Convert log10 1000 =3 to an exponential statement

10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

9966 [12]

$a_{5}=a+4d=11\\a_{10}=a+9d=41$

Solve the above equations,

$a_{10}-a_{5}=41-11\\a+9d-a-4d=30\\5d=30\\d=6\\a=11-24=-13$

First term is -13.

4 0

2 years ago

Read 2 more answers

Help! Need by 10:30 to turn in and I'm confused!

Alecsey [184]

Answer:

8 boxes of tissues

5 bags of cough drops

Step-by-step explanation:

You need to write a system of equations.

x = number of tissue boxes

y = number of cough drop bags

x (number of tissue boxes) + y (number of cough drop bags) = 13 (total number of tissues and cough drops combined.

So, your first equation is

x + y = 13

Then, you need to write the second equation.

(1.69 [cost of 1 tissue box] * [number of tissue boxes]) + (1.19 [cost of one bag of cough drops] * [number of cough drop bags] = 19.47 [total cost of tissues and cough drops]

That's a lot to read, so here's the equation simplified!

1.69x + 1.19y = 19.47

Now, you have two equations:

x + y = 13

1.69x + 1.19y = 19.47

I would solve with the substitution method.

the first equation can be changed to x = 13 - y by subtracting y from both sides.

Then, your two equations are:

x = 13 - y

1.69x + 1.19y = 19.47

Now, you can plug in that value of x into the second equation!

1.69(13 - y) + 1.19y = 19.47

21.97 - 1.69y + 1.19y = 19.47

subtract 21.97 from both sides

-1.69y + 1.19y = -2.5

Add the y values

-0.5y = -2.5

divide both sides by -0.5

so, y equals 5 bags of cough drops

now that you know what y equals, plug it back into your original equation to find x!

x + y = 13

plug in y

x + 5 = 13

x = 8

so, x = 8 boxes of tissues

Hope this helps! Let me know if you have any questions!

8 0

3 years ago

Prove that if {x1x2.......xk}isany

Radda [10]

Answer:

See the proof below.

Step-by-step explanation:

What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where $n\geq 2$ . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"

Proof

Since we have a if and only if w need to proof the statement on the two possible ways.

If X is linearly dependent, then a vector is a linear combination

We suppose the set $X= (x_1, x_2,....,x_n)$ is linearly dependent, so then by definition we have scalars $c_1,c_2,....,c_n$ in C such that:

$c_1 x_1 +c_2 x_2 +.....+c_n x_n =0$

And not all the scalars $c_1,c_2,....,c_n$ are equal to 0.

Since at least one constant is non zero we can assume for example that $c_1 \neq 0$ , and we have this:

$c_1 v_1 = -c_2 v_2 -c_3 v_3 -.... -c_n v_n$

We can divide by c1 since we assume that $c_1 \neq 0$ and we have this:

$v_1= -\frac{c_2}{c_1} v_2 -\frac{c_3}{c_1} v_3 - .....- \frac{c_n}{c_1} v_n$

And as we can see the vector $v_1$ can be written a a linear combination of the remaining vectors $v_2,v_3,...,v_n$ . We select v1 but we can select any vector and we get the same result.

If a vector is a linear combination, then X is linearly dependent

We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select $v_1$ and we have this:

$v_1 = c_2 v_2 + c_3 v_3 +...+c_n v_n$

For scalars defined $c_2,c_3,...,c_n$ in C. So then we have this:

$v_1 -c_2 v_2 -c_3 v_3 - ....-c_n v_n =0$

So then we can conclude that the set X is linearly dependent.

And that complet the proof for this case.

5 0

3 years ago

A researcher wants to estimate the mean commute time of residents in Westchester County. The researcher samples 40 commuters and

Ksenya-84 [330]

Answer:

21.759

Step-by-step explanation:

Given that :

Mean (m) = 25

Standard deviation (s) = 12.5

Sample size (n) = 40

α = 90%

The confidence interval is obtained using the relation:

Mean ± Zcritical * s/sqrt(n)

Zcritical at 90% confidence interval = 1.64

25 ± 1.64 * (12.5/sqrt(40))

Lower boundary : 25 - 1.64(1.9764235) = 21.75866546

Upper boundary : 25 + 1.64(1.9764235) = 28.24133454

(21.759, 28.241)

Hence, lower bound of confidence interval is : 21.759

4 0

2 years ago

The fuel capacity of a popular hybrid car is 11.9 gallons. The function for this situation is f(x) = -0.02x + 11.9, where x repr

Alla [95]

Answer:

-0.02 gallons per mile

Step-by-step explanation:

You're in luck. The fuel consumption of the car is linear, and the slope - ie, the coefficent of the x term gives you the rate of change. In this case, it's -0.02 gallons per mile.

6 0

3 years ago