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natulia [17]
3 years ago
14

!!!!!!!!!!!!!!!!!!!!!!!!!PLEASe HELP!!!!!!!!!!!!!!!!!!!!!!! Solve for x: -8 < x - 1 < 5

Mathematics
1 answer:
Crank3 years ago
7 0

Answer:  -7 < x < 6

<u>Step-by-step explanation:</u>

Isolate x in the middle

-8 < x - 1 <  5

<u>+1 </u>  <u>    +1  </u>  <u>+1</u>         <em>add 1 to all three sides</em>

-7 < x      < 6

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Radium-226 has a half-life of 1620 years. for a 150 gram sample, how many grams will remain after 200 years?
VashaNatasha [74]
Ah, yes

if you start with P amount of something and the half life is h units (in years) and the time elapsed is t (in years) then the amount left is A

the equation is
A=P(\frac{1}{2})^\frac{t}{h}


so
given
h=1620
P=150
t=200
so
A=150(\frac{1}{2})^\frac{200}{1620}
A=150(\frac{1}{2})^\frac{10}{81}
use your calculator
A≈137.69781917515g
about 138grams left
3 0
3 years ago
May 06,
Andre45 [30]

Answer:

343 cubic inches

Step-by-step explanation:

7 times 7 times 7 is 343

3 0
2 years ago
The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool
Mama L [17]

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²  

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

4 0
3 years ago
From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade,
natulia [17]

Answer:

1222 billion dollars.

Step-by-step explanation:

To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:

In the period 1960-1970, we have x = 1, and the growth is:

y(1) = 43e(1/2) = 70.895

In the period 1970-1980, we have x = 2, and the growth is:

y(2) = 43e(2/2) = 116.8861

The growth in the following 3 periods are:

y(3) = 43e(3/2) =192.7126

y(4) = 43e(4/2) = 317.7294

y(5) = 43e(5/2) =523.8472

So the total growth in the period 1960 - 2010 is:

Total = y(1) + y(2) + y(3) + y(4) + y(5)

Total = 70.895 + 116.8861+192.726+317.7294+523.8472

Total = 1222.08\ billion\ dollars

Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.

6 0
3 years ago
Plz help me and plz show work
Flauer [41]

Answer:

21. The slope is 50.

22. 0

23. y=50x

24. $2600

Step-by-step explanation:

21. The slope of the line is 50. Slope is defined as "rise over run". As the line increases, each segment moves up the y-axis by $50, and to the right on the x-axis 1 segment. (Work: 50 divided by 1)

22. The y-intercept is (0, 0), or simply 0. If you look at the graph you can see that the line crosses the y-axis at the origin. This makes the y-intercept equal to 0.

23. The slope tells you that the student makes $50 every week. The y-intercept is 0. Using the formula y=mx+b, an appropriate equation would be y=50x.

24. The equation found in problem 23 can me used to determine how much a student makes (y) after "x" weeks. Substitute 52 for x to solve for y. This becomes y=50(52). This can be simplified to y=2600. This means that after 52 weeks, the student will have made $2,600.

8 0
3 years ago
Read 2 more answers
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