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Sunny_sXe [5.5K]
2 years ago
5

How do we find the place value of 3a + b given that a=4, b=3, and c=-2

Mathematics
1 answer:
german2 years ago
4 0

Answer:

3a+b

3(4)+3

12+3

15

Step-by-step explanation:

You substitute the variables with the given numbers. I think this is correct.

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Find the equation of the line passing
Paraphin [41]
Rearrange the formula given to determine the slope, you will see that in y=mx+b form the slope is -2/3
You now have the slope (m) and two test points. Input those values into y=mx+b and you will have your answer!
I got y=(-2/3)x+(22/3) which I'm quite certain is correct.
8 0
3 years ago
Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv
Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

f_x = ycos(xy)

f_y = xcos(xy) - ze^{yz}

f_z = -ye^{yz}

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)  

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)

Where, again, the constant of integration depends on Z.

As a result,

f(x,y,z) = cos(xy) - e^{yz} + K(z)

if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0
3 years ago
Assume that the amount of beverage in a randomly selected 16-ounce beverage can has a normal distribution. Compute a 99% confide
ioda

Answer:

The question is incomplete, but the step-by-step procedures are given to solve the question.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.005 = 0.995, so Z = 2.575.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.575\frac{\sigma}{\sqrt{n}}

The lower end of the interval is the sample mean subtracted by M.

The upper end of the interval is the sample mean added to M.

The 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (lower end, upper end).

7 0
3 years ago
A community college has 150 word processors. The probability that any one of them will require repair on a given day is 0.025. T
DIA [1.3K]

Answer:

Binomial distribution

Step-by-step explanation:

For each processor, there is only two possible outcomes. Eithey they will require repair, or they will not. This means that we solve this problem using the binomial probability distribution.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

3 0
2 years ago
If angle 1 and angle 2 form linear pair and m angle 1 =50, then m angle = 2
Irina-Kira [14]
Measure of angle 2 would be 130 degrees because since it forms a linear pair the two angles added together have to equal 180 degrees so 
180 - 50 = 130
8 0
3 years ago
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