The rate of change in sales for a technology company from 2008 through 2013 can be modeled by: ds/dt = -0.0975t^2 + 2.116t - 11.73 where S is the sales (in billions of dollars) and t is the time in years, with t = 8 corresponding to 2008. In 2009, the sales for this company were $2.5 billion. (a) Find the model for the sales of this company. (b) What were the average sales (in billions of dollars) of this company from 2008 through 2013? (Do not round until you get final answer. Round your final answer to three decimal places.)
Answers
a. The equation that model the sales for this company is S = -1.426t³ + 15.46t² + 2.5
b. The average dales in this company within the time period is 18.1467.
What is the model for the sales of this company?(a) To find the model for the sales of this company, we need to integrate the rate of change function. We can do this using the following formula:
\(S = \int \frac{ds}{dt} dt\)
where S is the sales (in billions of dollars) and t is the time in years.
In this case;
\(\frac{ds}{dt} = -0.0975t^2 + 2.116t - 11.73.\)
Therefore, we have:
\(S = \int (-0.0975t^2 + 2.116t - 11.73) dt\)
Expanding the terms in the integral, we have:
\(S = -0.04875t^3 + 1.058t^2 - 11.73t\)
In 2009, the sales for this company were $2.5 billion. This means that when t = 9, S = 2.5.
We can now solve for the constants in the model.
\(2.5 = -0.04875(9)^3 + 1.058(9)^2 - 11.73(9)\)
Solving for the constants, we get:
A = -1.426
B = 15.46
C = 2.5
Therefore, the model for the sales of this company is:
S = -1.426t³ + 15.46t² + 2.5
(b) To find the average sales of this company from 2008 through 2013, we need to find the total sales and divide by the number of years.
The total sales from 2008 through 2013 is:
\(S = -1.426(6)^3 + 15.46(6)^2 + 2.5\)
S = 108.88
The number of years is 6.
Therefore, the average sales of this company from 2008 through 2013 is:
Average sales = 108.88 / 6 = 18.1467
Rounding to three decimal places, the average sales of this company from 2008 through 2013 is $18.15 billion.
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Related Questions
meter in length. What
The fairy fly is one of the world's smallest insects. It may measure no more than 1.39 x 10
the total length of 2 of these insects, placed end to end?
A 2.78 x 10-8 meter
B. 2.78 x 10
-4
aft
meter
C. 1.39 x 10
-8
meter
D. 1.39 x 10
0--2
meter
Answers
Explanatory-
Angle Measurements 84 degree
Answers
Answer:
yes angle measures 84°as they are alternate angles
Suppose we have an urn with 3 green balls and 4 yellow balls. We draw 3 balls from the urn one by one without replacement. Find the probability that our sample of 3 balls contains 1 green ball and 2 yellow balls
Answers
Let G represent the event that a green ball is drawn and let Y represent the event that a yellow ball is drawn. The possible ways to draw 1 green ball and 2 yellow balls are: GYGYGGY, and YGYGGY.
Therefore, the probability of drawing 1 green ball and 2 yellow balls is the sum of the probabilities of these two cases. There are a total of 7 balls, so the probability of drawing a green ball on the first draw is: P(G) = 3/7. Since we don't replace the first ball, there are 6 balls left, and the probability of drawing a yellow ball on the second draw is: P(Y | not G) = 4/6 = 2/3.
For the third draw, there are 5 balls left, and the probability of drawing another yellow ball is: P(Y| not G, Y) = 3/5.The probability of the first case, GYGYGGY, is: P(G) × P(Y| not G) × P(Y| not G, Y) = (3/7) × (2/3) × (3/5) = 18/105.The probability of the second case, YGYGGY, is: P(not G) × P(Y) × P(Y| not G, Y) = (4/7) × (3/6) × (2/5) = 24/105.The probability of drawing 1 green ball and 2 yellow balls is the sum of these probabilities: 18/105 + 24/105 = 42/105 = 2/5. The probability that our sample of 3 balls contains 1 green ball and 2 yellow balls is 2/5.
