A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 16 days. At the start of the experiment, 65.7 g is present.
(a) Lett be the time (in days) since the start of the experiment, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ei
(b) How much will be present in 13 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
08
X
Oina
3

Answer:

x = 67

Step-by-step explanation:

The two triangles are identail.

Answer:

x = 67

because 67 and x the same

Answer:

3π

Step-by-step explanation:

Given

Radius=9

Angle=60°

Since PQ is an arc

Perimeter of an Arc =(θ/360)×2πr

60/360×2π(9)

1/6×18π

3π

The maximum possible product of two numbers that have a sum of -8 is 16.

Let us name the two numbers "x" and "y".

We are aware of the following: x + y = -8

We're looking for the greatest possible product of x and y.

The number we're looking  that are as near together as feasible and have a sum of -8.

-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.

The sum of these two figures is:

x * y = (-4) * (-4) = 16

So, the maximum possible product of two numbers that have a sum of -8 is 16.

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James pays back approximately 82.33% of the total loan in interest over the 20-year period.

To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.

Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately

= 4.25% / 12

= 0.35% (4.25% annual rate divided by 12 months).

The monthly payment of $915.00 is comprised of both principal and interest.

In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.

To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months

20 years x 12 months/year = 240 months

and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.

To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:

$123,500 ÷ $150,000 x 100 ≈ 82.33%

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The percentage increase in the number of water bottles the company manufactured from February to April is 19%.

In March, the company manufactured 7% more water bottles than in February:

Number of water bottles in March = 4,100 + 7% of 4,100

Number of water bottles in March = 4,387

In April, the company manufactured 500 more water bottles than in March:

Number of water bottles in April = 4,387 + 500

Number of water bottles in April = 4,887

To find the percent increase from February to April, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

percent increase = (4,887 - 4,100) / 4,100 * 100%

percent increase = 787 / 4,100 x 100%

percent increase = 19%

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a) The future value of the account after 30 years can be calculated using the formula:

FV = P * ((1 + r/n)^(n*t))

where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:

FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60

So you will have $150,505.60 in the account after 30 years.

b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:

$300 * 360 = $108,000

c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:

$150,505.60 - $108,000 = $42,505.60

Answer:

a) you will have approximately $133,381.85 in the account in 30 years.

b) a total of $108,000 into the account over 30 years.

c) a total of $25,381.85 in interest over 30 years.

Step-by-step explanation:

The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413

Given data ,

Let the initial cost of the vehicle be = $ 29,800

Now , the rate of depreciation be r = 7 %

Let the number of years be n = 11 years

And , the exponential decay is given by the equation ,

x ( t ) = x₀ × ( 1 + r )ⁿ

On simplifying , we get

x ( 11 ) = 29800 ( 1 - 0.07 )¹¹

x ( 11 ) = 29800 ( 0.93 )¹¹

x ( 11 ) = 13,413.085

Hence , the cost of the vehicle after 11 years is A = $ 13,413

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Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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Tthe reserve rate was approximately 0.9434, or 94.34%.

This is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:

sum = a(1 - r^n) / (1 - r)

where a = 3000r is the first term.

As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:

3000r/(1-r) = 50,000

Solving for r, we get:

r = (50,000)/(3000 + 50,000) = 0.9434

Therefore, the reserve rate was approximately 0.9434, or 94.34%.

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The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°

A common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.

For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.

Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:

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Answer:

Step-by-step explanation:

no

The total area of the front of the figure is 21 [tex]feet^{2}[/tex].

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

To find the total area we need to add the area of the refrigerator and the area of the freezer.

The top part i.e refrigerator has a height of 5 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 5 * 3

                                                       = 15 [tex]feet^{2}[/tex]

The bottom part i.e freezer has a height of 2 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 2 * 3

                                                       = 6 [tex]feet^{2}[/tex]

The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section

                                                                   = 15 + 6 = 21[tex]feet^{2}[/tex]

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Answer:

3

Step-by-step explanation:

3 * 3 = 6

1/2 * 6 = 3 not 4.5

Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.

The 3 x 3 part turns into 9

So we have 1/2 x 9 or 9/2

Use long division to find that 9/2 gives a quotient of 4 and remainder 1

Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.

The "remainder 1" then leads to 1/2 = 0.5

quotient = 4

remainder = 1 ---> decimal portion = 1/2 = 0.5

So that's how we get to 4+0.5 = 4.5

You can use a calculator to see that 9/2 = 4.5

The result of engaging in the row multiplication operation in a matrix would be [ 1 /2   0 | 3 / 4 ]

[ -1   5 | 4 ].

First, you should multiply the first row by the value given of 1 / 4 to be:

( 1 / 4 ) x 2 = 1 / 2

( 1 / 4 ) x 0 = 0

( 1 / 4 ) x 3 = 3 / 4

Then you can replace the values found by the values in the matrix to be :

[ 1 / 2   0 | 3 / 4 ]

[   - 1     5 | 4      ]

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This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

A polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:

f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]

Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:

f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]

This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

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The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.

