Ralph’s shirt company sells t-shirts for $7. 50 each with a flat rate of $10 for shipping. Frank’s t-shirt company sells t-shirts for $10 each with free shipping. A. Write a system of equations to represent the t-shirt companies. B. Solve the system of equations by substitution. C. What does the solution mean in the context of the situation?

Step-by-step explanation:

\(a {b}^{2} = \frac{27}{5} \\ \\ {a}^{2} b = 135 \\ \)

\( {b}^{2} = \frac{5.4}{a} \\ {a}^{2} = \frac{135}{b} \)

\(b = \sqrt{ \frac{5.4}{a} } \)

\(b = { ( \frac{5.4}{a} ) }^{0.5 } \\ \\ b = \frac{2.32}{ {a}^{0.5} } \\ \)

\( {a}^{2} = \frac{135}{ \frac{2.32}{ {a}^{0.5} } } \\ {a}^{2} = \frac{135 {a}^{0.5} }{2.32} \\ \)

\( {a}^{2} = 58.19 {a}^{0.5} \)

\( {a}^{1.5} = 58.19\)

a =15.018(approximately)

\(b = \frac{2.32}{ {a}^{0.5} } \\ b = \frac{2.32}{3.875} \\ b = 0.598\)

b= 0.598 (approximately)

a+5b =18

Answer: (9, 9)

Step-by-step explanation:

\(\left(\frac{10+8}{2}, \frac{7+11}{2} \right)=\boxed{(9, 9)}\)

Complete Question:

Aisha reduced the size of her square driveway. she made one side 10 feet shorter and the other side 15 feet shorter. the smaller rectangular driveway will have an area of no more than 800 square feet. write an inequality to represent the area of the smaller driveway.

Answer:

The inequality that represents the area of the smaller drive way is \(x(x-25) \leq 650\)

Step-by-step explanation:

Let the original length of the sides of Aisha's square driveway be = x

She made one side 10 ft short, i.e. (x - 10) ft

She made the other side 15 ft short, i.e. (x - 15) ft

Since the sides are no longer equal, the driveway is now a rectangle

The question states that the smaller rectangular driveway will have an area of no more than 800 square feet

Area of a rectangle = length * Breadth

Area = (x - 10)*(x - 15)

\(Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150\)

Area ≤ 800

\(x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650\)

Solving the above, x = 40.9 or -15.9

Since the length of a square cannot be negative, x = 40.9 ft

Answer:

(x-10)·(x-15)≤800

Step-by-step explanation:

imagine math

Step-by-step explanation:

125°/360°×π×15²

=245.44cm²

g(x) = jawabannya A. g(x) = 7 - x2

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Answer:

(-7,22)

Step-by-step explanation:

X=-7 and y=22

\(A = B^-1 * BC\)

Since B is invertible, it can be used to solve the equation.

1. Calculate the inverse of B, \(B^-1\).

2. Multiply\(B^-1\) with BC, to obtain A.

Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, \(B^-1\). The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying \(B^-1\) with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.

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Tracker B has a greater radius and would be able to cover more area.

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Tracker A has a radius of 4.102 feet, hence:

Area covered = π * 4.102² = 52.86 ft²

Tracker B has a radius of 104 feet, hence:

Area covered = π * 104² = 33979.5 ft²

Tracker B has a greater radius and would be able to cover more area.

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Answer:

gsgdjdjchdvvdbdjzjsjsushsvvsvsvs I don't know

Answer:

see explanation

Step-by-step explanation:

h(- 3) with x = - 3, that is x ≠ 1 , then

h(- 3) = - \(\frac{1}{2}\) (- 3) + 2 = \(\frac{3}{2}\) + 2 = \(\frac{7}{2}\)

h(1) with x = 1 , then

h(1) = 1

h(3) with x = 3, that is x ≠ 1 , then

h(3) = - \(\frac{1}{2}\) (3) + 2 = - \(\frac{3}{2}\) + 2 = \(\frac{1}{2}\)

Step-by-step explanation:

distance between the two points is given by formula

d=

\( \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } = \sqrt{( - 2 - 4)^{2} + {( - 3 - 0)}^{2} } = \sqrt{( - 6)^{2} + ( - 3)^{2} } = \sqrt{36 + 9} = \sqrt{45} = \sqrt{9 \times 5} = 3 \sqrt{5} \)

One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

If you rent a car, you should choose Option 3 and accept the fixed price of $50 for gasoline if you expect to drive 150 miles.

