Damian has two summer jobs. He works as a tutor, which pays $12 per hours, and he works as a lifeguard, which pays $9.50 per hour. He can work no more than 20 hours a week, but he wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation, where x is the number of hours worked as a tutor, and y is the number of hours worked as a lifeguard? *
A 12x + 9.5y ≤ 220 AND x + y ≥ 20
B 12x + 9.5y ≤ 220 AND x + y ≤ 20
C 12x + 9.5y ≥ 220 AND x + y ≤ 20
D 12x + 9.5y ≥ 220 AND x + y ≥ 20

Answer:

84.64.

Step-by-step explanation:

(-9.2)^2

= (9.2)^2

= 84.64.

Answer:

20.76%

Step-by-step explanation:

\(33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169\)

which rounds to 20.76%

Answer:

About 0.2076 or 20.76%.

Step-by-step explanation:

Recall that compound interest is given by the formula:

\(\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}\)

Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.

Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:

\(\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}\)

Simplify and divide both sides by 8000:

\(\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}\)

Raise both sides to the 1/28th power:

\(\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}\)

Solve for r. Hence:

\(\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)\)

Use a calculator. Hence:

\(r=0.2076...\approx 0.2076\)

So, the quarterly rate of interest must be 0.2076, or about 20.76%.

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

C. 10 m/s²

Step-by-step explanation:

Given:

Δx = 45 m

v₀ = 0 m/s

v = 30 m/s

Find: a

v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2a (45 m)

a = 10 m/s²

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

Given that, a vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m.

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction-or change both.

Here, Δx = 45 m, v₀ = 0 m/s and v = 30 m/s

Using the formula v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2b (45 m)

b = 10 m/s

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

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Answer:

Option B

Step-by-step explanation:

Refer the the picture for working

Answer:

2,341.779

Step-by-step explanation:

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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Answer:

7.94 x 10⁸miles

Step-by-step explanation:

Given parameters:

Distance of earth from sun = 9.3 x 10⁷miles

Distance of earth from Saturn  = 8.87 x 10⁸miles

Unknown:

How much further from the sun is Saturn than Earth = ?

Solution:

To find the solution to this problem, let us find the difference between their distances:

           ( 8.87 x 10⁸ miles  - 9.3 x 10⁷ miles )

         = 88.7 x 10⁷ miles - 9.3 x 10⁷ miles

         = (88.7 - 9.3) x 10⁷miles

          = 79.4 x 10⁷miles

          = 7.94 x 10⁸miles

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

3.5 feet

I think is right

The total number of kilometers that the friends hiked in all would be 2. 02 km.

The total distance that Jordan, Jessica, Eloise, and James hiked in the Austrian Alps, can be found to be :

= Distance on Monday + Distance on Tuesday

= 1. 08 + 0. 94

= 2. 02 km

Using grids, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.

Add them up and you will get 202 cubes which would be 2.02 km.

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Answer:

no solution

Step-by-step explanation:

STEP 1: Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

\(7x+5-5x=12+2x-8\)

STEP 2: Subtract 5x from 7x.

\(2x+5=12+2x-8\)

STEP 3: Subtract 8 from 12.

\(2x+5=2x+4\)

STEP 4: Move all terms containing x to the left side of the equation.

\(5=4\)

STEP 5: Since 5≠4, there are no solutions.

No solution

Answer:

2km

Step-by-step explanation:

Distance = Speed ÷ Time

Distance = 3 ÷ 1.5 (as 1 hour and 30 minutes is an hour and a half)

Distance = 2km

Answer:

4.5 km

Step-by-step explanation:

it takes an hour to walk 3. 1 hour is 60 minutes cut that in half to get 30, so you have to cut the 3 in half as well. which is 1.5. add 3 and 1.5 to get your answer 4.5

Answer:

12/51 or 0.2353

Step-by-step explanation:

There are 13 spades in a deck of 52 cards.

If the first card drawn is a spade and it is not replaced, we will have 51 cards, of which 12 are spades.

So the probability of drawing a spade for the second card is 12/51 ~ 0.2353

Answer:D

Step-by-step explanation:

The Ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.

To find the ratio of the number of pairs of Jeanine to the cost of jeans, we need to first determine how many pairs of jeans Jeanine has and how much she paid for them. Let's assume Jeanine has 10 pairs of jeans and she paid $50 for each pair. Therefore, the total cost of Jeanine's jeans is $500.

Now we can calculate the ratio by dividing the number of pairs of jeans by the cost of jeans. So, the ratio of the number of pairs of Jeanine to the cost of jeans is:

10 pairs of jeans / $500 = 1/50

This means that for every $50 Jeanine spends on jeans, she gets one pair. Alternatively, we could also express the ratio as a decimal or percentage. In this case, the ratio as a decimal would be 0.02 or 2%, indicating that Jeanine spends 2% of the cost of one pair of jeans for each pair she owns.

Overall, the ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.

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With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

Answer:

The equation, 5+7=11+7 solved step by step is:

5 plus 7, which equals 12.

And then, 11 plus 7, which equals 18.

You put it all together, it turns into 12=18 which isn't true.

So, your problem is not real.

Step-by-step explanation:

Your question has no answer because the two sides aren't equal.

Hope this helped! :)

Answer:

The value of g(f(-3) would be -9

Answer:

(4n^2 + 1) (2n+1) (2n-1)

Step-by-step explanation:

use difference of squares

if my answer is correct, pls mark this is brainliest! thanks!

Since both terms are perfect squares, factor using the difference of squares formula,

a² − b² = (a + b) (a − b) where a = 4n² and b=1.

(4n² + 1) (2n + 1) (2n − 1)

Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.

The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.

Here,

We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:

=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon

Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.

Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:

=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.

As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.

Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.

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Answer:

-8 is the answers for the question

Step-by-step explanation:

please please give me brainlest

On solving the provided question, we can say that the equation that be formed is - 36x + 42y = 3 and the groom and the bride each have to pay 19.5 each

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation that be formed is -

36x + 42y = 3

the groom and the bride each have to pay 19.5 each

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Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

Answer:

Step-by-step explanation:

\( - \frac{1}{2} + c = \frac{31 }{4} \\ \\ c = \frac{31}{4} + \frac{1}{2} = \frac{31 - 2}{4} \\ \\ c = \frac{29}{4} \)

Hope this helps you

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer:

How much do the adukts weigh?

Step-by-step explanation:

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

x=1

Step-by-step explanation:

You can find the axis of symmetry from the equation of a function by using the formula x= -b / 2a          ( ax^2 + bx + c).

In this particular function, you can see that b is 1 and c is -3.

x= -b / 2a

x= - (-2) / 2(1)

x= 2 / 1

x= 1