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MatroZZZ [7]
4 years ago
7

Sarah's age is five less than twice her sister's age. Sarah is fifteen years old.

Mathematics
2 answers:
natka813 [3]4 years ago
8 0
The first one would be correct 
saul85 [17]4 years ago
3 0
Let her sisters age be x.
=>sister .....x

Sarah.
twice x=2x. then less than 5
=> (2x-5 )
if Sarah = 15 years
by substation, 2x-5=15
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As the value of the multiple coefficient of determination increases,
Leona [35]

Answer:

a.the goodness of fit for the estimated multiple regression equation increases.

Step-by-step explanation:

As the value of the multiple coefficient of determination increases,

a. the goodness of fit for the estimated multiple regression equation increases.

As we know that the coefficient of determination measures the variability of response variable with the help of regressor. As we know that if the value of the coefficient of determination increases strength of fit also increases.  

7 0
3 years ago
Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the ques
Korvikt [17]

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

s(t)=-16t^2+v_{0}t+h_{0}

where v_{0}t is the initial upwards velocity and

h_{0} is the initial height from which the object was launched.  Filling in that equation with those values gives you

s(t)=-16t^2+64t+3.  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

-16t^2+64t=-3

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

-16(t^2-4t)=-3

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

-16(t^2-4t+4)=-3

BUT since you added in a 4*-16 on the left you have to add it in on the right:

-16t^2(t^2-4t+4)=-3-64

which simplifies to

-16(t-2)^2=-67

Now bring the 67 over by addition and you have your vertex:

s(t)=-16(t-2)^2+67.

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

5 0
3 years ago
Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk pr
Jobisdone [24]

Answer:

B. A cow of 5 years is predicted to produce 5.5 more gallons per week.

Step-by-step explanation:

Let M(a) = 40.8-1.1\cdot a, where a is the age of the dairy cow, measured in years, and M(a) is the predicted milk production, measured in gallons per week.

Besides, we consider a_{1} and a_{2}, such that a_{1}\ne a_{2}, we define the difference between predicted milk productions (\Delta M) below:

\Delta M = -1.1\cdot (a_{2}-a_{1}) (1)

If we know that a_{1} = 5\,yr and a_{2} = 10\,yr, then the difference between predicted milk productions is:

\Delta M = -1.1\cdot (10-5)

\Delta M = -5.5\,\frac{gal}{week}

That is, a cow of 5 years is predicted to produce 5.5 more gallons per week than a cow of 10 years. Hence, the right answer is B.

6 0
3 years ago
What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation? u = x2 u = x3      u = x6      u = x12
Arada [10]
Sent a picture of the solution to the problem (s).

5 0
3 years ago
Read 2 more answers
Determine if there is a proportional relationship between the two quantities
Shalnov [3]

Answer:

The table a not represent a proportional relationship between the two quantities

The table b represent a proportional relationship between the two quantities

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

<u><em>Verify each table</em></u>

<em>Table a</em>

Let

A ----> the independent variable or input value

B ----> the dependent variable or output value

the value of k will be

k=\frac{B}{A}

For A=35, B=92 ---> k=\frac{92}{35}=2.63

For A=23, B=80 ---> k=\frac{80}{23}=3.48

the values of k are different

therefore

There is no proportional relationship between the two quantities

<em>Table b</em>

Let

C ----> the independent variable or input value

D ----> the dependent variable or output value

the value of k will be

k=\frac{D}{C}

For C=20, D=8 ---> k=\frac{8}{20}=0.40

For C=12.5, D=5 ---> k=\frac{5}{12.5}=0.40

the values of k are equal

therefore

There is a proportional relationship between the two quantities

The linear equation is equal to

D=0.40C

7 0
3 years ago
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