1. Total gasoline consumed (gallons):

To calculate the total gasoline consumed, divide the expected distance by the car's fuel efficiency:

Total gasoline consumed = Distance / Fuel efficiency

Total gasoline consumed = 150 miles / 28 miles per gallon

Total gasoline consumed ≈ 5.36 gallons

2. Option 1 cost:

In Option 1, you need to return the car with a full gas tank. Since the car has a 16-gallon tank and you've consumed approximately 5.36 gallons, you need to fill up the remaining 16 - 5.36 = 10.64 gallons.

Option 1 cost = 10.64 gallons * $3.95 per gallon = $42.01

3. Option 2 cost:

In Option 2, you return the car without filling it up and pay $5.45 per gallon. As calculated before, you've consumed approximately 5.36 gallons.

Option 2 cost = 5.36 gallons * $5.45 per gallon = $29.20

4. Option 3 cost:

In Option 3, you accept the fixed price of $50 for gasoline. This fixed price is the most cost-effective option compared to the other two choices.

Therefore, the best choice is Option 3, accepting the fixed price of $50 for gasoline, as it offers a better value for the expected distance of 150 miles.

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Answer:

30cm

Step-by-step explanation:

With reference to the scale,

1inch=2.5 cm

12 inch=12*2.5 cm =30 cm

Therefore, 1 foot =30 cm

The ratio of the volume of sphere B to the volume of sphere A is 125, since the volume of a sphere is proportional to the cube of its radius. Therefore, when the radius of sphere B is five times the radius of sphere A, the volume of sphere B is 5 cubed, or 125 times, the volume of sphere A.

The volume of a sphere is proportional to the cube of its radius. This means that if the radius of one sphere is increased by a certain factor, the volume of that sphere is increased by that same factor cubed. Therefore, if the radius of sphere B is five times the radius of sphere A, then the volume of sphere B is 5 cubed, or 125 times, the volume of sphere A. This means that the ratio of the volume of sphere B to the volume of sphere A is 125. The calculation for this is relatively simple. The formula for the volume of a sphere is 4/3π\(r^3\), where r is the radius of the sphere. In this case, the radius of sphere A is expressed as r, and the radius of sphere B is expressed as 5r. Therefore, the volume of sphere A is (4/3π)\(r^3,\) and the volume of sphere B is (4/3π)\((5r)^3\). The ratio of the two volumes is (4/3π)\((5r)^3\)/(4/3π)\(r^3\), which simplifies to 125. Therefore, the ratio of the volume of sphere B to the volume of sphere A is 125

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Answer:

y=5/4x+8 Answer Choice D).

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(18-13)/(8-4)

m=5/4

y-y1=m(x-x1)

y-13=5/4(x-4)

y-13=5/4x-20/4

y-13=5/4x-5

y=5/4x-5+13

y=5/4x+8

\( \bf \implies{m \angle{EHF} = 31 \degree}\)

\( \bigg( \bf \angle{DHE} \: and \: \angle{EHF} \: are \: \\ \bf{complementary \: angles} \bigg)\)

\({ \bf \longrightarrow{m \angle{EHF} = \: ? }}\)

We know that,

\( \bf \longrightarrow{6x - 1+ 3x + 1 = 90 \degree}\)

\( \bf \longrightarrow{6x \cancel{- 1} + 3x \cancel{+ 1 }= 90 \degree}\)

\( \bf \longrightarrow{6x + 3x = 90 \degree}\)

\( \bf \longrightarrow{9x = 90 \degree}\)

\( \bf \longrightarrow{x = \frac{ \cancel{90} \degree}{ \cancel{9}} }10 \degree\)

\( \bf \longrightarrow{x = 10 \degree}\)

\({ \bf \longrightarrow{m \angle{EHF} = \: 3 \times 10 \degree + 1 \mapsto31 \degree }}\)

\( \bf \longrightarrow{m \angle{EHF} = 31 \degree}\)

Answer:

40c

Step-by-step explanation:

it starts at 10c and goes up 30c you can just add 30 to 10 to get 40

The solution is, 40°C will be the new reading.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

the reading on the thermometer reads 10°C

and the temperature rises 30°C

now, we have to add the temperature ,

so, the new reading will be,

30+10

=40°C

Hence, The solution is, 40°C will be the new reading.

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Given :-

To Find :-

Solution :-

We know that in a square all the sides are equal . And hence the diagonal of the square is √2 times that of the side . So , if the diagonal is x then the side will be ,

\(\longrightarrow\) Side = x/√2

Now again we know that the area of the square is side² . So that ,

\(\longrightarrow\) Area = x/√2 * x/√2

\(\longrightarrow\) Area = x * x / √2*√2

\(\longrightarrow\) Area = x²/2

\(\longrightarrow\) Area = 1/2 * (diagonal)²

Hence the required answer is x²/2.

The critical point of the function f(x,y) is (-1, 4).

