MATHEMATICS COLLEGE

One number is 10 more than twice another. Their sum is 1. Find the numbers

Answers

Answer 1

Answer:

Answer:

-3 and 4

Step-by-step explanation:

We can start naming the first number x

Hence, the second number would be 10+2x

Set up an equation.

10+2x+x=1

Combine like terms

10+3x=1

Subtract 10 from both sides

3x=-9

Divide both sides by 3.

x=-3

The first number is he first is -3.

Plug that into the expression for the second number.

10+2x

10+2(-3)

10-6

The two numbers are -3 and 4.

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Recall that a test is statistically significant at a particular significance level if the null hypothesis is rejected when alpha is set at this value. Suppose a medical researcher conducts a statistical test of hypotheses and finds there is statistically significant evidence for the alternative hypothesis at a significance level alpha = 0.05. The researcher may conclude that...a) the test would also be statistically significant at level alpha = 0.01b) the test would also be statistically significant at level alpha = 0.10c) both of the above are trued) none of the above are true

Answers

Answer:

The correct option is: b) the test would also be statistically significant at level alpha = 0.10

Step-by-step explanation:

Consider the provided information.

Suppose a medical researcher conducts a statistical test of hypotheses and finds there is statistically significant evidence for the alternative hypothesis at a significance level alpha = 0.05.

It means that the test would be statically significant at level alpha = 0.10

As we know that if alternative hypothesis is true then the value of p must be less than α.

That means if the p-value is less than 0.05 then it must be less than 0.10.

Hence, the correct option is: b) the test would also be statistically significant at level alpha = 0.10

XYZW is a parallelogram with diagonals and that intersects at point A if YA=2t WA=3t-4 and XZ=5t find XA

Answers

Answer:

XA = 10 units

Step-by-step explanation:

Given parallelogram XYZW with:

XZ and YW intersect at point A.
YA = 2t
WA = 3t - 4
XZ = 5t
XA = ?

First, the diagonals bisect each- other:

YA = WA

Substitute values and solve for t:

2t = 3t - 4
3t - 2t = 4
t = 4

Find the diagonal XZ:

XZ = 5t = 5*4 = 20

Find the length of XA:

XA = XZ / 2 = 20 / 2 = 10

As Diagonals bisect each other in parallelogram

YA=WA
2t=3t-4
3t-2t=4
t=4

Diagonal XZ

5t
5(4)
20

Suppose y varies inversely with X, and y = 48 when x = 3. What is the value of x when y = 24?NO LINKS OR ANSWERING YOU DON'T KNOW.

a. 3
b. 12
c. 6
d. 24

Answers

Answer:

C. 6

Step-by-step explanation:

Recall that inverse variation is given by:

$\displaystyle y=(k)/(x)$

Where k is the constant of variation.

We know that y = 48 when x = 3. Substitute:

$\displaystyle (48)=(k)/((3))$

Solve for k:

$k=3(48)=144$

Hence, our equation is:

$\displaystyle y=(144)/(x)$

We want to find x when y = 24. Substitute:

$\displaystyle (24)/(1)=(144)/(x)$

Cross-multiply:

$24x=144$

Divide both sides by 24. Hence:

$x=6$

Our answer is C.

The expression below is a sum of cubes. 125x3 + 169

Answers

Answer:

$\text{The expression }125x^3+169\text{ is not the sum of cube}$

Step-by-step explanation:

Given the expression

$125x^3+169$

we have to tell the above expression is the sum of cube

The sum of cube is of the form

$a^3+b^3$ → (1)

$Expression: 125x^3+169$

125 is the cube of 5 and 169 is the square of 13

$125x^3+169$

$(5x)^3+13^2$

Comparing above with equation (1), we see the given expression is not the sum of cube

125x^3 = (5x)^3
125x^3 is the cube of 5x.

169 = 13^2
169 is the square of 13, but not the cube of a rational number.

The statement is false.

Lysera enjoys exploring her land on horseback with its lush green valleys and ancient forests. She can cover a great deal of ground on her horse, Princess Grey Dawn, traveling at 9 km/h. Unfortunately Lysera has allergies. How far would Lysera and Princess Gray Dawn have moved while Lysera’s eyes were shut for 0.50 s during a hard sneeze? (answer in kilometers)

Answers

Answer:

0.00125 km.

Step-by-step explanation:

Given,

Speed of the horse on which princess travelling, v = 9km/h

Time taken by Lysera to sneeze = 0.5 s

As we know

1 hour = 3600 seconds

$=>\ 1\ second\ =\ (1)/(3600)\ hour$

$=>\ 0.50 second\ =\ (1)/(3600)* 0.50$

$=\ 1.38* 10^(-4)\ hour$

So, time taken by Lysera to sneeze can be given by,

$t\ =\ 1.38* 10^(-4)\ hour$

According to definition of speed,

$Speed\ =\ (distance)/(time)$

=>distance = speed x time

$=\ 9\ km/h* 1.38* 10^(-4)\ hour$

= 0.00125 km

Hence, Princess Gray down will moved by 0.00125 km.

Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability that a randomly selected individual has the disease. Suppose n individuals are independently selected for testing. One way to proceed is to carry out a separate test on each of the n blood samples. A potentially more economical approach, group testing, was introduced during World War II to identify syphilitic men among army inductees. First, take a part of each blood sample, combine these specimens, and carry out a single test. If no one has the disease, the result will be negative, and only the one test is required. If at least one individual is diseased, the test on the combined sample will yield a positive result, in which case the n individual tests are then carried out. [The article "Random Multiple-Access Communication and Group Testing"† applied these ideas to a communication system in which the dichotomy was active/idle user rather than diseased/nondiseased.] If p = 0.15 and n = 5, what is the expected number of tests using this procedure? (Round your answer to three decimal places.)