Sun company has studied the collection pattern of sales for the past year and management has developed the following collection schedule:
55 percent in the month of sale with a 1 percent discount
30 percent in the month of sale
15 percent in the second month following the sale
Actual sales for past six months are:
January $200,100
February 220,450
March 300,700
April 251,200
May 275,890
June 180,460
Expected sales for the next six months are:
July $175,800
August 194,500
September 186,300
October 210,750
November 349,000
December 375,900
A) Determine the expected cash receipts by the month for July through September
B) Determine the expected cash discounts by month for July through September
C) Determine the expected ending balance of accounts receivable by the month of July through September

The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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Answer:

\(y=\frac{1}{3}x\)

*View attached graph*

Step-by-step explanation:

Point-slope: \(y-y_1=m(x-x_1)\)

m = slope (\(\frac{1}{3}\))

point (6,2)

\(y-y_1=m(x-x_1)\)

\(y-2=\frac{1}{3}(x-6)\)

\(y-2=\frac{1}{3}x-2\)  

  \(+2\)           \(+2\)

\(y=\frac{1}{3}x\)

Hope this helps!

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

Answer:

depends how much he chopped up

Step-by-step explanation:

Answer:

Nothing

Step-by-step explanation:

"5. Hamza chopped up

pineapple and gave ½ to his

mum. He also ate half himself.

How much was left to give to

his dad?"

1 - 1/2 - 1/2 = 2/2 - 1/2 - 1/2 = 1/2 - 1/2 = 0

Answer: There was nothing left for him.

The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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Answer:

Both natural and rational

Step-by-step explanation:

\(\frac{30}{6}=5\)

Answer:

Both natural and rational.

Step-by-step explanation:

Step-by-step explanation:

that is 12 over 5

12! / (5! × (12-5)!) = 12×11×10×9×8/5×4×3×2 =

= 11×9×8 = 792

A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.

(i) The exponential function that models the decay of the substance is given by:

\(N(t) = Noe^(-0.088t)\)

(ii) If \(400g\) of the substance is present at to, then  \(No = 400g\) . Therefore, the amount of the substance remaining after 3 days is:

\(N(3) = 400e^(-0.0883) = 309.21g\)  (rounded to two decimal places)

(iii) The rate of change of the amount of the substance after 3 days is given by:

 \(dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day\) (rounded to two decimal places)

(iv) To find the number of days it takes for half of the original \(400g\) of the substance to remain, we need to solve the equation:

\(N(t) = 0.5No\)

\(0.5No = Noe^(-0.088t)\)

\(0.5 = e^(-0.088t)\)

\(ln(0.5) = -0.088t\)

\(t = ln(0.5)/(-0.088) = 7.89 days\) (rounded to two decimal places)

Therefore, after  \(7.89\) days, half of the original  \(400g\) of the substance will remain.

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We are given:                                                                                                        

Density of glass in g/cm³ = 2.5

Finding the density in kg/m³:                                                                              

In converting 2.5 g/cm³ to kg/m³, we will first convert the g to kg

Converting the g to kg:

2.5 g/cm³ * 1

Since 1kg = 1000g, 1kg/1000g = 1

2.5 g/cm³ * 1kg / 1000g

the g in the numerator and the denominator will cancel out and we will get:

2.5 kg / 1000 cm³

Converting the cm³ to m³:

We know that 1 m³ = 10⁶ cm³

So, 10⁶ cm³ / 1 m³ = 1

Multiplying the density by 1

2.5 kg / 10³ cm³   *   1

2.5 kg / 10³ cm³   *   10⁶ cm³ / 1 m³

the cm³ in the numerator and the denominator will cancel out

2.5 * 10⁶ kg / 10³ m³

2.5 * 10³ * 10³ kg / 10³ m³

2.5 * 10³ kg / m³

2500 kg/m³

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

In the given diagram, the length of arc AB is 10.05.

From the question, we are to determine the length of arc AB.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended by the arc = 48°

Radius, r = 12

Therefore,

The length of the arc = 48/360 × 2×3.14×12

Length of the arc = 2/15 × 1884/25

Length of the arc = 10.05

Hence, the length of AB is 10.05

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length of arc PQ = 3.14 meters (option B)

The angle given is in degrees:

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Answer:

3y+5

Step-by-step explanation:

(4y+3)-(y-2)

4y+3-y+2

3y+5

= x² - 4x + 58 - 23 = 0

= x² - 4x + 35 = 0

Sorry but it cann't be solved more futher.

