Shawn earned 5% commission on a $500 sale. How much did he earn

Answer:

90.379826087 times

Step-by-step explanation:

99779.328 ÷ 1104 = 90.379826087

Answer:

the time taken for the radioactive element to decay to 1 g is 304.8 s.

Step-by-step explanation:

Given;

half-life of the given Dubnium = 34 s

initial mass of the given Dubnium, m₀ = 500 grams

final mass of the element, mf = 1 g

The time taken for the radioactive element to decay to its final mass is calculated as follows;

\(1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s\)

Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.

The time required to decay 500 grams to 1 gram is 304.8 seconds and this can be determined by using the given data.

Given :

Dubnium-262 has a half-life of 34 s.

Final mass = 1 gram

Initial mass = 500 gram

Time taken by a radioactive element to decay is:

\(1 = 500(0.5)^{\frac{t}{34}}\)

Simplify the above equation.

\(\rm \dfrac{1}{500} = (0.5)^{\frac{t }{34}}\)

Now, take the log on both sides in the above equation.

\(\rm log(0.002 ) = \dfrac{t}{34}\times log(0.5)\)

\(\rm \dfrac{log(0.002)}{log(0.5)} \times 34 = t\)

t = 304.8 sec

So, the time required to decay 500 grams to 1 gram is 304.8 seconds.

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Answer:

1: 90º

2: 25º

Step-by-step explanation:

Hey there!

Well we know that all the middle angles are 90º right angles,

so we can conclude that angle 1 is 90º.

All the angles in a triangle add up to 180 so we can set up the following,

65 + 90 + x = 180

Combine like terms

155 + x = 180

-155 to both sides

x = 25º

So angle 2 is 25º.

Hope this helps :)

Answer:

Below

Step-by-step explanation:

From the kite you easily notice that 1 is a right angle so its mesure is 90°.

2 is inside a triangle. This triangke has two khown angles: a right one and a 65° one.

The sum of a triangle's angles is 180°.

● (2) + 90+65 = 180

● (2) +155 =180

● (2)= 180-155

●(2) = 25°

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

The scientist needs to use 90 ounces of solution A and 60 ounces of solution B to obtain 150 ounces of a mixture that is 75% salt.

The scientist needs to determine the amount of each solution needed to make 150 ounces of a mixture containing 75% salt. To solve this problem, the following variables are used:
- Let X represent the number of ounces of solution A used
- Let Y represent the number of ounces of solution B used
Since the scientist wants to obtain 150 ounces of a mixture, the following equation can be used to relate X and Y:
X + Y = 150
To determine the amount of salt in the content loaded

the following equation can be used:
0.65X + 0.90Y = 0.75(150)
Simplifying this equation:
0.65X + 0.90Y = 112.5
To solve this system of equations, either substitution or elimination method can be used. Let us use the substitution method here:
X + Y = 150
Y = 150 - X
Substitute 150 - X for Y in the second equation:
0.65X + 0.90(150 - X) = 112.5
0.65X + 135 - 0.90X = 112.5
-0.25X = -22.5
X = 90
Substitute the value of X into the first equation to find Y:
X + Y = 150
90 + Y = 150
Y = 60
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Answer:

The magnitude of the boat's velocity is 5.66 m/s

Step-by-step explanation:

Given;

Radius of curvature of the circular path, r = 40 m

speed of the boat, v = 0.8 t m/s

The magnitude of the boat's velocity when it has traveled 20 m is ?

a = dv / dt,

v = 0.8 t (differentiate with respect to t)

dv / dt = 0.8 = a

thus, a = 0.8 m/s²

If the boat starts from rest, initial velocity, u = 0

Apply kinematic equation, to solve for the boat velocity at 20 m

v² = u² + 2as

v² = 0 + 2 x 0.8 x 20

v² = 0 + 32

v² = 32

v = √32

v = 5.66 m/s

Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s

Answer:

The answer is B. i.e. 6.6units.

The term central location or central tendency relates to the way data tend to cluster around some middle or central value

It is a number located towards the center of the distribution of the values of a series of observations, that are called measures, in which the set of data is located. The most commonly used measures of central tendency are: mean, median and mode.

Statistics is a branch of mathematics that allows you to collect, organize and analyze data according to the need you have, for example: to obtain a result, compare information, make better decisions, among many other things.

