Answer:
(a)Adult:10.99+0.99x, Kid: 5.99+0.99x
(b)Adult's Total cost = $15.94, Kid's Total cost =$10.94
Explanation:
Cost of a ride = $0.99
Let x be the number of rides.
Cost of an Adult Ticket = $10.99
An equation for adult tickets will therefore be: 10.99+0.99x
Similarly, the cost of a kid ticket =$5.99
An equation for adult tickets will therefore be: 5.99+0.99x
(b)If they ride 5 tickets each, the amount of money spent will be:
x=5 rides
Total cost for an adult=10.99+0.99(5)
=10.99+4.95
=$15.94
Total cost for a kid = 5.99+0.99(5)
=5.99+4.95
=$10.94
Find the derivative of each function. Simplify each derivative and express all exponents as positive values.
Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]Explanation:
Step 1. The function we have is:
[tex]f(x)=\frac{x^3}{3}-\frac{x}{2}[/tex]And we are asked to find the derivative of the function. The rule to find the derivative for this type of function is:
[tex]\begin{gathered} \text{for a function }of\text{ the form} \\ f(x)=ax^n \\ \text{The derivative is:} \\ f^{\prime}(x)=a(n)x^{n-1} \end{gathered}[/tex]Step 2. Before we apply the derivative rule, remember the following:
[tex]\begin{gathered} \text{for a function } \\ f(x)=g(x)+h(x) \\ \text{The derivative is:} \\ f^{\prime}(x)=g^{\prime}(x)+h^{\prime}(x) \end{gathered}[/tex]This means that we need to derivate each part or term of the function and combine them for the total derivative.
Step 3. Apply the derivative rule from step 1 to the given function.
First we rewrite the function as follows:
[tex]\begin{gathered} f(x)=\frac{x^3}{3}-\frac{x}{2} \\ \downarrow \\ f(x)=\frac{1}{3}x^3-\frac{1}{2}x^1 \end{gathered}[/tex]Apply the derivative rule:
[tex]f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1}[/tex]Step 4. The last step is to simplify the expression:
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1} \\ \downarrow \\ f^{\prime}(x)=\frac{1}{3}(3)x^2-\frac{1}{2}(1)x^0 \\ f^{\prime}(x)=x^2-\frac{1}{2}x^{^0} \\ \sin ce^{} \\ x^0=1 \\ \downarrow\text{ The result is }\downarrow \\ f^{\prime}(x)=x^2-\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]Which of the following systems of equations can be used to find a, the number of adults attending, and s, the number of students attending the game?
The problem can be expressed in the following system of linear equations:
A total of 120 adults (a) and students (s) attended a school:
a + s = 120
Each adult paid $2.50, mathematically, that is 2.5a
Each student paid $1, mathematically, that is 1s
and the total paid by adults and students attending the game was $189
then, we have:
2.5a + 1s = 189
then, we can conclude that the problem can be expressed as follows:
a + s = 120
2.5a + 1s = 189
or equivalently:
a + s = 120
2.5a + s = 189
so, the correct answer is D.
how long will it take $600 to earn $72 at the rate of 0.03 percent annual?
It takes 400 years for $600 to earn $72 at the rate of 0.03 percent annual
What is Simple Interest?"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.
The formula for calculating Simple interest
I=PRT
Where I is the Interest
P=Principle amount
I is interest Amount
R is rate of interest per year as a percent
T is time period involved
P=600
I=72
r=0.03%
t=?
I=PRT
Plug in the values P, R and I
72=600×(0.03%)×T
72=600×0.0003×T
72=0.18×T
400=T
Hence it takes 400 years, for amount $600 to earn $72 at the rate of 0.03 percent annual.
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When given a line of 3x + 6y = 8, how do you find slope intercept?
The line is given by 3x + 6y = 8
To find the slope and the y-intercept, we must rewrite the equation in the form y = ax + b, where a is the slope and b is the y-intercept.
The first step is subtract 3x from both sides of the equation:
3x + 6y - 3x = -3x + 8
6y = -3x + 8
Then, we divide both sides by 6:
6y/6 = (-3x + 8)/6
y = -x/2 + 4/3
Therefore, the slope is -1/2 and the y-intercept is 4/3
HELP PLEASE MARKING BRAINLIEST Han cell phone plan cost $200 to start then there's $50 charged each month(a)what is the total cost to use the cell phone plan for one month(b)what is the total cost for x months (c)which graph shows the cost of the cell phone plan over a period of two years using months as the units of time(d) is there a proportional relationship between time and the cost of the cell phone plan explain how you know
Answer:
• $250
,• y=200+50x
,• Graph A
,• Yes
Explanation:
(a)Han cellphone's plan costs a fixed fee of $200 and an extra $50 per month.
Therefore:
[tex]\begin{gathered} \text{The total cost for one month=}200+50 \\ =\$250 \end{gathered}[/tex](b)If Han uses the phone for x months
Extra Cost = 50x
Therefore:
[tex]\text{The total cost for x months, y=}200+50x[/tex](c)Since the number of months = x; and
Total cost for x months = y
When x=24
[tex]\begin{gathered} y=200+50(24) \\ =1400 \end{gathered}[/tex]The graph that shows the cost of the cell phone plan over a period of two years using months as the units of time is Graph A.
(d)We see that the equation y=50x+200 has a proportional constant (50).
Another approach is to say that it is a linear equation.
Therefore, there is a proportional relationship between time and the cost of the cell phone plan.
????????????????????
we have
m=-2
point (1,2)
step 1
find the equation of the line in point slope form
y-3=-2(x-1)
convert to slope intercept form
y-3=-2x+2
y=-2x+2+3
y=-2x+5
To graph the line we need two points
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
y=5
so
the y-intercept is (0,5)
Find the x-intercept
Value of x when the value of y is equal to zero
For y=0
0=-2x+5
2x=5
x=2.5
the xintercept is (2.5,0)
Plot the points (0,5) and (2.5,0), join them and graph the line
using a graphing tool
see the attached figure
please wait a minute
At the Kerry Hotel Pudong in Shanghai, China, theonce swimming pool is now the world's largest ballpit. The ball pit is 82 feet long and 41 feet wide,with an average depth of 4.25 feet. Each ball in the ball pit is the same size. They each have a diameterof 4 inches. 1. What is the volume of this pool? 2. How many ball pit balls will we need to fill the pool up to the top?
Answer: We have to find the volume of the pool and the number of pit balls that can fill it.
(1) We can find the volume of the pool with the following formula:
[tex]V=L\times W\times D\rightarrow(1)[/tex]Using the equation (1) the volume of the pool is determined as follows:
[tex]\begin{gathered} L=82ft \\ \\ W=41ft \\ \\ D=4.25ft \\ \\ \therefore\rightarrow \\ \\ \begin{equation*} V=L\times W\times D \end{equation*} \\ \\ V=(82ft)\times(41ft)\times(4.25ft)=14,288.5ft^3 \\ \\ V=14,288.5ft^3 \end{gathered}[/tex](2) The number of ball pits that can fill the pool is as follows:
[tex]\begin{gathered} V_b=\frac{4}{3}\pi r^3 \\ \\ \\ 4in=\frac{1}{3} \\ \\ \therefore\rightarrow \\ \\ V_b=\frac{4}{3}\pi(\frac{1}{3})^3=\frac{4}{81}\pi ft^3 \\ \\ V_b=\frac{4}{81}\pi ft^3=0.16ft^3 \end{gathered}[/tex]Therefore the answer is:
[tex]\begin{gathered} N=\frac{V}{V_b}=\frac{14,288.5ft^3}{0.16ft^3}=89,303.125 \\ \\ N=89,303.125 \end{gathered}[/tex]OutcomeAnswer the following. Round your answers to the nearest thousandths.Number of SpinsExplanationCheckRed(a) From Donna's results, compute the experimental probability of landing on yellow.394аYellowJ420(b) Assuming that the spinner is fair, compute the theoretical probability of landing on yellow.(c) Assuming that the spinner is fair, choose the statement below that is true.O With a large number of spins, there might be a difference between the experimental andtheoretical probabilities, but the difference i need help with this math problem
ANSWERS
(a) 0.420
(b) 0.400
(c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small
EXPLANATION
(a) The experimental probability is given by,
[tex]P_{exp}=\frac{number\text{ }of\text{ }successes}{number\text{ }of\text{ }trials}[/tex]In this case, Donna spun the dial 1000 times and 420 times it landed on yellow,
[tex]P_{exp}=\frac{420}{1000}=0.420[/tex]Hence, the experimental probability of landing on yellow is 0.420.