To find the critical points of the function f(x, y) = x^2 + y^2 + 2x - 8y + 3, we need to find the points where the gradient of the function is equal to zero. The gradient is a vector that contains the partial derivatives of the function with respect to each variable.

Step 1: Find the partial derivative with respect to x (f_x):

To find f_x, we differentiate the function f(x, y) with respect to x while treating y as a constant. The derivative of x^2 with respect to x is 2x, and the derivative of 2x with respect to x is 2. Therefore, the partial derivative f_x is 2x + 2.

Step 2: Find the partial derivative with respect to y (f_y):

To find f_y, we differentiate the function f(x, y) with respect to y while treating x as a constant. The derivative of y^2 with respect to y is 2y, and the derivative of -8y with respect to y is -8. Therefore, the partial derivative f_y is 2y - 8.

Step 3: Set the partial derivatives equal to zero:

We set f_x = 0 and f_y = 0 and solve for x and y to find the critical points.

2x + 2 = 0

2x = -2

x = -1

2y - 8 = 0

2y = 8

y = 4

Step 4: Identify the critical point:

The solutions x = -1 and y = 4 satisfy both partial derivative equations. Therefore, the critical point of the function f(x, y) is (-1, 4).

In conclusion, the critical point of the function f(x, y) = x^2 + y^2 + 2x - 8y + 3 is (-1, 4).

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Answer:

hifgreeg33ctvtvunu

Step-by-step explanation:

highhb tug 5h6g6g5g5g

The probability that at least one of the lights is defective is 0.2661 .

in the question ,

it is given that

the total number of bulbs in the pack of new light bulbs is (n) = 5

percent of bulb that did not work is  = 6%

probability that lights did not work is (p) = 0.06

probability that lights work is (q) = 1 - 0.06 = 0.94

let x be the number of defective lights

So ,the probability that at least one of your lights is​ defective

is P(x ≥ 1) = 1 - P(x<1)

= 1 - P(x = 0)

By Binomial Probability

= 1 - ⁿCₓ*(p)ˣ*(q)ⁿ⁻ˣ

= 1 - ⁵C₀*(0.06)⁰*(0.94)⁵⁻⁰

= 1 - 1*1*(0.94)⁵         ...because ⁵C₀ = 1

= 1 - (0.94)⁵

= 1 - 0.7339

= 0.2661

Therefore , The probability that at least one of the lights is defective is 0.2661 .

The given question is incomplete , the complete question is

You purchased a​ five-pack of new light bulbs that were recalled because ​6% of the lights did not work. What is the probability that at least one of your lights is​ defective ?

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From , the properties of triangle;

Angle M + Angle N + Angle O = 180

(3x -16) + (x + 6) + x = 180

3x - 16 + x + 6 + x = 180

5x - 10 = 180

5x = 180 + 10

5x = 190

x = 190/5

...

Answer:

53700

Step-by-step explanation:

Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years

in the beginning of 2017 it'll be 0.92*75000

so it'll be (1-8%)^4 = 0.71639

multiply by 75000 = 53729.  to the nearest 100 = 53700

Answer:

5x-7y+14=0

y= -14/5+7/5y

Step-by-step explanation:

Answer:

y-intercept = 2

Step-by-step explanation:

Write in slope y-intercept form

y = mx + b

5x - 7y = -14

    -7y = -5x - 14

Divide the equation by (-7)

\(\frac{-7y}{-7}=\frac{-5x}{-7} -\frac{14}{-7}\\\\y = \frac{5}{7}x+2\)

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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The roots of the function f ( x ) are x = 1 and x = 3

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁴ - 13x³ + 38x² - 23x - 3

On simplifying , we get

The possible factors of the constant term (-3) are ±1 and ±3, while the possible factors of the leading coefficient (1) are ±1.

Now, we can test these factors by substituting them into the function and checking if the result is zero:

f(1) = (1)⁴ - 13(1)³ + 38(1)² - 23(1) - 3 = 1 - 13 + 38 - 23 - 3 = 0

f(-1) = (-1)⁴ - 13(-1)³ + 38(-1)² - 23(-1) - 3 = 1 + 13 + 38 + 23 - 3 = 72

f(3) = (3)⁴ - 13(3)³ + 38(3)² - 23(3) - 3 = 81 - 351 + 342 - 69 - 3 = 0

f(-3) = (-3)⁴ - 13(-3)³ + 38(-3)² - 23(-3) - 3 = 81 + 351 + 342 + 69 - 3 = 840

From the above calculations, we can see that f(1) = f(3) = 0. This means that x = 1 and x = 3 are roots of the polynomial function

Hence , the function is solved and x = 1 and x = 3

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