The functions S(t) = 1.0841t + 17.392 models the amount of money, S, in billions of dollars, the United States government spent on science, space, and technology for the time period 1999-2009, where t is the number of years since 1999.
a. Write the constraints for the variable t using set-builder notation.
b. Determine the value of S(7)
c. Interpret the value of S(7) in context
d. Name the key feature that is found when solving S(t) = 0. Then, label the key feature on the graph of S(t) = 1.084t + 17.392.
e. determine if the value for S(t) = 0 is reasonable for the context. Explain why or why not.
Answers
Hello,
I hope you and your family are doing well!
a. The variable t represents the number of years since 1999, so the constraints for t can be written as t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
b. To find the value of S(7), we substitute t = 7 into the function: S(7) = 1.084(7) + 17.392 = 22.688.
c. In context, the value of S(7) represents the amount of money, in billions of dollars, that the US government spent on science, space, and technology 7 years after 1999.
d. The key feature that is found when solving S(t) = 0 is the y-intercept of the graph of S(t). The y-intercept is the point where the graph crosses the y-axis.
e. The value for S(t) = 0 is not reasonable for the context because it represents the amount of money spent on science, space, and technology in 1999, which would be a negative number of years after 1999.
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Related Questions
PLEASE!! i really need helping and i’m willing to give a lot of points for this page to be done ASAP
Answers
15. The value of x in the rhombus is 1.94.
16. The value of x is 13 and length AB is 31.
17. The value of x and y is 3 and 8 respectively.
18. The perimeter of the square is 45.24 ft.
What is the value of x?
The value of x in each of the given shapes is calculated as follows;
for question 15;
the diagonals of rhombus are perpendicular to each other;
if CE = 4x, then CG = 2x
(2x)² + (3x)² = 7²
4x² + 9x² = 49
13x² = 49
x² = 49/13
x² = 3.77
x = √ (3.77)
x = 1.94
for question 16; the value of x is calculated as follows;
angle D = angle B (opposite angles of a rhombus are equal)
6x - 17 = 4x + 9
2x = 26
x = 26/2
x = 13
The length of AB = 2x + 5
= 2(13) + 5
= 31
For question 17, the value of x and y is calculated as follows;
PT = RT ( the diagonals of a parallelogram bisect each other)
5x - y = 7 ------ (1)
ST = QT (the diagonals of a parallelogram bisect each other)
4x + 2y = 28 ------- (2)
from equation (1), y = 5x - 7
4x + 2 (5x - 7) = 28
4x + 10x - 14 = 28
14x = 42
x = 42/14
x = 3
y = 5x - 7
y = 5(3) - 7
y = 8
For question 18, the perimeter of the square is calculated as follows;
Let the side length of the square = L
L² = 8² + 8²
L² = 128
L = √128
L = 11.31 ft
The perimeter of the square = 4 x 11.31 ft = 45.24 ft
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26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Answers
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
(look at the graph below)
Function 2
f(x) = −x2 + 2x − 15
Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (−14, 1).
Function 2 has the larger maximum at (1, −14).
Answers
A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).
How to determine the function that has a larger maximum?In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;
f(x) = −x² + 2x - 15
f(x) = −2x + 2
0 = −2x + 2
2x = 2
x = 2/2
x = 1
For the maximum value of function 2, we have:
f(1) = −(1)² + 2(1) - 15
f(1) = -14
For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.
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Use the to the right the value of PT. T is the midpoint of PQ
PT=7x+5 and TQ=9x-9
Answers
By using the figure below, the value of line segment PT is equal to 54 units.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).
Since T is the midpoint of PQ, we have the following:
Line segment PT = Line segment TQ
7x + 5 = 9x - 9
9x - 7x = 9 + 5
2x = 14
x = 14/2
x = 7.
Now, we can determine the value of PT:
PT = 7x + 5
PT = 7(7) + 5
PT = 54 units.
