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Klio2033 [76]
2 years ago
13

For centuries, mathematics seemed to exist in service to the natural sciences. Many of the great mathematical breakthroughs, lik

e Newton's Calculus, were spearheaded in the effort to solve scientific questions. In the nineteen century, though, mathematicians made it clear that the primary object of mathematical study were the abstract creations of mathematics—numbers and shapes and functions and their more abstruse extensions—irrespective of whether this study has any bearing on scientific investigation. Therefore, mathematics is not properly one of the natural sciences.
Which of the following is an assumption that supports drawing the conclusion above from the reasons given for that conclusion?

A) Mathematics can also be used to serve social sciences, such as economics.
B) The object of a natural science must be something tangible that can be perceived by the senses.
C) Some great scientists, like Einstein, by their own admission, were not very good at math.
D) If one discipline serves another discipline, it can never rise to the same rank as the discipline it serves.
E) At times in the natural sciences, especially in Physics, mathematical calculations have led to extraordinary breakthroughs in scientific understanding.
Mathematics
1 answer:
adell [148]2 years ago
4 0

Answer:

b,d

Step-by-step explanation:

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8x + 20y = 20<br> 14x + 35y = k<br> For the above system of equations to be consistent, k must equal
Goshia [24]

Answer:

  35

Step-by-step explanation:

The equations will be "consistent" when they describe lines that are not parallel.

<h3>Slopes</h3>

The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:

  line 1 slope = -8/20 = -2/5

  line 2 slope = -14/35 = -2/5

These lines have the same slope, so will be parallel unless they have the same y-intercept.

<h3>Y-intercept</h3>

The y-intercept of each line is the ratio of the constant to the y-coefficient:

  line 1 y-intercept = 20/20 = 1

  line 2 y-intercept = k/35

We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...

  k/35 = 1

  k = 35

For the equations to be consistent, we must have k = 35.

__

<em>Additional comment</em>

Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."

Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)

7 0
2 years ago
Given right triangle MUD such that mD = 23.1 and d = 38, which of the following statements are true? Round to the nearest hundre
Zigmanuir [339]
∠M=90°-23.1°=66.9° - it's a right answer.

u=d/sin∠D=97.25
m=cos∠D*u=89.52
4 0
2 years ago
Read 2 more answers
Help please! answer correctly for brainliest . ( look at picture for question and answer choices )
Alik [6]

Answer:

C

Step-by-step explanation:

7 0
3 years ago
What is the volume of this shape?
jenyasd209 [6]
Answer:
600 ft cubed
Step-by-step explanation:
Triangle volume formula V = 1/2(l*w*h)
1/2(4*12*9) = 216 ft cubed

Formula for rectangular prism V = (l*w*h)
(4*16*6) = 384 ft cubed

Adding the values: 600 ft
6 0
2 years ago
Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table
hammer [34]

Answer:

Step-by-step explanation:

a. P(Z > 1.12) = 1-N(1.12) = 1-0.8686431=0.1313569

b. <em>P(Z S-2.35)</em>  => P(Z <= 2.35) = 0.009386706

(please check interpretation of question b)

c. <em>POSZ s 1.34)</em> => P(0 <= Z <= 1.34) =  0.9098773 - 0.5 = 0.4098773

(please check interpretation of question c)

d. P(-0.8 sz s 2.44) => P(-0.8 <= 2.44) = 0.9926564 - 0.2118554 = 0.780801

(please check interpretation of question d)

7 0
3 years ago
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