1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viktor [21]
3 years ago
6

The process of finding such equations to describe​ real-world phenomena is called mathematical​ _______. Such​ equations, togeth

er with the meaning assigned to the​ variables, are called mathematical​ _______.
Mathematics
1 answer:
Brrunno [24]3 years ago
3 0

Answer:

1st blank - mathematical modeling.

2nd blank - mathematical models.

Step-by-step explanation:

The process of finding such equations to describe real-world phenomena is called mathematical modeling.

Such formulas, together with the meaning assigned to the variables, are called mathematical models.

You might be interested in
3. What are the intersection points of the line whose equation is y=3x +3 and the
densk [106]

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

                                   → (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = \frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}

x = \frac{-7\pm \sqrt{169}}{10}

x = \frac{-7\pm13}{10}

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

6 0
3 years ago
Suppose that W1, W2, and W3 are independent uniform random variables with the following distributions: Wi ~ Uni(0,10*i). What is
nadya68 [22]

I'll leave the computation via R to you. The W_i are distributed uniformly on the intervals [0,10i], so that

f_{W_i}(w)=\begin{cases}\dfrac1{10i}&\text{for }0\le w\le10i\\\\0&\text{otherwise}\end{cases}

each with mean/expectation

E[W_i]=\displaystyle\int_{-\infty}^\infty wf_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac w{10i}\,\mathrm dw=5i

and variance

\mathrm{Var}[W_i]=E[(W_i-E[W_i])^2]=E[{W_i}^2]-E[W_i]^2

We have

E[{W_i}^2]=\displaystyle\int_{-\infty}^\infty w^2f_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac{w^2}{10i}\,\mathrm dw=\frac{100i^2}3

so that

\mathrm{Var}[W_i]=\dfrac{25i^2}3

Now,

E[W_1+W_2+W_3]=E[W_1]+E[W_2]+E[W_3]=5+10+15=30

and

\mathrm{Var}[W_1+W_2+W_3]=E\left[\big((W_1+W_2+W_3)-E[W_1+W_2+W_3]\big)^2\right]

\mathrm{Var}[W_1+W_2+W_3]=E[(W_1+W_2+W_3)^2]-E[W_1+W_2+W_3]^2

We have

(W_1+W_2+W_3)^2={W_1}^2+{W_2}^2+{W_3}^2+2(W_1W_2+W_1W_3+W_2W_3)

E[(W_1+W_2+W_3)^2]

=E[{W_1}^2]+E[{W_2}^2]+E[{W_3}^2]+2(E[W_1]E[W_2]+E[W_1]E[W_3]+E[W_2]E[W_3])

because W_i and W_j are independent when i\neq j, and so

E[(W_1+W_2+W_3)^2]=\dfrac{100}3+\dfrac{400}3+300+2(50+75+150)=\dfrac{3050}3

giving a variance of

\mathrm{Var}[W_1+W_2+W_3]=\dfrac{3050}3-30^2=\dfrac{350}3

and so the standard deviation is \sqrt{\dfrac{350}3}\approx\boxed{116.67}

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

\mathrm{Var}[W_1+W_2+W_3]

=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])

and since the W_i are independent, each covariance is 0. Then

\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]

\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3

and take the square root to get the standard deviation.

8 0
3 years ago
Find the sum of 0.2126 and 0.7145 correct to 3 significant figures​
Afina-wow [57]

Answer:

0.927

Step-by-step explanation:

add then round the last digit (it doesnt matter if it is a decimal number or not).

3 0
2 years ago
The graph of the function y=f(x)+35 can be obtained from the graph of y=f(x) by one of the following actions:
SCORPION-xisa [38]
I’m pretty sure it’s the second one if not I’m so sorry
3 0
3 years ago
Help me please I need helpp
kvv77 [185]

Answer:

172.8 = 32 x 5.40

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Need help don't know how to solve ​
    15·2 answers
  • Your family has a circular swimming pool. The radius of the pool is 9 feet and and its depth is 4 feet. What is the volume of th
    8·1 answer
  • Which shows all the prime factors for 96?
    13·2 answers
  • Traci can take one of 3 different buses to and from school (bus A, B or C). She randomly catches one bus in the morning and anot
    14·1 answer
  • Pls help quick number 2 and 3 pls!
    7·1 answer
  • Find the value of x from this figure
    13·2 answers
  • Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. If Erica made $42.80 on Monda
    14·2 answers
  • Let p= fg where f (0,5) and g (-4,-3). what is the direction angle of -3/2p?
    15·1 answer
  • Need assistance on this problem
    5·1 answer
  • Yaritza purchased 9 pints of ice cream for a party. If each guest will be served
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!