Answers
9514 1404 393
Answer:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
Additional comment
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
Related Questions
How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answers
Answer: 34,650 permutations
let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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There are vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%.
Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
Red
Total
Question content area bottom
Part 1
Complete the table.
Row Relative Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
enter your response here%
enter your response here%
100%
Red
enter your response here%
enter your response here%
100%
Total
enter your response here%
enter your response here%
100%
Answers
Answer:
you su ck hah lol
Step-by-step explanation:
ez
To celebrate the holiday season this year, the Gaylord Texan has created an extreme eight-lane, tubing hill
with real snow called the "Kung Fu Panda Awesome SNOW Tubing Ride." The cost of each ticket for one day
is $21. This can be modeled by the function f(x) = 21x. The number of tickets purchased by groups is given
by the domain (4, 6, 103. which would be a reasonable range for the total cost of the tickets the groups
would pay?
Answers
The reasonable range for the total cost of the tickets the groups
would pay is {84, 126, 2163}.
What is Domain and Range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
Given:
The Function modeled for the situation is
f(x) = 21 x where x is the number of tickets sold.
So, For x= 4 Tickets
Fare, F(x) = 21 x 4= $84
and, For x= 6 Tickets
Fare, F(x) = 21 x 6 = $126
and, For x= 103 Tickets
Fare, F(x) = 21 x 103 = $2163.
Hence, the range is {84, 126, 2163}.
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Arrange the following temperatures in ascending order and descending order.
a) 37°C, -15°C, 16°C, -12°C, 0°C, 96°C, -73°C
b) 20°C, -1°C -15°C 0°C, -7°C, 23°C, -36°C.
Answers
Answer:
a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C
a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C
b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C
b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C
A cylinder has a radius of 4 millimeters. Its volume is 200.96 cubic millimeters. What is the height of the cylinder?
Answers
Answer:
3.999 millimeters.
Step-by-step explanation:
To find the height of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).
200.96 = π(4²)h
200.96 = 16πh
To solve for h, we can divide both sides of the equation by 16π:
200.96 / (16π) = h
Using a calculator, we can calculate the approximate value of h:
h ≈ 200.96 / (16 × 3.14159)
h ≈ 3.999
Therefore, the height of the cylinder is approximately 3.999 millimeters.
find the value of p so that the quadratic solution x(2 x+p) + 8 = 0 has real and distinct roots
Answers
Answer:
p = -17, x = 8
p = -10, x = 1
p = -10, x = 4
p = 10, x = -1
Step by Step:
x (2 x + p) + 8 = 0
x = 1/4 (-sqrt(p^2 - 64) - p)
Hope I helped!
You work as an industrial designer. You are creating specifications for workstations. Each station will have a work surface of 2.5 feet from the floor, 2 feet deep, and 4 feet wide. How many square feet is the area of the work stations?
Answers
Answer:
The area of the work surface of each station is:
2 feet x 4 feet = 8 square feetTo find the total area of all the workstations, we need to know how many workstations there are. Let's assume there will be 10 workstations.Total area of workstations = 8 square feet x 10 workstations = 80 square feetTherefore, the area of the workstations is 80 square feet.
what is wrong in this question???
Answers
You failed to start the end points of the frequency polygon from a x-value of 0.
How to draw a frequency polygon?First of all, we would determine the midpoint of the data set as follows:
0 < t ≤ 5 = (0 + 5)/2 = 2.5.
5 < t ≤ 10 = (10 + 5)/2 = 7.5.
10 < t ≤ 15 = (10 + 15)/2 = 12.5.
15 < t ≤ 20 = (15 + 20)/2 = 17.5.
In order to draw a frequency polygon for the given data set, we would construct the frequency table as follows:
Time, t minutes Frequency_
0 < t ≤ 5 7
5 < t ≤ 10 8
10 < t ≤ 15 6
15 < t ≤ 20 4
Finally, we would connect the end points of the data set on the frequency polygon by starting from a x-value of 0 as shown in the image attached below.