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Answer:

1.28

is the answer :) since the number after 7 is 5 you round up

Answer: 1.28

The 7 is in the hundredth's place, and since there is a 5 after it, we round up.

Answer:

Step-by-step explanation:

200 divides into 1000 so that is part of the HCF.

x^2 and x^3 are present so the HCF contains x^2

y^2 and y^5 are present so the HCF contains y^2

HCF = 200*x^2 * y^2

The height of the ball as a function of the time is given by the following formula:

A. Maximum height of the ball

To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:

Solving the last equation for t, we get time t when the height is maximum:

So the maximum height is given by the value of h(t) when t = 2.5:

The maximum height is 196ft.

B. Time until the ball hits the ground

The ball will hit the ground when h(t) = 0. So we must find the value of t such that:

Solving this equation is equivalent to finding the roots of a second-order polynomial:

Where:

• a = -16,

• b = 80,

• c = 96.

The roots of this polynomial are given by the following formula:

s

A. The maximum height of the ball is 196 ft.

B.

Answer:

                          Have a cat         Do not have cat

Have a dog                 7                            5

Do not have a dog      6                            0

Step-by-step explanation:

                                           Have a cat   Do not have a cat

Have a dog                              7                 5

Do not have a dog                     6               0

The interesection of the two circles represents the number of patrons that have both dogs and cats. The number in the circle that represents the number of people that have dogs only is 5 and the number in the circle that represents the number of people that have cats only is 6.

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Answer:90

Step-by-step explanation:

Answer:

(1, 2)

Step-by-step explanation:

You are moving up 4 units, so that means you need to add to the y coordinate, which is 0.  0 + 4 = 4

The new coordinate is (1, 4)

Now you move down 2 units, that means you need to subtract from the y coordinate, which is now 4. 4 - 2 = 2

You will end at (1, 2)

The given series is of the form Σn^(-5), so we have p = 5. Since p > 1, the series converges. The series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

We can use the integral test to determine whether the series ∑(n=5 to infinity) 4/((n-1)^5) converges or diverges. According to the integral test, if the integral of the function f(x) = 4/((x-1)^5) from 4 to infinity converges, then the series converges. If the integral diverges, then the series diverges.

Let's evaluate the integral:

∫(4 to infinity) 4/((x-1)^5) dx = [-1/4(x-1)^4] (4 to infinity)

= [-1/4((infinity-1)^4 - (4-1)^4)]

= [-1/4(infinity^4 - 81)]

= infinity

Since the integral of f(x) diverges, we conclude that the series ∑(n=5 to infinity) 4/((n-1)^5) also diverges. Therefore, the series is not convergent.

To further illustrate this, let's consider the limit comparison test. We can compare the series to a known divergent p-series, such as the series ∑(n=1 to infinity) 1/n^2. We can then take the limit as n approaches infinity of the ratio of the two series:

lim(n→∞) (4/((n-1)^5)) / (1/n^2)

= lim(n→∞) (4n^2/(n-1)^5)

Applying L'Hopital's rule, we get:

= lim(n→∞) (8n/(n-1)^6)

= 8/lim(n→∞) (n-1)^(-6)

Since the limit of (n-1)^(-6) is zero, the limit comparison test tells us that the series ∑(n=5 to infinity) 4/((n-1)^5) diverges, since it can be compared to the divergent series ∑(n=1 to infinity) 1/n^2.

In conclusion, the series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

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Answer:

  +4.5 feet

Step-by-step explanation:

The change in level is computed by subtracting the beginning level from the ending level.

  change = ending - beginning

  change = (6 ft) - (1.5 ft)

  change = 4.5 ft

The change in level from 7 pm to 8 am was +4.5 feet.

Answer:

D

Step-by-step explanation:

-12 + 5 ≤ 4

-7 ≤ 4

this inequality is true

The answer to the question is D

Answer:

27218

Step-by-step explanation:

17000 * (1.04)^12

Then, find the number in the whole number place 7 and look one place to the right for the rounding digit on the right side of the decimal point 5. 5 or more, let it soar. 4 or less, let it rest.

ANSWER:

27218

Answer:

256= 4 power 4 and 125 = 5 power 3

The length οf οne side οf the square is √17 and the area οf the square is 17 square units.

