juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x)=10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container.

Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?

0.8 units
1.3 units
8.2 units
9.8 units

Answer:

9.7959 sec

Step-by-step explanation:

For the arrow to reach the same height as the bow again, - 4.9x^2+48x=0, 48=4.9x, x=48/4.9=9.7959

The time arrow take to come back to a height even with his bow height is 9.79 seconds.

We have an equation of the height of the arrow with respect to time -[tex]y = -4.9x^{2} +48x[/tex] where y is the height of the arrow in meters above Andrew's bow and x is the time in seconds since Andrew shot the arrow.

We have to find out - how long it takes the arrow to come back to a height even with his bow height.

It is an example of two - dimensional Projectile motion.

We have the function that depicts the variation of height of the arrow with respect to time given by -

[tex]y=-4.9x^{2} +48x[/tex]

To find the time taken by the arrow to come to a height even with his bow height, we should equate y = 0.

[tex]y=-4.9x^{2} +48x=0\\-4.9x(x-9.79)=0\\-4.9x=0\;\;\;and\;\;\;x-9.79=0\\x =0\;\;\;and\;\;\;x=9.79[/tex]

Time cannot be 0, hence the time arrow take to come back to a height even with his bow height is 9.79 seconds.

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Answer:

5/8 boxes

Step-by-step explanation:

1/3 ⋅ 1 7/8 = ?

1/3 ⋅ 15/8 = 15/24

15/24 = 5/8

5/8 boxes

Answer:

q = 3+1/2 r

Step-by-step explanation:

10q -5r = 30

Add 5r to each side

10q -5r+5r = 30+5r

10q = 30 +5r

Divide by 10

10q/10 = 30/10 +5r/10

q = 3+1/2 r

The image of this question is missing and so i have attached it.

Answer:

dd/dt = 4.47 ft/s

Step-by-step explanation:

From the image attached, let's denote the following;

d = horizontal distance beneath pulley

h = height of pulley

l = diagonal from the pulley to the head of the person

v = velocity of rope rising

Using pythagoras theorem;

l² = d² + h²

Differentiating with respect to time and considering h = c^(te) gives;

2l(dl/dt) = 2d(dd/dt)

We are given;

d = 20 ft

h = 10 ft

v = 4 ft/s

We know that velocity in this case is change in diagonal distance with time. Thus;

v = dl/dt = 4 ft/s

From earlier, we saw that;

2l(dl/dt) = 2d(dd/dt)

Thus, reducing it gives

(dl/dt)(l/d) = dd/dt

Now, l² = d² + h²

l = √(d² + h²)

Also, v = dl/dt = 4

Thus;

4(√(d² + h²))/d = dd/dt

4(√(20² + 10²))/20 = dd/dt

dd/dt = 4.47 ft/s

Answer:

[tex]\left(\dfrac{8}{7} , \ \dfrac{17}{35} \right)[/tex]

Step-by-step explanation:

The given system of equations is presented as follows;

[tex]\dfrac{s}{2} + 5 \cdot t = 3[/tex]

3·t - 6·s = 9

Making t the subject of both equations, gives;

In the first equation; t = (3 - s/2)/5

In the second equation; t = (9 + 6·s)/3

Equating both values of t to find the the values that satisfies both equations, gives;

(3 - s/2)/5 = (9 + 6·s)/3

3 × (3 - s/2) = 5 × (9 + 6·s)

9 - (3/2)·s = 45 + 30·s

45 - 9 = (30 + (3/2))·s

36 = (63/2)·s

s = 36/(63/2) = 8/7

t = (3 - s/2)/5

∴ t = (3 - (8/7)/2)/5 = 17/35

Therefore, the ordered pair is (8/7, 17/35)

Answer:

7x the answer i think

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]

Step-by-step explanation:

We are asked to check is -2 is the solution of the following equation.

[tex]2-x= 4x+3[/tex]

We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.

[tex]2- (-2) = 4(-2)+3[/tex]

Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Let's start with the left side.

[tex]2+2= 4(-2)+3 \\[/tex]

[tex]4= 4(-2)+3[/tex]

Now solve the right side. Remember to multiply first.

[tex]4= -8+3[/tex]

[tex]4= -5[/tex]

[tex]4\neq -5[/tex]

4 is not equal to -5, so -2 is not the solution for this equation.

Answer:

The value of this number is 31.

Step-by-step explanation:

To solve this you could set up an equation and solve for x.

Sum means add, so you are going to add 2n and 13 to get 75.

2n + 13 = 75

Subtract 13 from both sides.

2n = 62

To get n alone, divide by 2 on both sides.

n = 31

The value of this number is 31.

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[tex]we conclude that option B:[/tex]

[tex]y + 5 = -\frac{1}{2}*(x - 3)^2[/tex]

[tex]Is the graphed function.[/tex]

On the graph we can see a parabola that opens downwards, so it has a negative leading coefficient.