= 16 × 2 + 56 + 2√4

= 32 + 56 + 2√4

= 88 + 2√4

The volume of the composite figure is

The volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes

The simple shapes used here include

Volume of rectangle = length x width x depth

= 30 * 9 * 7

= 1890 cubic yd

Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth

= 1/2 (30 + 19) x 10 x 9

= 2205 cubic  yd

Total volume

= 1890 cubic yd + 2205 cubic yd

=  4095 cubic yd

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Answer:

Step-by-step explanation:

The first step is to find the volume of the cube with the circular hole in the middle. The volume of the cube can be calculated as:

V_cube = (side length)^3 = 14^3 = 2744 mm^3

The hole is a cylinder with radius 6 mm and height 14 mm (the same as the side length of the cube). The volume of the cylinder can be calculated as:

V_cylinder = π(radius)^2(height) = π(6^2)(14) ≈ 1,657 mm^3

Therefore, the total volume of plastic used in each prototype is:

V_total = V_cube - V_cylinder ≈ 1,087 mm^3

To find the total volume of plastic needed for 9,000 prototypes, we can multiply the volume per prototype by the number of prototypes:

V_total_9000 = 9,000 * V_total ≈ 9,783,000 mm^3

Finally, we can calculate the cost of the plastic by multiplying the total volume by the cost per cubic millimeter:

Cost = V_total_9000 * $0.07/mm^3 ≈ $685,810

Therefore, the plastic for the prototypes will cost approximately $685,810.

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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Answer:

.8

Step-by-step explanation:

S= studies for

B= score of b or higher

we want P(S|B)

Using Bayes' theorem we can solve for the probability

\(S|B=\frac{B|S*S}{B|S*S+B|S'*S'}=\frac{.55*.6}{.55*.6+.2*.4}=0.80487804878\)

Answer:

a) -7/9

b) 16 / (n² + 15n + 56)

c) 1

Step-by-step explanation:

When n = 1, there is only one term in the series, so a₁ = s₁.

a₁ = (1 − 8) / (1 + 8)

a₁ = -7/9

The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.

sₙ = sₙ₋₁ + aₙ

(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ

(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ

aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)

If you wish, you can simplify by finding the common denominator.

aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]

aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)

aₙ = 16 / (n² + 15n + 56)

The infinite sum is:

∑₁°° aₙ = lim(n→∞) sₙ

∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)

∑₁°° aₙ = 1

Answer:

D

Gradient = rise/run

=2/3

Y-intercept is 2

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

24 look it up on Google and your welcome I hope I'm right good day

Step-by-step explanation:

Body fat 18.9% of 183 pounds

= 18.9/100 × 183 = 34.587 pounds

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

The value of the required missing angle is;

m<JKM = 35°

We know from geometry that the sum of angles in a triangle sums up to 180 degrees.

Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.

We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.

Thus to find the angle m<JKM, we can write the name expression as;

m<JKM = 180 - (90 + 55)

m<JKM = 35°

Thus that's the value of the required missing angle.

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The used values are;

p = $10,000

r = 3.3%

n = 9 years

And, The amount after 9 years will be $14,593.

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A bank features a savings account that has an annual percentage rate of r = 3.3% with interest compounded quarterly.

And, Maia deposits $10,000 into the account.

Now,

Since, The interest rate is for compounded quarterly.

So, The used formula is,

⇒ \(A = P (1 + \frac{r}{4} )^n^t\)

Here, P = $10,000

r = 3.3% = 0.033

n = 4

t = 9

Substitute all the values, we get the amount after 9 years,

⇒ \(A = P (1 + \frac{r}{4} )^n^t\)

⇒ A = $10,000 (1 + 0.033/4)³⁶

⇒ A = $10,000 (1 + 0.008)³⁶

⇒ A= 10,000 × (1.008)³⁶

⇒ A = 10,000 x 1.45

⇒ A = $14,593

Thus, The amount after 9 years will be $14,593.

Therefore, The used values are;

p = $10,000

r = 3.3%

n = 9 years

And, The amount after 9 years will be $14,593.

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