MATHEMATICS HIGH SCHOOL

2. Which of the following is contained in the solution for theinequality 5x < 3(x + 2) + 2 ? Justify your answer for full credit.
A.
4
C. 7
B.
2
D.
15

Answers

Answer 1
Answer: The answer should be D
Answer 2
Answer: X>- 16/3
I used the calculator

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Solve the equation . (-2 1/7)p=-3

Answers

Answer:

p = (7)/(5)

Step-by-step explanation:

change the mixed number to an improper fraction

- 2 (1)/(7) = - (15)/(7), hence

- (15)/(7) p = - 3 ( multiply both sides by 7 )

- 15p = - 21 ( divide both sides by - 15 )

p = (-21)/(-15) = (7)/(5)

Final answer:

To solve this question, convert '-2 1/7' to an improper fraction (-15/7), then divide both sides of the equation by this value. This simplifies to p = 1.4 which is the solution.

Explanation:

In order to solve the equation (-2 1/7)p=-3, it's helpful to remember that multiplying each side of an equation by the same value does not change the solution. In this case, (-2 1/7) represents a fraction (-15/7) when converted to an improper fraction. Now, to isolate p on one side of the equation, divide both sides of the equation by (-15/7). This provides the solution: p = -3 / (-15/7), which simplifies to p = 1.4. Therefore, the solution to the equation is p = 1.4

Learn more about Solving Equations here:

brainly.com/question/18322830

#SPJ3

Point G is located at (3, −1) and point H is located at (−2, 3). Find y value for the point that is 2 over 3 the distance from point G to point H.

Answers

Answer: The answer is (5)/(3).

Step-by-step explanation:  Given that the co-ordinates of point G and H are (3, -1) and (-2, 3) respectively.

We are to find the y-value of the point P that is located at two-third distance from point G to point H.

As shown in the attached figure, the ration in which the point P divides the line segment GH is 2 : 1.

Therefore, the co-ordinates of point P will be

\left((2* (-2)+1* 3)/(2+1),(2* 3+1* (-1))/(2+1)\right)\n\n\n=\left((-4+3)/(3),(6-1)/(3)\right)\n\n=\left((-1)/(3),(5)/(3)\right).

Thus, the y-value of the point P is (5)/(3).
B. 1.67
m : n = 2 : 1
 ( x, y ) = ( (1*3 + 2*(-2))/(2+1) ;  (1 * (-1) + 2 * 3) /(2 + 1) ) =
 = ( (3-4)/3  ; (-1+6)/3 ) 1.67

The width of a rectangular window is 2 feet more than its height. If the area is 35 square feet, what is the height?

Answers

h-height\nh+2-width\n35 ft^2-Area\n\nArea=h(h+2)\n\nh(h+2)=35\nh^2+2h-35=0\n\na=1;\ b=2;\ c=-35\n\n\Delta=b^2-4ac;\ if\ \Delta > 0\ then\ h_1=(-b-\sqrt\Delta)/(2a)\ and\ h_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=2^2-4\cdot1\cdot(-35)=4+140=144;\ \sqrt\Delta=√(144)=12\n\nh_1=(-2-12)/(2\cdot1)=(-14)/(2)=-7 < 0;\ h_2=(-2+12)/(2\cdot1)=(10)/(2)=5\n\nAnswer:Height\ is\ 5\ ft.

A company has developed a new ink-jet cartridge for its printer that it believes has a longer life-time on average than the one currently being produced. To investigate its length of life, 40 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. Calculate the appropriate test statistic to test the hypotheses.

Answers

Answer:

Step-by-step explanation:

Given that

mu = 1502.5 pages

Sample mean x bar = 1511.4 pages

Std deviation =s= 35.7 pages

Sample size n = 40

By assuming random samples since only sample std dev is know we can say that sample mean x bar follows a t distribution with

mean =1511.4 and std error =(35.7)/(√(40) ) \n=5.64

Test statistic t = Mean diff/STd error = 1.613

df = 39

What multiplies to get -210 and adds up to 11

Answers

210÷10=21. ....10 and 21
make the 10 neg n 21 pos

-10x21=-10
-10+21=11

Jack is playing a game where he flips a coin and rolls a number cube labeled 1 through 6. He listed the possible outcomes in the sample space shown below.{(H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Which two elements did he leave out by mistake?

(H, 1) and (T, 6)
(H, 6) and (T, 1)
(H, 2) and (T, 6)
(T, 1) and (T, 6)

Answers

Answer:  The correct option is (A) (H, 1) and (T, 6).

Step-by-step explanation: Given that Jack is playing a game where he flips a coin and rolls a number cube labeled 1 through 6.

Jack listed the possible outcomes in the sample space 'S'' as follows:

S' = {(H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

We are given to select the correct option that contains the two elements Jack left out by mistake.

The sample space for the event of flipping a coin is {H, T}

and

the sample space for the event of rolling a number cube labeled 1 through 6 is {1, 2, 3, 4, 5, 6}.

Let, 'S' represents the actual sample space for the event.

Then, we get

S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}.

Comparing S with S', the two missing elements were (H, 1) and (T, 6).

Thus, the correct option is (A).
The answer is (H, 1) and (T, 6)
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