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HELP 100 POINTS PLEASE WILL MARK BRAINLIEST
Answers
The adjusted trial balance for revenue in the accounting worksheet is 20,000.
What is Trial Balance?Trial balance in the accounting worksheet is a financial report where the credit entries and debit entries are listed which is used to audit the accounting system of business or organization internally. It is used to confirm that the sum of all credits and debits must be equal.
Here we have the credit of 15,000 for revenues.
Then the trial balance is adjusted with a credit of 5000.
If we have two debits or credits, we will add them.
So the adjusted trial balance = 15,000 + 5,000 = 20,000
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Can some one pls help me
Answers
Answer:
\(\frac{11}{13}\)
Step-by-step explanation:
You could think of \(\sqrt{\frac{121}{169} } \\\) as \(\frac{\sqrt{121} }{\sqrt{169} }\).
\(\sqrt{121}\) can be simplified to 11.
\(\sqrt{169}\) can be simplified to 13
so this overall expression can be simplified to \(\frac{11}{13}\)
the diameter of a penny 19.05mm.and the thickness is 1.52mm. what is the approximate volume of the roll of pennies, to the nearest tenth
Answers
To the nearest tenth, the approximate volume of a roll of pennies is 21650.0 mm³.
To find the approximate volume of a roll of pennies, we'll first calculate the volume of a single penny and then multiply that by the number of pennies in a roll (usually 50).
We will use the terms diameter and thickness in the calculation. Here are the steps:
Calculate the radius of the penny by dividing the diameter by 2:
Radius = Diameter / 2
= 19.05 mm / 2
= 9.525 mm.
Calculate the volume of a single penny using the formula for the volume of a cylinder (Volume = π × Radius² × Thickness):
Volume = π × (9.525 mm)² × 1.52 mm ≈ 433.0 mm³
Calculate the volume of a roll of 50 pennies:
Roll Volume = Single Penny Volume × Number of Pennies.
= 433.0 mm³ × 50 ≈ 21650 mm³.
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The employees at a baseball bat factory need to make 350,000 bats in 6 months. They make 2,750 bats each day and work 127 days in the 6 months. Do the employees make enough bats?
Answers
Answer:
75 boxes
Step-by-step explanation:
If you divide 24000 bats by 50 boxes, you get 480. Then, if you divide the 36000 by 480, you will get 75
May u give all the answers to these? please and thank you! <3
---------------------------------------------------------------------
Write an equation for the statement
(this applies for all of them <3)
1. The product of nineteen and a number x is seven
2. The sum of a number x and negative thirty is two
3. A number x divided by negative twenty-seven is eight
4. Twelve less than a number x is five
5. One-third of a number x is three
Answers
Answer:
1. 19 (x) = 7
2. -32 + x = 2
3. x ÷ -27 = 8
4. x - 12 = 5
5. 1/3 (x) = 3
Step-by-step explanation:
:)
three times a number is 180 less than seven times the number. what is the number?
Answers
In a rectangle, the length is 5m less than twice the width and the area is 97m^2 . Approximate the dimensions to the nearest tenth of a meter. Do not round any intermediate steps. Find the length and width.
Answers
Therefore, the approximate dimensions of the rectangle to the nearest tenth of a meter are width = 7.9 m and length = 10.8 m.
What is area?Area is a measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).
Here,
Let's denote the width of the rectangle as "w" in meters. Then, according to the problem statement, the length of the rectangle can be expressed in terms of the width as:
length = 2w - 5
The area of the rectangle is given as 97 square meters, so we can write:
area = length × width
Substituting the expression for length in terms of the width, we get:
area = (2w - 5) × w
Expanding this expression, we get a quadratic equation in standard form:
2w² - 5w - 97 = 0
We can solve this equation using the quadratic formula:
w = (-(-5) ± √((-5)² - 4×2×(-97))) / (2×2)
Simplifying this expression, we get:
w ≈ 7.9 or w ≈ -6.2
Since the width of a rectangle cannot be negative, we discard the negative solution and approximate the width to the nearest tenth of a meter:
w ≈ 7.9 m
Using the expression for the length in terms of the width, we can find the length:
length = 2w - 5
≈ 10.8 m
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What are the answers for these questions
Answers
Answer:
4 = 151.70
5a=75.85
Step-by-step explanation:
Resmund works as a hotel clerk. He earns $5.60 per hour for a 40 hour week.