We also can see that the vertex of the parabola is on the point (3, -5)

Then the equation of the parabola is something like:

y + 5 = a*(x - 3)^2

Where a is a negative real number.

The only option of this form is option B, so we conclude that option B:

[tex]y + 5 = -\frac{1}{2}*(x - 3)^2[/tex]

Is the graphed function.

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9 in 8956 = 900

9 in 95675 = 90000

9 = 9 in 124569

9 in 68795 = 90

90000 = 9 in 2549652.........

hope it helps...

Answer:

O Yes, because 1 kilogram = 1000 grams, and 1 liter = 100 centiliters.

Yes, because 1 gram per liter is the same as 1 kilogram per centiliter.

Step-by-step explanation:

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

Answer: He bought 20 ice cream bars and 14 popsicle

Step-by-step explanation:

To solve this I used the elimination method, you could use substitution as well

Here are our two equations

x+y=34 Because the total number of ice creams bought must be given to 34 children and no more

2x+5y=128 because that is the cost for each ice cream and the amount he spent

For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68

2x+5y=128 Then we get

3y=60 so

y=20

Now we can go back to the first equation and plug in y.

x+20=34

  -20  -20

x=14

So he bought 14 popsicles and 20 ice cream bars.

Answer:

SR = 22 cm

Step-by-step explanation:

area = bh/2

(21 cm)(h)/2 = 231 cm^2

21h = 462 cm

h = 22 cm

SR = 22 cm

Answer:

Step-by-step explanation:

There are 2 possibilities. Either you need to know the angles connect to the common side (that would give you ASA) or you need to know GF = UT. The latter would give you SAS

Answer:

all of them are REAL numbers

1. is also RATIONAL

2. is also IRRATIONAL

3. is also IRRATIONAL

4. is also NATURAL, WHOLE, INTEGER and RATIONAL

5. is also INTEGER and RATIONAL

6. incorrect, because integer is just the whole numbers extended by their additive counterparts (the negative natural numbers). in other words, their absolute values are whole numbers. 5.5 as well as -5.5 are not fitting that criteria.

7. incorrect, because this pattern does not fit the definition of a radical number, where the number eventually begins to repeat the same finite sequence of digits over and over. in this example the pattern is not based on a finite sequence of digits.

Answer:

x=24,y=33

hopefully this answer can help you to answer the next question

Answer:

x=-3

Step-by-step explanation:

Answer:

A. 272 cm^2

Step-by-step explanation:

The area of the rectangle is 17cm * 7cm = 119 cm^2

The area of the right triangle is (25-7) * 17cm * 1/2 = 153cm^2

Answer: 119+153 = 272 cm^2

Answer: 75%

Step-by-step explanation:

Only 9 students have taken fewer than 21 courses

9/12 = 0.75 or 75%

Answer:

2.07648468018

Step-by-step explanation:

Answer:

2,400,000,000,000

Step-by-step explanation:

2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)

So by moving the decimal point 12 times you get this: 2,400,000,000,000

The reason why there are only 11 zeroes is because the 4 was a decimal place  to the right of 2, thus losing a zero.

Answer:

6

Step-by-step explanations:

The remainder is what is left over after dividing whatever from d. So if you add one to d, then the remainder would increase from 5 to 6.

Hope this helps.

Answer:

see below

Step-by-step explanation:

point A(x,y) becomes A'(-x,-y).

So point E (-3,-5) becomes  E'( 3,5)

F (-1,-1) becomes F'(1,1)

and G (0,-5) becomes G'( 0,5)

Answer:

hope this help

Step-by-step explanation:

Answer:

90

51

10

Step-by-step explanation:

We know

[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]

[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto x=47(0.9)[/tex]

[tex]\\ \sf\longmapsto x=42.3[/tex]

=========================================================

Explanation:

Let x be the unknown angle we want to find. This angle is in degrees.

The diagram shows 19 is the opposite of this angle, and the side 35 is adjacent to the angle.

We use the tangent ratio to tie the two sides together

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(x) = \frac{19}{35}\\\\x = \tan^{-1}\left(\frac{19}{35}\right)\\\\x \approx 28.4956386\\\\x \approx 28\\\\[/tex]

Note: The notation [tex]\tan^{-1}[/tex] refers to the inverse tangent, or arctangent.

Add the ratio: 3 + 5 = 8

Divide total students by that:

32/8 = 4

The ratio for girls is 3, multiply the 4 by 3:

4 x 3 = 12

There are 12 girls

Answer:

12

Step-by-step explanation:

If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:

[tex]\frac{3}{8}[/tex] of 32

= [tex]\frac{3}{8} * 32[/tex]

[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]

There are 12 girls.

Answer: 3 and 47/100

Step-by-step explanation:

Answer:

a) 30

b)600pi

Step-by-step explanation:

For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30

Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi