(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even? ​

Answer:

-45j - 9k

Step-by-step explanation:

-9(5j + k)

-9(5j) + -9(k)

-45j - 9k

Helping in the name of Jesus.

The quotient using a synthetic method of division is 8x² + 15x + 7/8 and the remainder is 71/64

The quotient expression is given as

(8x³ + 14x² - 2x + 1) divided by x - 1/8

Using a synthetic method of quotient, we have the following set up

1/8 |   8    14   -2   1

    |__________

Bring down the first coefficient, which is 8:

1/8 |   8    14   -2   1

    |__________

       8

Multiply 8 by 1/8 to get 1, and write it below the next coefficient and repeat the process

1/8 |   8    14   -2      1

    |_____1_15/8__7/64_

       8      15     7/8      71/64

So, the quotient is 8x² + 15x + 7/8 and the remainder is 71/64

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Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.

Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:

Unused yearly pass income = Modern cost x Modern amount requested

Unused yearly pass income = $25.25 x 2482 = $62,678.50

We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:

Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income

Alter in yearly pass income = $62,678.50 - $62,500 = $178.50

The endpoints of the latus rectum of the parabola are (3, -2) and (3, -4)

Given data ,

Let the equation of the parabola be (y + 3)² = (x - 2)

Now , y² + 6y + 9 = x - 2

y² + 6y = x - 11

Now we can see that the vertex of the parabola is (2, -3), and the axis of symmetry is parallel to the y-axis. This means that the focus and directrix will also be parallel to the y-axis.

x = h - p

where (h, k) is the vertex and "p" is the distance between the vertex and the focus. In this case, (h, k) = (2, -3) and p = 1, so

x = 2 - 1

x = 1

Therefore, the equation of the directrix is x = 1

And , the axis of symmetry of the parabola is parallel to the y-axis, the latus rectum will be parallel to the directrix, and its endpoints will be equidistant from the focus and the directrix

The distance between the focus and the directrix is 1 unit, so the distance between the endpoints of the latus rectum will also be 1 unit

Therefore, the endpoints of the latus rectum will be at the points where the perpendiculars drawn from the focus to the directrix intersect the parabola

To find the points of intersection between this line and the parabola, we can substitute x = 3 into the equation of the parabola and solve for y

(y + 3)² = (x - 2)

(y + 3)² = (3 - 2)

(y + 3)² = 1

y + 3 = ±1

y = -2 or y = -4

Hence , the points of intersection between the perpendicular and the parabola are (3, -2) and (3, -4)

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Answer:

B.

Step-by-step explanation:

As the steps imply,

840 different numbers can be created selecting 4 of the digits from the number

From the question, we have the following parameters that can be used in our computation:

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499

To solve this problem, we need to know the minimum sample size required. The formula for this is given as;

n = (z² * p(1 - p))/ E²

Substituting the values into the formula;

n = (1.645² * 0.21(1 - 0.21))/ 0.03²

n = 498.8

The sample size should be at least approximately 499

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The measure of angle U = 41.83 degree.

In the given right angle triangle

VW = 6

UV = 9

Since sinΘ  = (opposite side)/(hypotenuse)

Therefore,

sin U = VW/UV

        = 6/9

        = 0.667

Take inverse of sin both sides

     ∠U =  arcsin(0.667)

            = 41.83

Hence  ∠U = 41.83 degree

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Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

Or

4x=3

X=3/4

The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.

The cost in dollars of the admission ticket is $ 37.50.

Let x be the cost, in dollars, of each admission ticket, including tax.

The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.

The total cost of 4 admission tickets and parking is given as $175.00, so we can write:

4x + $25.00 = $175.00

Simplifying the equation, we can solve for x:

4x = $175.00 - $25.00

4x = $150.00

x = $37.50

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Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The surface area of the larger solid is,  171.7 mm²

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The volumes of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The surface area of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The surface area of the larger solid is,  171.7 mm²

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The total cost for the first 25 units is given as follows:

$140.

The marginal cost function is defined as follows:

[tex]c(x) = \frac{14}{\sqrt{x}} = 14x^{-\frac{1}{2}}[/tex]

The total cost function is the integral of the marginal cost function, hence it is given as follows:

[tex]t(x) = \int c(x) dx[/tex]

[tex]t(x) = 28\sqrt{x}[/tex]

Applying the Fundamental Theorem of Calculus, the total cost from x = 0 to x = 25 is given as follows:

t(25) - t(0).