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Complete Question:
Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5
What is the surface area of a sphere with diameter 8 cm?
Answers
Answer:
As = 256\(\pi\) or 804.25cm
Step-by-step explanation:
By formula As = \(4\pi r^{2}\)
As = 256\(\pi\) or 804.25cm
. Estimate the area of a parallelogram with a base of 3 ¼ yards and a height of 5 ½ yards.
Answers
We are given the dimensions of a parallelogram and are asked to estimate its area
Recall that the area of a parallelogram of base b and height h is given by the formula
\(A=b\cdot h\)So the area of the parallelogram would be
\(3\frac{1}{4}\cdot5\frac{1}{2}\)as 3 1/4 and 5 1/2 are mixed numbers, we need to transform them to fractions
Recall that given a mixed number of the form
\(a\frac{b}{c}\)we can transform it into a fraction by multiplying the whole number by the denominator and adding the result to the numerator while leaving the denominator fixed. In this case, that is
\(a\frac{b}{c}=\frac{a\cdot c+b}{c}\)So, applying this formula to both numbers, we get
\(3\frac{1}{4}=\frac{3\cdot4+1}{4}=\frac{13}{4}\)and
\(5\frac{1}{2}=\frac{5\cdot2+1}{2}=\frac{11}{2}\)so the area of the parallelogram would be
\(\frac{13}{4}\cdot\frac{11}{2}=\frac{143}{8}\approx18\)so the area of the parallelogram is approximately 18 square yards
The gold standard is
Answers
The Gold Standard was a system under which nearly all countries fixed the value of their currencies in terms of a specified amount of gold, or linked their currency to that of a country which did so.
Step-by-step explanation:
Answer:
No longer used.
Step-by-step explanation:
Due to too much paper money being printed, some countries did not have enough gold reserves to exchange for the excessive amounts of paper promissory notes. (China's overprinting of printed money during the 9th and 15th centuries foreshadowed England's overprinting during WWI some 200 years later.) This rendered the paper money worthless. (One of the causes of the Great Depression.)
The gold standard is no longer used now, but the system it inspired is currently used between nations.
Susan makes 12 cups of curd in 1 week. after 10 weeks how many cups are made
Answers
Answer:
120
Step-by-step explanation:
12 x 10 = 120
Please answer this correctly without making mistakes.Please simplify the correct answer
Answers
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
Finding the derivative of a function at a point x gives
A.) The slope of the secant line of the function at x
B.) A line parallel to the function
C.) The slope of the tangent line of the function at x
D.)None of the above
Answers
Answer:
C.)
Step-by-step explanation:
that is exactly the definition of the derivative.
the derivative is the limit of
(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h
with h going to 0.
this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.
32,005,008 in expanded form
Answers
Answer:(3 x 10000000) + (2 x 1000000) + (0 x 100000) + (0 x 10000) + (5 x 1000) + (0 x 100) + (0 x 10) + (8 x 1)
Step-by-step explanation: Use the place value to help you .
Answer:
30,000,000+2,000,000+5,000+8
Step-by-step explanation:
Expanded form is when you break the number apart and write it as an addition expression. You break it where ever there is isn't a 0
*haven't done this type of math in a while, hope this helps!*
what the perimeter and area of this shape?
Answers
Answer:
P = 55 feet
A = 237 sq feet
Step-by-step explanation:
P = 2(4) + (3.14 x 15)
A = (4 x 15) + (3.14 x 7.5²)
a taxpayer earned wages of $213,600 received 1400 in interest from a savings account and contributed 19,300 to a tax deferred retirement plan. She had itemized deductions totaling $24,290, which is more than the standard deduction of 12,550 for her filing status
Answers
Her total gross income is $234,300
What is her gross income?The taxpayer's gross income is $234,300. This amount is calculated by adding her wages, interest income, and retirement plan contributions. Her itemized deductions are not included in her gross income since they are subtracted from her adjusted gross income to establish her taxable income.