(b) The theoretical probability is given by the geometry of the spinner and, if it is fair, the number of yellow sections,
[tex]P_{th}=\frac{number\text{ }of\text{ }favorable\text{ }outcomes}{total\text{ }posible\text{ }outcomes}[/tex]In this case, the spinner is divided into 10 equally sized slices, and 4 of them are yellow,
[tex]P_{th}=\frac{4}{10}=0.400[/tex]Hence, the theoretical probability of landing on yellow is 0.400.
(c) As we can see in parts a and b, for 1000 trials, the experimental and theoretical probabilities are almost the same - i.e. there is a small difference. This is known as the law of large numbers which states that if the number of trials of an experiment is large, the experimental probability of each event should be close to the theoretical probability.
Hence, the true statement is the first one: with a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
please help me out thanks
A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].
We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
A² = A x A
If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]
This is called matrix multiplication.
Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
So any matrix of the form [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0
In particular, A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.
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The graph is blurry but the y axis is going up by 25 and x axis is going up by 1s
The predicted temperature of the substance after 3.5 minutes implies that x =3.5, and we are to find y.
Therefore,
[tex]\begin{gathered} y=5(3.5)+23 \\ y=17.5+23 \\ y=40.5^0C \end{gathered}[/tex]Therefore, the predicted temperature of the substance, 3.5 minutes after the start of the experiment is 40.5 degrees Celsius
what is 1 trillion to the thenth power? .. .. ..
[tex]\sf{}[/tex]
1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
What is a trillion?1,000,000,000,000One trillion is equal to one million million, or 1,000,000,000,000, and on the short scale, we write this as 1012. (ten to the twelfth power). This number is now commonly referred to as one trillion because it is a thousand times bigger than the short-scale billion.We need to determine how many crores one trillion represents. Therefore, by dividing one trillion by one crore, we can find the solution to the puzzle. As a result, we discover that 100000 = 1000000000000/10000000. As a result, we learn that $1 trillion is equivalent to 100,000 Indian Rupees.So, 1 trillion to the tenth power:
1 trillion to the tenth power = (10¹⁴)¹⁰ or (10¹³)¹⁰Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
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I need help solving this question
Answer: 0.77
Step-by-step explanation:
Write in point slope form the equation for the line that goes through the points (0,0) and (-4,7)
PROBLEM:
To find the point-slope form of the equation of the line passing through points (0, 0) and (-4, 7)
METHOD:
The point-slope form of the equation of a line is given to be:
[tex]\begin{gathered} (y-y_0)=m(x-x_0) \\ \text{where} \\ m=\text{ slope} \\ (x_0,y_0)=\text{ Point on the line} \end{gathered}[/tex]Step 1: Find the slope of the line.
The formula to calculate the slope of a line is given to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can use the two points provided to find the slope of the line such that:
[tex]\begin{gathered} (x_1,y_1)=(0,0)_{} \\ (x_2,y_2)=(-4,7) \end{gathered}[/tex]Therefore, the slope is given to be:
[tex]\begin{gathered} m=\frac{7-0}{-4-0} \\ m=-\frac{7}{4} \end{gathered}[/tex]Step 2: Pick a point on the line to use for the equation.
[tex](x_0,y_0)=(-4,7)[/tex]Step 3: Use the values gotten from Steps 1 and 2 to write out the equation of the line in the point-slope form:
[tex]\begin{gathered} \Rightarrow y-7=-\frac{7}{4}(x-\lbrack-4\rbrack) \\ \therefore \\ y-7=-\frac{7}{4}(x+4) \end{gathered}[/tex]ANSWER:
The slope-intercept form of the line is given to be:
[tex]y-7=-\frac{7}{4}(x+4)[/tex]Sam biked 2/3 km in 4 minutes. How far did he bike in 1 minute?
we can make a relation
[tex]\begin{gathered} \frac{2}{3}\longrightarrow4 \\ \\ x\longrightarrow1 \end{gathered}[/tex]where x is the missing value
if she bikes 2/3km in 4 minutes how much kilometers she bike on 1 minute?
we solv using cross multiplication
we multiply 1 and 2/3 and the divide by 4
[tex]\begin{gathered} x=\frac{1\times\frac{2}{3}}{4} \\ \\ x=\frac{\frac{2}{3}}{4} \\ \\ x=\frac{1}{6} \end{gathered}[/tex]she will bike 1/6km in one minute
A jar contains 5 red marbles, 7 green marbles, and 6 blue marbles.