His overtime rate is 1.5 times his regular hourly rate. This week he worked his
regular 40 hours plus 3.75 hours of overtime. What is his total pay?
Answers
Overtime rate = $8.4
(40 hours * $5.6) + (3.75 hours * $8.4)
$224 + $31.5
Total pay = $255.5
Which graph represents the function
f (x) = |x+2| +1?
Answers
Answer: The first graph
Step-by-step explanation:
Graph the absolute value using the vertex and a few selected points.
Hope this helps !
The weather report says the temperature is 20°C and will drop 5°C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10°C, should Daryl move his plant to a warmer location before leaving? An inequality to model the problem is . The solution is
Answers
Answer:
he is right if u need further explonation it is b and c
Step-by-step explanation:
The inequality is given as –5h + 20 > –10. And the solution of the inequity will be h < 6.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The weather report says the temperature is 20 °C and will drop 5 °C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10 °C.
Let h be the number of hours.
The inequality is given as,
–5h + 20 > –10
And the solution of the inequity will be
–5h > –30
5h < 30
h < 6
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I NEED HELP ASAP
Given Matrix A consisting of 3 rows and 2 columns. Row 1 shows 6 and negative 2, row 2 shows 3 and 0, and row 3 shows negative 5 and 4. and Matrix B consisting of 3 rows and 2 columns. Row 1 shows 4 and 3, row 2 shows negative 7 and negative 4, and row 3 shows negative 1 and 0.,
what is A + B?
Matrix with 3 rows and 2 columns. Row 1 shows 10 and 1, row 2 shows negative 4 and negative 4, and row 3 shows negative 6 and 4.
Matrix with 3 rows and 2 columns. Row 1 shows 2 and 1, row 2 shows negative 4 and negative 4, and row 3 shows negative 6 and 4.
Matrix with 3 rows and 2 columns. Row 1 shows 2 and negative 5, row 2 shows 10 and 4, and row 3 shows negative 4 and 4.
Matrix with 3 rows and 2 columns. Row 1 shows negative 2 and 5, row 2 shows negative 10 and negative 4, and row 3 shows 4 and negative 4.
Question 5(Multiple Choice Worth 4 points)
Answers
Adding matrices A and B produces a resulting matrix with three rows. The values in the first row are 10 and 1, the second row has -4 and -4, and the third row has -6 and 4. Option A.
To find the sum of matrices A and B, we add corresponding elements from both matrices. Given:
Matrix A:
6 -2
3 0
-5 4
Matrix B:
4 3
-7 -4
-1 0
Adding corresponding elements, we get:
6 + 4 = 10, -2 + 3 = 1
3 + (-7) = -4, 0 + (-4) = -4
-5 + (-1) = -6, 4 + 0 = 4
Therefore, the sum of matrices A and B is:
Matrix C:
10 1
-4 -4
-6 4
In summary, the sum of matrices A and B is a matrix with 3 rows and 2 columns. The first row shows 10 and 1, the second row shows -4 and -4, and the third row shows -6 and 4. Option A is correct.
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A sphere has a volume of V=2304 in^3. Find its surface area.
Answers
Answer:
The surface area of the sphere is:
\(Surface_{sphere}=843.6\,\, in^2\)
Step-by-step explanation:
Recall the two following important formulas:
\(Volume_{sphere}=\frac{4}{3} \,\pi\,\,R^3\\\\Surface_{sphere}=4\,\pi\,R^2\)
where R is the radius of the sphere.