Before any deductions are done, a person's or a business's gross income is the whole amount of money they receive. It also covers commissions, gratuities, interest, dividends, and other forms of income in addition to salary and wages.
Gross income less specific deductions like alimony, student loan interest, and IRA contributions equals adjusted gross income. Adjusted gross income less personal exemptions, basic deductions, and itemized deductions equals taxable income.
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Which property is represented by the equation (8 x 5) x 6.75 = 8 x (5 x 6.75)?
Answers
The property represented by the equation (8 x 5) x 6.75 = 8 x (5 x 6.75) is the associative property of multiplication. The associative property of multiplication states that when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors.
This means that if there are multiple numbers to multiply, it does not matter which numbers you multiply first.Here, both sides of the equation are equal: (8 x 5) x 6.75 = 340.5, and 8 x (5 x 6.75) = 340.5.
This shows that you can multiply the numbers in any order and still end up with the same product. Therefore, this equation represents the associative property of multiplication.
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Question A class of 25 students took a spelling test. Two students scored 100 on each test, nine students scored 95 on each test, ten students scored 90 on each test, three students scored 80 on each test and one student scored 70. What is the average score of the spelling test rounded to one decimal place? Enter your answer in the box.
Answers
The average score of the spelling test is 90.6%
To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.
First, let's add up all the scores:
2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265
Next, we divide by the total number of students:
Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%
Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.
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Find the vertex of the graph of f(x) = - | 0.75 plus 1.5 |
Answers
The vertex of the absolute value graph given by; f(x) = - | 0.75x + 1.5 | as required is; ( -1.5, 0).
What is the vertex of the absolute value graph as given?It follows from the task content that the graph of the absolute value graph defined by the given equation is to be determined.
According to the task content; the given absolute value equation is;
f(x) = - | 0.75x + 1.5 |
Hence, by comparison with the standard absolute value equation; f(x) = a | x - h | + k where the vertex is; (h, k).
Therefore, h = -1.5 and k = 0.
On this note, the required vertex of the graph is; (-1.5, 0).
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what is 25 divided by 1 1/4
Answers
Answer:
20
Step-by-step explanation:
25 ÷ 1.25 = 20
find the formula for g(x) if it is known that (x-3)=2x-6
Answers
Answer: g(x) = 2*x
Step-by-step explanation:
We want to find the formula of g(x) if we know that g(x - 3) = 2*x - 6
Well, the first step is to find the expression (x - 3) = y in the g(x - 3)
Then:
g(x - 3) = 2*x - 6 = 2*x - 2*3
Now we can just take the common factor 2, and write this as:
2*x -2*3 = 2*(x - 3) = 2*y
then:
g( x - 3) = g(y) = 2*y
if we just replace x by y, we get:
g(x) = 2*x
This is the formula of g(x)
The area of a rectangle is 3x2 - 12x square yards. If the width is 3x yards, what is the length of the rectangle?
Answers
Answer:
x - 4 yards.
Step-by-step explanation:
Given:
Area of rectangle = 3x^2 - 12x square yards
Width = 3x yards
To find:
Length of rectangle
Solution:
The area of a rectangle is equal to the product of its length and width.
Area of rectangle = Length * Width
Substituting the given values, we get:
3x^2 - 12x = Length * 3x
Length =( 3x^2 - 12x )3x
Length = x-4
Therefore, the length of the rectangle is x - 4 yards.
Answer: The length of the rectangle is x - 4 yards.
Step-by-step explanation:
We can create an equation to solve this word problem, where the variable L = length.
3x × L = \(3x^2 - 12x\)
We need to solve for the variable L, to find the length of the rectangle.
First lets factor the right side of the equation to make it easier to divide with.
3x × L = \(3x^2 - 12x\)
We can factor out 3x from the right side of the equation.
3x × L = 3x(x - 4)
Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.
3x × L = 3x(x - 4)
/3x /3x
L = x - 4
The length of the rectangle is x - 4 yards.