What is the probability that you draw 3 green marbles in a row if you do replace the marbles after each draw? =
What is the probability that you draw 7 blue marbles in a row if you don't replace the marbles after each draw? =
Probability of drawing 3 green marbles in a row with replacement is 0.059
The probability that you draw 7 blue marbles in a row without replacement is 0
What is the probability?
Probability is used to determine the odds in favor or against a random event happening. The probability that the random event happens lie between 0 and 1. The more likely it is that an event would happen the closer the probability value would be to 1.
Probability of drawing 3 green marbles in a row with replacement = (7/18) x (7/18) x (7/18) = 0.059
The probability that you draw 7 blue marbles in a row without replacement = (6/18) x (5/17) x (4/16) x (3/15) x (2/14) x (1/13) x 0 = 0
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HURRY!!
Describe the end behavior of f(x) = −3x4 + 7x2 − x + 13.
The end behavior of the given function will be given by Down on the left down on the right.
A function may be defined as the expression in which for one value of input variable there is only one value of output variable. The input variable or the independent variable is x, and the output variable or the dependent variable is y. In the given function f(x) = -3x⁴ + 7x² - x + 13 we will use the Power and Polynomial Functions features. For final behavior of power functions of the form f(x) = axⁿ where n is represented as a non-negative integer depends on the power and the constant. Here, the leading coefficient is -3x⁴. So, when x → ∞ the value of f(x) → -∞ and when x → -∞ then the value of f(x) → -∞. So, the final answer for the behavior will be given by "Down on the left, down on the right".
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What is the y-value when the x-value is 18?
Answer: -11
Step-by-step explanation:
please help !!!!!!!!!!!!!!!!!!!!!
5⁶ is the simplified form of the expression ( 5⁶/5³ )².
What is the simplified form of the given expression?Given the expression in the question;
( 5⁶/5³ )²
To simplify the expression; us the law of indices.
xᵃ ÷ xᵇ = xᵃ⁻ᵇ
Hence, perform the operation inside the parenthesis
( 5⁶/5³ )²
( 5⁶ ÷ 5³ )²
( 5⁶⁻³ )²
( 5³ )²
To remove the parenthesis, apply the law of indices.
( xᵃ )ᵇ = xᵃ ˣ ᵇ
( 5³ )²
5³ ˣ ²
5⁶
Therefore, the simplified form of the expression is 5⁶.
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An architect is standing 250 feet from the base of a building and would like to know the height of the building. If he measures the angle of elevation to be 55°, what is the approximate height of the building? Round any intermediate calculations if needed to know less than six decimal places and round the final answer to the nearest 10th of a foot
see the figure below to better understand the problem
we have that
[tex]\begin{gathered} tan55^o=\frac{h}{250}---->\text{ by TOA} \\ \\ solve\text{ for h} \\ h=250*tan55^o \\ h=357.0\text{ ft} \end{gathered}[/tex]The answer is 357.0 feetWhat was the most common button length? Write your answer on the line below.Answer inches
Answer:
3/4 inches
Explanation:
The most number of cross symbols (vertical line) is on the length 6/8 inches, that is, 3/4 inches.
So, the most common button is of length 3/4 inches.
The costs of repairing iPads in UAE are normally distributed with a standard deviation 73 Dhs. If 8% of the costs exceed 279 Dhs, find the mean of the costs. Round your answer to the nearest diham.
The costs of repairing iPads in UAE are normally distributed with a standard deviation of 73 Dhs. If 8% of the costs exceed 279 Dhs, then the mean of the costs is 1.405072
The mean of the Costs stands for the typical sum of money spent on a product's production. Depending on how many units are made, this amount may change.
Let X be the price of fixing iPads in the UAE (in Dhs)
X ~ N (μ, σ = 73)
if 8% of the costs are greater than 297 Dhs.