To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.

The volume of a cylinder is given by the formula  [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.

Container A has a radius of  [tex]4[/tex] feet and a height of 18 feet, so its volume is:

[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet

Container B has a radius of 5 feet and a height of 15 feet, so its volume is:

[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex]  cubic feet

When the water from Container A is transferred to Container B, the volume of water in Container B will be:

V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet

The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:

V(empty in  [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet

To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:

Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]

[tex]= (87\pi / 375\pi) \times 100[/tex]

[tex]= 23.2[/tex]%

Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

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Answer:

Step-by-step explanation:

The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).

To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:

0.3 * sqrt(100) = 3

So the margin of error in terms of the number of vehicles is ±3.

Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.

So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.

Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

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The total cost of the several items that originally cost $128.25 with a coupon for 35% off and sales tax of 4% is C. $86.70.

The original cost is discounted by 35% using a discount factor of 0.65 and increased by a sales tax factor of 1.04.

After the multiplications, the product shows the total cost that Mary incurred for buying the items.

Original cost of several items Mary is buying = $128.25

Coupon discount = 35%

Discount factor = 0.65 (100 - 35)

Sales tax rate = 4%

Sales tax factor = 1.04 (100 + 4)

The total cost of the items = $86.70($128.25 x 0.65 x 1.04)

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Answer: The coordinates of F' are (14, 21).

Step-by-step explanation:

       Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.

               (21, -14) ➜ (14, 21)

               The coordinates of F' are (14, 21).

To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).

Expected number of dog owners who brush their dog's teeth = 639 x 0.18

= 115.02 (rounded to the nearest whole number)

So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.

Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.

Using a standard normal distribution table or   calculator, we can find the z   scores corresponding to 35,000 miles and 40,000 miles...

z 1 = ( 35,000 - 40,000) / 3,700 = -1.35

z 2 = (40,000 -   40,000) / 3,700 = 0

Then, we can find the area between these z  scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:

P( -1.35  < Z < 0) = 0.4119 or 41.19%

What it means is that , about 41.19% of the tires would qualify for a free replacement.

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The cost of each chair and table is $2.5 and $8.75 respectively.

Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.

We need to find the cost of each chair and table,

Let the cost of each chair and table be x and y respectively,

3x+2y = 25.......(i)

5x+6y = 65.........(ii)

Multiply the equation (i) by 3 and subtract ii from i,

9x+6y = 75 - (5x+6y = 65)

4x = 10

x = 2.5

Put x = 2.5 in any equation to find the value of y,

3(2.5)+2y = 25

2y = 17.5

y = 8.75

Hence, the cost of each chair and table is $2.5 and $8.75 respectively.

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In the given diagram, angle WAX and angle YAU are vertical angles

From the question, we are to determine if angles WAX and YAU are vertical angles or not

Vertically opposite angles are pairs of angles that are opposite each other and formed by the intersection of two straight lines.

When two straight lines intersect, they form four angles at the point of intersection. Vertically opposite angles are the angles that are opposite each other, that is, they are located on opposite sides of the intersection point and are formed by the pair of opposite rays.

Vertically opposite angles are congruent, which means that they have the same angle measure. This property holds true for any pair of vertically opposite angles, regardless of the angle size or the orientation of the lines.

Hence, angle WAX and angle YAU are vertical angles

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The pressure using Pete's model based on the information will be 2.79 N/cm³

A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.

Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..

Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's

The pressure using Pete's model based on the information will be:

= 834 / 299.25

= 2.79 N/cm³

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Answer:

1.54

Step-by-step explanation:

Trapezium=

12+24=36

36 x (length) 15 = 540cm^2

Pressure= force/area

832/540 = 1.54N/cm^2

Answer:

Step-by-step explanation:

We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.

We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:

cos(60°) = 4ft/x

solving for x:

x = 4ft/cos(60°) = 8ft

Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:

tan(60°) = y/4ft

y = 4ft*tan(60°)

Then using Pythagorean's theorem we get:

x = √( (4ft)² + (4ft*tan(60°))²)

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Answer:

B) The other number is even.

Answer:

Step-by-step explanation:

To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.

We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's find the length of each side of the triangle:

AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34

BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136

CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170

Now, let's check if the Pythagorean theorem is satisfied:

AC² = AB² + BC²

170 = 34 + 136

Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.

We know that,

the distance between two points=√(x2-x1)²+(y2-y1)²

∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²

                                                                         =√(9+25)

                                                                         = √(34)

∴ The length of side AB = √(34)

Again,

The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]

                                                                      = √(100+36)

                                                                      = √136

∴ The length of side BC =√136

Also,

The distance between points A and D, AC= √(-8-5)²+(3-2)²

                                                                      = √(169+1)

                                                                      = √170

∴ The length of side AC=√170

Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170

Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,

AC²=170

BC²=136

AB²=34

Clearly, 170=136+34

or, AC²=AB²+BC²

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