Then, since we know the sphere's volume (2304 \(in^3\)), we can calculate the sphere's radius:
\(Volume_{sphere}=\frac{4}{3} \,\pi\,\,R^3\\2304=\frac{4}{3} \,\pi\,\,R^3\\\frac{3\,*\,2304}{4\,\pi} =R^3\\R=\sqrt[3]{\frac{6912}{4\,\pi} } \, in\\R=8.1934\,\, in\)
Now, knowing the radius, we can estimate the surface of the sphere using the other formula;
\(Surface_{sphere}=4\,\pi\,R^2\\Surface_{sphere}=4\,\pi\,(8.1934)^2\\Surface_{sphere}=843.6\,\, in^2\)
Someone please help im struggling on these
Answers
Answer:
Step-by-step explanation:
3) 9732.8/20 = 486.64
4) 0.75x4= 3
43.6- 3= 40.6
40.6/30= 1.35
8x +34 = -46 WHAT DOES X EQUAL
Answers
Answer:
\(x = - 10\)
Step-by-step explanation:
1. Subtract 34 from both sides.
\(8x = - 46 - 34\)
2. Simplify -46 - 34 to - 80.
\(8x = - 80\)
3. Divide both sides by 8.
\(x = - \frac{ 80}{8} \)
4. Simplify 80/8 to 10.
\(x = - 10\)
Therefor, the answer is, x = -10
How can we use the distributive property to find an expression equivalent to 15(x+2)? place the steps in order.
Answers
We can use the distributive property to find an expression equivalent to 15(x+2) as 15x + 30.
The given equation is 15(x+2).
The distributive property can be used on the component outside of the brackets, that is 15.
Therefore, we would multiply 15 by each term inside the rounded brackets.
It becomes, 15 times x = 15x and 15 times 2 = 30
That is, 15*(x+2) = 15* x +15* 2 = 15x + 30
Hence, the equation 15(x+2) becomes 15x + 30.
By using the distributive property, expression equivalent to 15(x+2) is 15x + 30
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PLEASE HELP!!!!!!!------- Ann sells boxes of cookies for $10 each. Abdul sells boxes of cookies for $8 each. Each of them sold the same dollar amount. It was the smallest dollar amount which this was possible.
Answers
Answer:
They both sold $40 worth of cookies.
Step-by-step explanation:
Using multiples the first multiple that 10 and 8 have in common is 40.
10,20,30,40
8,16,24,32,40
If f(x) = x3 – 4x^2 + 10, determine the concavity when x=1. Hint: First find the second derivative f(x) is neither concave up nor down when x=1 f(x) is concave up when x=1 f(x) is concave down when x=1
Answers
When x=1, the second derivative of f(x) is 6, indicating that f(x) is concave up.
To determine the concavity of a function at a given point, we need to look at the sign of the second derivative. The second derivative of \(f(x)=x^3-4x^2+10 is f''(x)=6x-8. When x=1, f''(1)=6(1)-8=-2.\)
Since f''(1) is negative, this indicates that f(x) is concave down when x=1. This means that the graph of the function at x=1 has a downward curvature,
where the tangent line will lie below the curve. Intuitively, this means that the rate of change of slope is decreasing as we move towards the point x=1. In contrast, if f''(1) were positive,
it would indicate that f(x) is concave up at x=1, meaning that the graph would have an upward curvature and the tangent line would lie above the curve.
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Can someone please help me with this.Please help me I really need help
Answers
Answer:
102, 118, 134, 150Step-by-step explanation:
As per given, the relationship is:
p(m) = 16m + 86To fill in the table we get:
m = 1 ⇒ p(1) = 16*1 + 86 = 102m = 2 ⇒ p(2) = 16*2 + 86 = 118m = 3 ⇒ p(3) = 16*3 + 86 = 134m = 4 ⇒ p(4) = 16*4 + 86 = 150The rectangular prism has a height of 3in,width of 4 in and length of 5in.if the length is doubled,what is the new volume
Answers
Answer:
\( \boxed{\boxed{\sf{\:\:\:\green{120 \: in^3}\:\:\:}}} \)\(\\\)
Step-by-step explanation:
The original volume of the rectangular prism is given by:
\(\sf\implies Volume = Length \times Width \times Height\)
\(\sf\implies Volume = 5\: in \times 4\: in \times 3\: in\)
\(\sf\implies Volume = 60\: in^3\)
\(\\\)
If we double the length of the prism, the new length will be:
\(\sf\implies Length = 2 \times Length\)
\(\sf\implies Length = 2 \times 5\: in\)
\(\sf\implies Length = 10\: in\)
\(\\\)
The width and height of the prism remain the same. Therefore, the new volume of the prism is:
\(\sf\implies Volume = Length \times Width \times Height\)
\(\sf\implies Volume = 10\: in \times 4\: in \times 3\: in\)
\(\sf\implies \boxed{\boxed{\sf{\:\:\:Volume = \green{120\: in^3}\:\:\:}}}\)
\(\\\)
\(\\\)
Therefore, the new volume of the rectangular prism is 120 cubic inches.