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can someone help me?
Answers
Answer:
I'd say 2
Step-by-step explanation:
Leigh plans to estimate the area of the figure on the grid by identifying the full and partial squares that make up the figure.
Answers
Evaluate your expression to find the number of scoops Zack needs. I WILL MAKE BRAINLIEST IF RIGHT!!!!!!!!!!!!
Answers
Answer:
2 1/2 beacuse he needs 1 1/4 for one feeder
Step-by-step explanation:
p(x)=5x^4+7x^3-2x^2-3x+c divided by (x+1)
Answers
The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.
To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.
Let's set up the long division:
\(5x^3 + 2x^2 - 4x + 4\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:
\(5x^3(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
- (\(5x^3 + 5x^2)\)
This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:
\(5x^3(x + 1) + 2x^2(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
-\((5x^3 + 5x^2)\)
_______________________
\(2x^2 - 3x + c\)
We continue this process until we reach the constant term, resulting in the remainder of the division.
At this point, we have:
\(5x^3(x + 1) + 2x^2(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
- \((5x^3 + 5x^2)\)
_______________________
\(2x^2 - 3x + c\)
-\((2x^2 + 2x)\)
_______________________
- 5x + c
- (-5x - 5)
_______________________
5 + c
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Answers
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
\(22.6 < \mu < 24.4\)
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)
The upper bound of the interval is then given as follows:
\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)
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A = {1, 2, 3, 4}
B = {3, 4, 5}
vertical line A intersection B vertical line =
Answers
The intersection of vertical lines A and B is 3 and 4.
How to find the intersection of the vertical linesWe are going to apply the sets theory here. In sets theory, the intersection of two elements means the values those elements have in common.
So given: A = {1, 2, 3, 4} and B = {3, 4, 5}
The intersection of A = {1, 2, 3, 4} and B = {3, 4, 5} is {3,4} since they both have 3 and 4 common.
Therefore, vertical lines A and B have intersection of 3 and 4.
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PLZZZ HELP
On a map of a school, 3 inches represents 9 ft how many inches would represent 1 foot 6 inches.
Answers
Answer:
Step-by-step explanation:
3/9 = x/1.5
4.5=9x
x=0.5
0.5 inches
What is the Slope from graph
Answers
Answer:
3/4 I'm pretty sure that right
please answer asap please
A piano mover uses a ramp to move a piano into a house. The doorway to the house is 2 feet above the ground and the ramp starts 7 feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.
Answers
Help me with number 7 (geometry) hint= x is 18 1/3 (show work)
Answers
Answer:
2x-15+10x-25=180
2x-10x=180+15+25
-5x=220
=44
ı hope its true
Step-by-step explanation:
A cylinder has a height of 10 ft and a volume of 25,456 ft^3.The radius of the cylinder is approximately ___ feet.Round your answer to the nearest whole number.
Answers
From the question given, they provided us with the height,h = 10ft, and volume, V=25,456 cubic feet.
Thus, we have:
\(\begin{gathered} V=\pi\times r^2\times h \\ 25,456=\pi\times r^2\times10 \\ \frac{25,456}{10\pi}=r^2 \\ \text{Taking the value of }\pi\text{ as 3.142, we have:} \\ r^2=\frac{25,456}{10\times3.142} \\ r^2=810.1846 \\ r=\sqrt[]{810.1846} \\ r=28.46ft \end{gathered}\)Hence, the radius of the cylinder is 28.46ft
What step should be taken to isolate the variable in the following
equation? 7d=49*
add 7 to both sides
subtract 7 from both sides
multiply 7 on both sides
divide 7 from both sides
Answers
Answer:
Divide 7 on both sides.
Step-by-step explanation:
What is the total interest on a 4-year term loan of
$1,700 with a simple annual interest rate of 8%?
