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geniusboy [140]
3 years ago
11

PLEASE ONLY ANSWER IF YOU'RE GOING TO GIVE A LEGITIMATE ANSWER AND NOT USE ME AS POINTS

Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0
5/15 and -1/3 because 5 dived by 5 =1 and 15 dived by 5=3 so it’d be positive and negative 1/3
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Choose an algebraic expression for: 9 more than w
denis-greek [22]
The answer is a.w+9 because it means the w plus 9 more it the same as 9 more than w
3 0
3 years ago
F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa
DerKrebs [107]

a. Parameterize C by

\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath

with 0\le t\le1.

b/c. The line integral of \vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath over C is

\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt

=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt

=\displaystyle10\int_0^1\mathrm dt=\boxed{10}

d. Notice that we can write the line integral as

\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)

By Green's theorem, the line integral is equivalent to

\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy

where D is the triangle bounded by C, and this integral is simply twice the area of D. D is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0
3 years ago
The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
2 years ago
A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Fin
yarga [219]
Well the formula:

V = Bh
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54= 24w
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w= 54/24
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4 0
3 years ago
A company produces x units of a product per month, where c(x) represents the total cost and r(x) represents the total revenue fo
Nat2105 [25]

Answer:

The total profit P(x) or the month is P(x)=-0.5x^2+500x-350.

Step-by-step explanation:

A company produces x units of a product per month.

The total cost represents by the function C(x).

C(x)=300x+250

The total revenue represents by the function R(x).

R(x)=-0.5x^2+800x-100

The profit is the difference between revenue and cost.

P(x)=R(x)-C(x)

P(x)=-0.5x^2+800x-100-(300x+250)

P(x)=-0.5x^2+800x-100-300x-250

Combine like terms.

P(x)=-0.5x^2+(800x-300x)+(-100-250)

P(x)=-0.5x^2+500x-350

Therefore, the total profit P(x) or the month is P(x)=-0.5x^2+500x-350.

5 0
3 years ago
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