Thus:

Hence:

140 - 0 = $140.

(Applying the Fundamental Theorem of Calculus, we subtract the numeric values at each endpoint of the integral).

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To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.

How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.

For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:

V = l × w ×h

The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.

Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.

V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.

We arrive at a total volume of 792 cubic meters by adding these volumes together.

To the nearest hundredth=904.600 cubic meters.

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The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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Answer:

60

Step-by-step explanation:

2$ times 30 luna bars at harmons is $60

If line A is parallel to line B then the value of x is 18.

Given that a line A is parallel to line B

We have to find the value of x

3x+7x=180

Combine the like terms

10x=180

Divide both sides by 10

value x=18

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If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:

45/100 = 18/x

where "x" is the unknown number of minutes it would take to mow 100% of the garden.

To solve for "x," we can use cross-multiplication:

45x = 100 * 18

Simplifying the right-hand side:

45x = 1800

Dividing both sides by 45:

x = 40

Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.

To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.

The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972

An exponential function is one in which the input variable is part of the exponent of the expression for the function.

The function for the population of the bacteria indicates;

[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]

The population of the bacteria after t = 1 hour is P(1) = 10,532

Therefore;

[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]

[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]

[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]

[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]

Taking the natural logarithm of both sides, we get;

[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)

-k ≈ -0.0972

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The distance between the points (6,−10) and (6,−7) is 3 units

From the question, we have the following parameters that can be used in our computation:

Points (6,−10) and (6,−7)

Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates

Using the above as a guide, we have the following:

Distance = -7 - -10

Evaluate

Distance = 3

Hence, the distance between the points (6,−10) and (6,−7) is 3 units

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Answer:

I dont know the answer I dont know  what it is I just needed points bye

Step-by-step explanation:

The value of x in the circle is 4.2

From the question, we have the following parameters that can be used in our computation:

The circle

Using the intersecting chords equation, we have

(5x - 8) * 4 = (x + 1) * 10

When solved for x, we have

x = 4.2

Hence. the value of x is 4.2

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Answer:

The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Step-by-step explanation:

To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.

2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.

The slope of this line is 1/2.

Since we want a line parallel to this line, the slope of the new line will also be 1/2.

Next, we can use the point-slope form of a line to write the equation of the new line.

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get:

y - 3 = (1/2)(x - (-4))

Simplifying, we get:

y - 3 = (1/2)x + 2

Adding 3 to both sides, we get the final equation in slope-intercept form:

y = (1/2)x + 5

Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 10.

First quartile (Q₁) = 13.75.

Median (Med) = 20.

Third quartile (Q₃) = 26.25.

Maximum (Max) = 55.

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 26.25 - 13.75

IQR = 12.50

For the range, we have;

Range = maximum - minimum

Range = 55 - 10

Range = 45.

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In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug  can be expressed as 41%.

From the question, the total mass =400 g

The solvent mass = 236 g

Then the mass of the drug = 400-236

= 164

Then the mass percentage of the drug can be calculated as 164/400 * 100

= 41%

Therefore, the strenght of the drug can be expressed as  41%

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The matrix  that represents the solution to this system of equations is

1   0  0     2

0   1   0    -4

0   0   1      3

Therefore option B is correct.

A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

We solve a matrix by Arranging  the elements of equations in matrices and find the coefficient matrix, variable matrix, and constant matrix.

We then go ahead to write the equations in AX = B form.

we then take the inverse of A by finding the adjoint and determinant of A. Multiply the inverse of A to matrix B, thereby finding the value of variable matrix X.

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Answer:

a. Let's denote the number of bacterial cultures after n hours by B_n. We know that the number of bacteria triples every hour, so we can write:

- Recursive formula: B_n = 3*B_(n-1) with initial condition B_0 = 250.

- Explicit formula: B_n = 250 * 3^n.

b. To predict the number of bacterial cultures after 8 hours, we can use the explicit formula and substitute n=8:

B_8 = 250 * 3^8 = 250 * 6561 = 1,640,250

Therefore, there will be 1,640,250 bacterial cultures in the dish after 8 hours.

c. Yes, this sequence represents a function. For each input value (number of hours), there is a unique output value (number of bacterial cultures). The explicit formula gives a direct way of computing the output for any input, so it satisfies the definition of a function.