Cοοrdinate geοmetry is a branch οf mathematics that uses algebraic equatiοns tο describe the relatiοnships between pοints and shapes in a plane. It invοlves using the Cartesian cοοrdinate system tο represent pοints with οrdered pairs οf numbers.

We can start by finding the distance between twο οppοsite vertices οf the square using the distance fοrmula:

d = √[(x2 - x1)² + (y2 - y1)²]

Let's find the distance between the pοints (5, 4) and (1, 5), which are οppοsite vertices οf the square:

d = √[(1 - 5)² + (5 - 4)²] = √[16 + 1] = √17

Sο the length οf οne side οf the square is √17.

Tο find the area οf the square, we can use the fοrmula:

area = side²

Substituting the value οf the side that we fοund abοve, we get:

area = (√17)² = 17

Therefοre, the area οf the square is 17 square units.

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Answer:

Billy= 14

Josh= 12

I think i over thank this

Answer:

Step 1 : Multiple both sides by 2

3x + 2y = 1

4x - 2y = 20

Step 2 : Eliminate 1 variable by adding the equations

7x = 21

Step 3 : Divide both sides by 7 to solve for x

x = 3

Step 4: Substitute the value of x into 3x + 2y = 1

3(3) + 2y = 1

Step 5: Solve for y

2y = 1 - 9

2y = -8

*divide by 2

y = - 4

Solution:

(x,y) = (3, -4)

Answer:

3

Step-by-step explanation:

m = y2 - y1 / X2 - X1

-1 is your X1 . -4 is your y1

2 is your X2 . 5 is your y2

just replace what's in the equation

m= 5 - (-4) / 2 - (-1)

m= 9 / 3

m = 3

hi there

the explanation is in the picture

The required number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
The number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

The inequality may involve a variable x, and the number line would represent all possible values of x that satisfy the inequality. The solutions could be, for example, all values of x greater than 3, in which case the number line would start at 3 and extend to the right to represent all values of x greater than 3. Alternatively, the solutions could be all values of x less than or equal to -2, in which case the number line would start at -2 and extend to the left to represent all values of x less than or equal to -2.

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If the polynomial p(x) is divided by (x-1) three times and has a remainder of 1 at the end, then -1 is a double root of p(x). This means that (x+1) is a factor of p(x) raised to the power of 2.

When a polynomial is divided by (x-1), the remainder represents the value of the polynomial at x=1. Since the remainder is 1, it implies that p(1) = 1. Dividing p(x) by (x-1) three times indicates that the polynomial has been factored by (x-1) three times. Consequently, the polynomial can be written as p(x) = (x-1)^3 * q(x) + 1, where q(x) is the quotient obtained after dividing p(x) by (x-1) three times. Since the remainder is 1, it means that when x=1, p(x) leaves a remainder of 1.

Thus, (1-1)^3 * q(1) + 1 = 1, which simplifies to q(1) = 0. This implies that (x-1) is a factor of q(x), meaning that q(x) can be written as q(x) = (x-1) * r(x), where r(x) is another polynomial.

Substituting this into the earlier expression for p(x), we get p(x) = (x-1)^3 * (x-1) * r(x) + 1. Simplifying further, p(x) = (x-1)^4 * r(x) + 1. Now, we can see that p(x) is divisible by (x+1) since (x+1) is a factor of (x-1)^4, and the remainder is 1. Therefore, -1 is a double root of p(x) because (x+1) appears twice in the factored form of p(x).

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Answer: the population density is approximately 121.75 people/km^2.

Step-by-step explanation: Assuming a scenario whereby the island in question is entirely populated and encompasses a total expanse of 100 square kilometers, it follows that the resulting population density would be as follows:

The formula for population density can be expressed as the ratio of total population to a given geographic area. Mathematically, it is written as Population density = Population / Area.

The metric for measuring population density yields a value of 121.75 individuals per hectare.

The metric expressing the number of individuals residing in a given geographic area is referred to as population density. In this specific instance, the population density is calculated to be 121.75 persons per square kilometer.

Assuming a complete occupancy of the island and a cumulative surface area of 100 square kilometers, it can be posited that...

Answer:

I think the answer will be d