A. $544
B. $554
C. $564
D. $574
Answers
Answer:
a
Step-by-step explanation:
The formula to calculate simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time period
Given:
Principal amount (P) = $1,700
Rate of interest (r) = 8% per annum
Time period (t) = 4 years
Using the formula of simple interest:
I = P * r * t
I = 1,700 * 0.08 * 4
I = $544
Therefore, the total interest on a 4-year term loan of $1,700 with a simple annual interest rate of 8% is $544.
Answer: A. $544
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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A box of cupcakes feeds 5 people. If you are having a party and invited 148 people, how many boxes of cupcakes would you need to buy?
LABEL AND PLZZ HURRY UP!!!
Answers
Answer: 30 boxes of cupcakes
Step-by-step explanation:
Answer:
yea top is right i 29.6 estimate yea 30
There are five main roads between the cities A and B and 4 between B and C. In how many ways can a person drive from A to C and return without driving on the same road twice?
Answers
There are 20 possible routes that a man could take to go between cities and then take a different route back.
What is meant by permutation?In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.
Let the number of roads between the cities A and B = 5.
The rules of permutation must be used in this situation.
A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.
The man uses five different routes to get from A to B because there are five different routes accessible.
He can get back by 4 (5 1) methods because he needs to take a different route.
Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.
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The box plot below represents some data set. What percentage of the data values are between 110 and 170?
Answers
The percentage of the data values are between 110 and 170 = 37.5%
We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.
The second quartile is nothing but between 25.1% and 50% (i.e., till median)
The third quartile: 51% to 75% (above the median)
And the fourth quartile: 25% of largest numbers.
In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.
So, each unit length measures 10 units.
Also, the median of the data = 110
We need to find the percentage of the data values are between 110 and 170.
i.e., the percentage of the data values are in the third quartile.
The range of this box plot is: 190 - 30 = 160
The data values are between 110 and 170 = 60
Using percentage formula,
P = (60/160) × 100
P = 37.5%
This is the required percentage.
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Find the complete question below.
101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Answers
Distribute the summation over the sum.
\(\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i\)
Now plug in the known sums and simplify.
\(\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}\)
Ryan buys lunch for $16.83. If sales tax is 8.4%, How much money does Ryan need total for lunch
Answers
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)
three subtracted from the product of two and a number n
Answers
Answer:
(2+n)-3
That's how you write if that is what you want.
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. Let I(t) denote the number of infected individuals. Suppose that the total population is 2000, the proportionality constant is 0.0001, and that 1% of the population is infected at time t-0, write down the intial value problem and the solution I(t).
dI/dt =
1(0) =
I(t) =
symbolic formatting help
Answers
Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
\(I(t)=\frac{2000}{1+99e^{-0.2t}}\)
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
\(\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}\)
Given total population is 2000. So the non infected population = 2000 - I.
\(\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I\)
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
\(\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k\)
\(\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}\)
The required expressions are presented below:
Differential equation\(\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)\) \(\blacksquare\)
Initial value\(I(0) = \frac{1}{100}\) \(\blacksquare\)
Solution of the differential equation\(I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}\) \(\blacksquare\)
Analysis of an ordinary differential equation for the spread of a disease in an isolated population
After reading the statement, we obtain the following differential equation:
\(\frac{dI}{dt} = k\cdot I\cdot (n-I)\) (1)
Where:
\(k\) - Proportionality constant\(I\) - Number of infected individuals\(n\) - Total population\(\frac{dI}{dt}\) - Rate of change of the infected population.Then, we solve the expression by variable separation and partial fraction integration:
\(\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}\)
\(\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}\)
\(\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C\)
\(\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}\)
\(I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}\), where \(C = \frac{I_{o}}{n}\) (2, 3)
Note - Please notice that \(I_{o}\) is the initial infected population.
If we know that \(n = 2000\), \(k = 0.0001\) and \(I_{o} = 20\), then we have the following set of expressions:
Differential equation\(\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)\) \(\blacksquare\)
Initial value\(I(0) = \frac{1}{100}\) \(\blacksquare\)
Solution of the differential equation\(I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}\) \(\blacksquare\)
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