P (X > 297) = 8%
P(X > 297) = 0.08
We must determine the mean value (μ)
P (X > 297) = 0.08
P [(X - μ) / σ > (297 - μ) / 73] = 0.08
P [Z < (297 - μ) / 73] = 0.08
P [Z < (297 - μ) / 73] = 1 - 0.08
P [Z < (297 - μ) / 73] = 0.92
(297 - μ) / 73 = Z⁻¹(0.92)
(297 - μ) / 73 = 1.405072 (Using R software)
297 - μ = 73 * 1.405072
μ = 297 - (73 * 1.405072)
μ = 297 - 102.5702
μ = 194.4298
μ ≅ 194
Therefore, the mean of the cost (μ) = 194 dhs.
Using R Software, we can compute;
Z⁻¹ (0.92) is,
=qnorm(0.92) ` → (Command)
'1.405072 → (Output)
⇒ Z⁻¹ (0.92) = 1.405072
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You may write negative infinity, positive infinity or all reals if you must use these as part of your answer. Separate numbers using commas and use the word bone if needed. Round numerical numbers to the hundredths.
Given
The function,
[tex]h(x)=|x+2|+4[/tex]To find the type of function, domain, range, x-intercept, y-intercept, one minimum or maximum, intervals where the function is positive, intervals where the function is negative.
Explanation:
It is given that,
[tex]h(x)=|x+2|+4[/tex]Since the function is related to modulus value.
Then, the type of the function is Absolute value function.
Also, Since
[tex]h(x)=|x+2|+4[/tex]Then, the domain of the function is,
[tex](-\infty,\infty)[/tex]Set h(x)=z,
[tex]z=|x+2|+4[/tex]The range of the absolute function c | a x + b | + k is f(x) is greater than equal to k.
Then,
[tex]f(z)\ge4[/tex]Therefore, the range is,
[tex][4,\infty)[/tex]From, the graph
From the figure there is no x-intercept.
Also, the y-intercept is 6.
Now, to find the critical points
Jen draws a polygon with Vertices E (-2, 3.5), F (3,3.5) G (3,-1.5) And H (-2, "-1.5)." Is EFGH a square? Justify your answer
The polygon EFGH is a polygon.
What is polygon?
A polygon is a form of planar figure in geometry and is defined as a closed polygonal chain made up of a finite number of straight line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both is referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.
To check the polygon EFGH is a square or not, first to find the length of each side of polygon.
If the length of each side is equal then the polygon EFGH is a square.
(Since length of each side of square is equal).
We know,
[tex]d \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex]
where,
d = distance
[tex](x_1, x_2)[/tex] = Coordinates of the first point.
[tex](x_2, y_2)[/tex] = Coordinates of the second point.
So,
[tex]EF = \sqrt{(3-(-2))^2 + (3.5-3.5)^2} = \sqrt{25 + 0} = 5[/tex]
[tex]FG = \sqrt{(3-3)^2 + (-1.5-3.5)^2 } = \sqrt{0 + 25} = 5[/tex]
[tex]GH = \sqrt{(-2-3)^2 + (-1.5-(-1.5))^2} = \sqrt{25 + 0} = 5[/tex]
[tex]EH = \sqrt{(-2-(-2))^2 + (-1.5-3.5)^2} = \sqrt{0 + 25} = 5[/tex]
From above the length of each side is equal.
Therefore, given polygon EFGH is a square.
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select the correct answer what is the simplified form of 45
The solution is option C.
(4x + 7) + 35 = 90 solve for x
Answer:
x=12
Step-by-step explanation:
(4x + 7) + 35 = 90
(4x+7)=90-35
4x+7=55
4x=55-7
4x=48
x=12
Answer:
x=12
Step-by-step explanation:
it just is.,...........
Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, AAA, in dollars, that he receives from the first donor given that he walks ddd kilometers is given by the formula A(d)=10dA(d)=10dA, left parenthesis, d, right parenthesis, equals, 10, d. The money, BBB, in dollars, that he receives from the second donor given that he walks ddd kilometers is given by the formula B(d)=2d+d^2B(d)=2d+d
2
B, left parenthesis, d, right parenthesis, equals, 2, d, plus, d, squared.
Let TTT be the total money that Onur raises from those donors by walking ddd kilometers in the walkathon.
Write a formula for T(d)T(d)T, left parenthesis, d, right parenthesis in terms of A(d)A(d)A, left parenthesis, d, right parenthesis and B(d)B(d)B, left parenthesis, d, right parenthesis.
The function of the total money raised from both donors after walking d kilometers is T(d) = 12d + d^2
How to determine the composite function of the total amount?From the question, the given parameters are:
First donor at d kilometers, A(d)=10dSecond donor at d kilometers, B(d) = 2d + d^2Also, from the question, T is the total money raised from both donors at d kilometers
This means that the equation of the total money can be represented a
T(d) = A(d) + B(d)
Substitute the known values in the above equation
So, we have the following equation
So, we have
T(d) = 10d + 2d + d^2
Evaluate the like terms in the above equation
T(d) = 12d + d^2
The equation cannot be further simplified
Hence, the composite function is T(d) = 12d + d^2
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Complete question
Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, A, in dollars, that he receives from the first donor given that he walks d kilometers is given by the formula A(d)=10d
The money, B, in dollars, that he receives from the second donor given that he walks d kilometers is given by the formula B(d)=2d+d^2
Let T be the total money that Onur raises from those donors by walking d kilometers in the walkathon.
Write a formula for T(d) in terms of A(d) and B(d)
A map state where your friend lives have a scale 1/2 inch: 10 miles.
Your friend measured the distance between her town and the state capital on the map. Her measurements were 4 1/2 inches. Based on your friend's measurement, what is the actual distance in miles between her town and the state capital?
The actual distance is 90 miles between the town and the state capital based on the scale of the map
1/2 inch on the map = 10 miles
So, 1 inch = 20 miles
Distance between the town and state capital = 4 1/2 inches
The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.
The actual distance in miles between the town and the state capital is given by:
Distance between town and state capital* Scale of the map
= 4.5*20
= 90 miles
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Given f(x) = x3 - 5, find f-'(x).
the inverse function = f^-1(x) is option C
First let's state what we are given:
f(x) = x^3 - 5
We are to find the inverse of f(x).
To do this, first let's represent f(x) with y
y = = x^3 - 5
Then, we would interchange x and y
[tex]\begin{gathered} x=y^3\text{ - 5 (make y the subject of formula)} \\ x+5=y^3 \\ find\text{ cube root both sides} \\ \sqrt[3]{y^3\text{ }}=\sqrt[3]{(x+5)} \\ y\text{ = }\sqrt[3]{(x+5)} \end{gathered}[/tex]From the answer we got, the inverse function = f^-1(x) is option C
Which of the following graphs shows a parabola with a vertex of (-4,4) and solutions of (-6,0) and (-2,0)?
Equation is -(x+4)² +4.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. The vertex form of a quadratic equation is y = a (x h) 2 + k as opposed to the regular quadratic form, which is an x 2 + b x + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
Given Data
Solutions (-6, 0) and (-2,0)
y = a(x - (-6)) (x-(-2))
y = a(x+6) (x+2)
Vertex (-4,4)
at x = -4 and y = 4
4 = a(-4+6)(-4+2)
4 = a (2)(-2)
a = -1
y = -1(x+6)(x+2)
y = -(x²+8x+12)
y = =(x² + 3x +4x+4²-4²+12)
y = -(x+4)² +4
Equation is -(x+4)² +4.
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Write a function and use a table and graph to predict when the population will reach 20,000
The formula for exponential growth is expressed as
y = a(1 + r)^t
where
y is the population after t years
ais the initial population
r is the growth rate
t is the number of years
From the information given,
a = 350
r = 14% = 14/100 = 0.14
By substituting these values into the equation, the function to model th growth rate is
y = 350(1 + 0.14)^t
y = 350(1.14)^t
We would substitute values of t into the equation to determine corresponding values of y. We have
For t = 2, y = 350(1.14)^2 = 454.86
For t = 6, y = 350(1.14)^6 = 768.24
For t = 10, y = 350(1.14)^10 = 1297.52
We would plot these values of y on the y axis and the corresponding values of t on the x axis. The graph is shown below
The time when the population will reach 20000 would be the value of x at the point where y = 20000 on the graph. It is around y = 30.87
Thus, the population will reach 20000 in approximately 31 years
We can confirm this by solving the equation. We have
20000 = 350(1.14)^t
20000/350 = 1.14^t
57.14 = 1.14^t
Taking natural log of both sides, we have
ln 57.14 = ln1.14^t = tln1.14
t = ln 57.14/ln1.14
t = 30.87505