72 is 120% of what number?
Answers
Answer:60 percent
Step-by-step explanation:
Step 1) 72 = 120% × Y
Step 2) 72 = 120/100× Y
Multiplying both sides by 100 and dividing both sides of the equation by 120 we will arrive at:
Step 3) Y = 72 × 100/120
Step 4) Y = 72 × 100 ÷ 120
Step 5) Y = 60
Enter the correct answer in the box. Simplify the expression (6^2)^4
Answers
Answer:
6^8 or 1679616
Step-by-step explanation:
Answer:
1679616
Step-by-step explanation:
Question 1 of 10
Use multiplication to decide if the quotient is correct or incorrect.
28 - 8 = 2 r4
A. Incorrect
B. Correct
SUBMIT
Answers
Answer:
i think a
Step-by-step explanation:
in a survey of employee satisfaction , 60% of the employees are male and 45% of the employees are satisfied. what is the probability of randomly selecting an employee who is male and satisfied
Answers
Answer:
27%
Step-by-step explanation:
6/10*45/100=270/1000 which is 27/100 which is 27%
pls help me with this — show work pls
Answers
Answer:
D
Step-by-step explanation:
if the address of variable list is 0x20000100, what are the values at each of the following memory addresses?
Answers
the value of variable num in decimal is 1+3 = 4 and values of of each memory address is given below.
0x20000100 = 0x01, 0x20000101 = 0x00, 0x20000102 = 0x02, 0x20000103 = 0x00, 0x20000104 = 0x03, 0x20000105 = 0x00, 0x20000106 = 0x04, 0x20000107 = 0x00.
The calculation for num value in decimal is my-ptr = 0X 20000/00 = 0X300AF. num =* (0x20000 100) + 3. num = 1+3 = 4. A numeric variable, sometimes known as a quantitative variable, is a quantifiable attribute with numerical values, as opposed to numbers, which are codes for categories. Both continuous and discrete numerical variables are possible. When a variable is given a value for the first time, it is said to be initialized. The assignment operator is represented by the symbol =. On addition, you can create a variable and then give it a value in the same line by writing int I = 9 rather than int I and then I = 9.
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Complete Question
Pointers and Memory Given the following code, answer 2a - 2b. = short num; short list[] {1,2,3,4}; short *my_ptr list; *my_ptr + list[2]; num Question 2a After the code executes, what is the value of variable num in decimal? Question 2b If the address of variable list is 0x20000100, what are the values at each of the following memory addresses?
Ox20000100 [Choose] Ox20000102 [Choose ] Ox20000103 [ Choose ] Ox20000104 [Choose ] Ox20000105 [Choose ] Ox20000106 [Choose ] Ox20000107 [Choose ]
Pls help me with this it’s due in one day
Answers
Analyze picture
since both sides are congruent, ang H-I-G= angle H-G-I
angle H-I-G=32 degrees, so H-G-I is 32 degrees as well
180-32-32=
180-64=
116
x=116 degrees
it is an obtuse triangle
20 is 16% of what number?
Answers
Answer:
80-
Step-by-step explanation:
20 percent (calculated percentage %) of what number equals 16? . well ofc as i said- its 80
Please help
What is the value of x?
Answers
so x=32 :)
Answer:use this procidure
Step-by-step explanation:
Please save all 3 will mark brainliest im seriously lost guys!
Answers
Answer:
12.2acute 3.7Step-by-step explanation:
Triangle with sides of 10, 7 and x
x² = 10² + 7²x² = 149x = √149x = 12.2-------------------
Triangle with sides 3, 16 and 17
The two bigger angles are close in measure, so all 3 angles are less than 90°
The triangle is acute
------------------
Right triangle with sides 9 and x and a angle 24°
sin 24° = x/9x = 9 sin 24°x = 3.7sue eats 3/8 of a cherry pie. Jan
eats
Answers
Answer:
If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?
then the answer is 5/32
Step-by-step explanation: