x-37)}}
15x−6y+2(4x−37)
1
5
−
6
+
8
−
7
4
15x-6y+{\color{#c92786}{8x-74}}
15x−6y+8x−74
3
Combine like terms
1
5
−
6
+
8
−
7
4
15x−6y+8x−74
2
3
−
6
−
7
423x}}-6y-74
23x−6y−74
Solution
2
3
−
6
−
7
4
Step-by-step explanation:
Mathematical Literacy Assignment no 2021
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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What effects did the introduction of the nutria have on ecosystems throughout the U. S.? Nutria, in fact, do feed on noxious weeds. Nutria feed on native plants that hold wetland soil together. The largest nutria populations are located in freshwater rocky coastal areas of New England. Another name we could give to nutria would be invasive species. Nutria's digging, rooting, and swimming causes massive erosion, converting healthy marsh habitat for native species into open water habitat. The nutria’s relatively low reproductive rate help keep their numbers in check.
Answer:
Step-by-step explanation:
1. Nutria, in fact, do feed on noxious weeds.
2. Nutria feed on native plants that hold wetland soil together.
3. The largest nutria populations are located in freshwater rocky coastal areas of New England.
4. Another name we could give to nutria would be invasive species.
5. Nutria's digging, rooting, and swimming causes massive erosion, converting healthy marsh habitat for native species into open water habitat.
6. The nutria’s relatively low reproductive rate help keep their numbers in check.
The answer for this is 1, 2 and 4, 5
This is USAtest prep
Nutria have these effects on ecosystems in U. S:
Nutria, in fact, do feed.. Nutria feed on native plants... Another name... Nutria's digging...What is ecosystem?An ecosystem serves as an area in a particular place that contains plants as well as animals and weather.
Therefore, with the introduction of Nuria in U.S there is abundant of it in wetlands and we can consider them as invasive species.
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