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4. Make up a system of equations with infinite<br> solutions

Taya2010 [7]

Answer:

$\left \{ {{x+y=1} \atop {2x+2y=2}} \right.$

Step-by-step explanation:

As long as the two equations represent the same straight line on the coordinate plane (they overlap), there will be infinite many intersections and infinite number of solutions.

6 0

2 years ago

In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen

Lesechka [4]

Step-by-step explanation:

Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.

Type ni xi si

Graded 42 0.486 0.187

No-fines 42 0.359 0.158

To find - a. Formulate the above in terms of a hypothesis testing problem.

b. Give the test statistic and its reference distribution (under the null hypothesis).

c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.

Proof -

a.)

Hypothesis testing problem :

H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

b)

Test statistic :

$Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }$

$Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }$

$Z = \frac{0.127 }{\sqrt{0.001468}}$

$Z = \frac{0.127 }{0.0377}$

⇒Z(cal) = 3.3687

Z(tab) = 1.96

As Z (cal) > Z(tab)

So, we reject H0 at 5% Level of significance

p-value = 0.99962

Hence

There is significant difference in mean conductivity at the two materials.

5 0

3 years ago

A store has a 25\%25% off sale on coats. With this discount, the price of one coat is \$34.50$34.50. What is the original price

timama [110]

Answer:

$46

Step-by-step explanation:

A percent is a portion of 100. If we receive 25% off then we pay 75% of the price. 100%-25%=75%. $34.50 is 75% of the original price. We find the new price through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare percent over percent to an equal ratio of $ to $.

$\frac{75}{100} =\frac{34.50}{y}$