find f(14) when using the function f(x) =9x+43
Answers
169
Step-by-step explanation:Functions are represented as a rule in terms of x as the independent variable and f(x) as the dependent variable.
Function Notation
Functions are written like f(x)=x. This might look unfamiliar but it is the same as y=x. In both examples, y and f(x) are the dependent variables.
If the x in f(x) is replaced by a constant, then the equation represents the function with x equals that constant.
So, the question asks to find the value of the function when x equals 14.
Solving the Function
Now to solve the function, we can plug 14 in for x.
f(14) = 9(14) + 43First, we can multiply 9*14
f(14) = 126 + 43Next, add together the remaining terms.
f(14) = 169This gives us the final answer of 169.
H28−−√ was simplified and the final answer is 87√. What was the value of H in the original question?
Answers
Solution
To solve this problem, we only need to equate and solve for H
\(\begin{gathered} H\sqrt{28}=8\sqrt{7} \\ divide\text{ both sides by }\sqrt{28} \\ H=\frac{8\sqrt{7}}{\sqrt{28}} \\ \\ H=\frac{8\sqrt{7}}{2\sqrt{7}} \\ \\ H=4 \end{gathered}\)
Assume the probabilities of a child being allergic to the following foods are as follows:
.014 for nuts
.043 for dairy
.031 for gluten
Calculate the probability that a child is NOT allergic to nuts.
Answers
The probability that a child is not allergic to nuts is 0.986, or 98.6%.
The probability that a child is not allergic to nuts can be calculated by subtracting the probability of being allergic to nuts from 1.
Given the probabilities of a child being allergic to nuts, dairy, and gluten, we are interested in finding the probability that a child is not allergic to nuts.
The probability of being allergic to nuts is given as 0.014.
To find the probability that a child is not allergic to nuts, we subtract this value from 1.
P(Not allergic to nuts) = 1 - P(Allergic to nuts) = 1 - 0.014 = 0.986
Therefore, the probability that a child is not allergic to nuts is 0.986, or 98.6%.
This calculation is based on the assumption that being allergic to nuts and being allergic to other foods are independent events.
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Write the following equations.
Answers
Answer:
Step-by-step explanation:
4. 2x + 1 = 17
5. x-13 = 94
6. x/2 = 7
7. 5x = 35
8. x + 43 = 84
9. x-18 = 36
10. x = 8y
11. x = y - 5
12. x + (x+1) + (x+2) = 18
13. x = y + 4
14. 2x + 8 = 24
pls help ill give brainiest
For your trip to Austin you know you are going to travel 182 miles and your car can do that in 14 gallons. How far can your car travel on 8 gallons of gas?
Answers
Answer:
Step-by-step explanation:
for 182 miles you need 14 gallons
??????? 8 gallons
8/14=x/182
x=182*8/14
x miles=104 miles
I need help with this question the answers are in the picture
Answers
Answer:
1:1
Step-by-step explanation:
The ratio from the initial figure PQ: QR is 1:1 because the figure is a square.
The ratio of P'Q': Q'R' is still 1:1 because even if we dilated the figure we actually compare the sides P'Q' to Q'R' that had the proportions preserve.
Select all equations that have graphs with the same y-intercept.
Group of answer choices
y=3x - 8
y=3x - 9
y=3x + 8
y= 5x-8
y=2x -8
y=1/3x -8