The value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
The value of the car is given as:
[tex]J(t)=27000(0.9)^{2t+2}[/tex]
The equation can be written as:
[tex]J(t)=27000(0.9)^{2t} (0.9)^2\\\\J(t) = 27000(0.81)^t(0.81)\\\\J(t) = 21870(0.81)^t[/tex]
Hence, the value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].
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Could you please help me with 13, 14, and 15 please
Answer:
your mom a cow your dad left for milk
36 divided s =4; 9,10,11,
Answer:
Step-by-step explanation:
The expression 36 divided by s = 4 can be solved for s by dividing both sides of the equation by 36:
36/s = 4
Dividing both sides of the equation by 4:
s = 36/4 = 9
So, the value of s that makes the equation true is 9. This means that if you divide 36 by 9, the result will be 4.
Create a graph of the equation 3y=-6x-12
Answer:
Step-by-step explanation:
To graph the equation 3y = -6x - 12, we can start by finding the x and y intercepts.
The x-intercept is the point where y = 0, so we can substitute 0 for y in the equation:
3y = -6x - 12
3 * 0 = -6x - 12
0 = -6x - 12
12 = -6x
x = -2
So the x-intercept is (-2, 0).
The y-intercept is the point where x = 0, so we can substitute 0 for x in the equation:
3y = -6x - 12
3y = -6 * 0 - 12
3y = -12
y = -4
So the y-intercept is (0, -4).
Now that we have the x and y intercepts, we can plot the points on the graph and draw a line that passes through both points. This line will be the graph of the equation.
In this case, the graph of the equation 3y = -6x - 12 is a downward sloping line that passes through the points (-2, 0) and (0, -4).
a box has n socks, 3 of which are red. what is the value of n if, when 2 socks are chosen randomly from the box, the probability of both socks being red is 1/2?\
The total number of socks are n, 3 of which are red. when 2 socks are chosen randomly from the box, the probability of both socks being red is 1/2 so the value of n is 4.
The information given by question is
Total number of socks = n
Number of red socks = 3
when 2 socks are chosen randomly from the box
Probability of both socks being red = 1/2
Ways of choosing 2 socks from n = [tex]_nC_2[/tex]
Ways of choosing 2 red socks from 3 = [tex]_3C_2[/tex]
Probability of both socks being red = [tex]\frac{_3C_2}{_nC_2}[/tex]
[tex]\frac{6}{n(n-1)}[/tex] = [tex]\frac{1}{2}[/tex]
12 = n² - n
n² - n -12 = 0
n² - 4n + 3n - 12 = 0
n(n - 4) + 3(n - 4) = 0
(n - 4)(n + 3) = 0
n = 4 or -3
Ignore negative value, therefore n = 4
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.Is this equation linear or non linear? explain why.
Answer:
Non-linear
Step-by-step explanation:
y = 10/x is non-linear!
Because a linear equation is an equation of a straight line, which means the degree of a linear equation must be 0. In this case, the degree of variable y is 1; the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not linear.
i forgot what this is even though i learned it someone please help me or at least explain to me what I'm looking at and how to solve it
Answer: C, I hope this helps
PLEASE HELP!! (Click on Image for questions 5 and 6)
Answer:
5
a 113b 67c 676
a 77b 77c 103Find all the zeros of the quadratic function. y=x^2+11x+18 If there is more than one zero, separate them with commas. If there are no zeros, click on "None".
None. The discriminant of the quadratic equation is [tex]b^{2}[/tex]-4ac = [tex]11^{2}[/tex] - 4(1)(18) = 121 - 72 = 49, which is not a perfect square.
What is perfect square ?A perfect square is a number that can be expressed as the product of two equal integers. For example, 9 is a perfect square because it can be written as 3 x 3.
The zeros of this quadratic function can be found by setting the equation equal to 0 and solving for x.
0 = [tex]x^{2}[/tex] + 11x + 18
To solve for x, we can use the quadratic formula:
x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a
Substituting in our values from the equation above, we get:
x = [-11 ± √([tex]11^{2}[/tex] - 4(1)(18))]/2(1)
x = [-11 ± √(-63)]/2
Since the square root of a negative number is not a real number, there are no zeros.
Therefore, the answer is None.
So, there are no real solutions.
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Help please, check photo
The value of x in function cos(3pi/2+2x/3)=1/2 is x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
We are given;
6sinx=5, 6cosx=7, sin2x=0, sin(x+pi/3)+1=0, cos(2x/3-pi/4)=[tex]\sqrt{2} /2[/tex], cos2x-1=0, 2sin3x=-1, cos(3pi/2+2x/3)=1/2
Now,
1. 6sinx=5
sinx=5/6
x=0.98511078
2. sin2x=0
x=n*pi/2
3. sin(x+pi/3)+1=0
x-intercept= (pi/6+2n*pi)
y-intercept= (0, [tex]\sqrt{3}[/tex]/2 -1)
4. cos(2x/3-pi/4)=[tex]\sqrt{2}/2[/tex]
x= (pi/4+n*pi, pi+n*pi)
6. cos2x-1=0
x=n*pi
7. 2sin3x=-1
x= 7pi/18 + 2pi*n/3, 11pi/18+2pi*n/3
8. cos(3pi/2+2x/3)=1/2
x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n
For any value of integer n
Therefore, the answer of trigonometric function will be x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.
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How many solutions does the system of equations below have?
10x + 4y = -1
20x + 8y = -13
no solution, one solution, or infinitely many solutions
simplify (10x3−x2+6x+3)+(x4−3x3+8x2−9x+16)
Answer: =x^4+7x^3+7x^2-3x+19
Step-by-step explanation:
= 10x^3 -x^2 +6x +3 +x^4 -3x^3 +8x^2-9x+16
Step 1. Group like-terms. x^4+10x^3-3x^3-x^2+8x^2+6x-9x+3+16
Step 2. Add similar elements. x^4+7x^3-x^2+8x^2+6x-9x+3+16
Step 3. Keep adding similar elements. x^4+7x^3+7x^2+6x-9x+3+16
Step 4. Add similar elements, again. x^4+7x^3+7x^2-3x+3+16
Step 5. Final adding elements. x^4+7x^3+7x^2-3x+19
every day, the logan pet store uses 9/10 of a bag of dog food to feed the dogs. how many days will 1 4/5 bags of dog food last? write your answer as a fraction or as a whole or mixed number.
1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.
The Logan pet store uses 9/10 of a bag of dog food every day, which means they need 9/10 * 1 bag = 9/10 bags of dog food per day. To determine how many days 1 4/5 bags of dog food will last,
we need to divide the total amount of dog food by the amount used per day: 1 4/5 bags / (9/10 bags/day) = (9/10)*(18/5) / (9/10) = 18/5 days. Therefore, 1 4/5 bags of dog food will last for 18/5 days.
One 4/5 bags of dog food will last the Logan Pet Store (LPS) for approximately 8 and 3/10 days. This is because if the LPS uses 9/10 of a bag of dog food every day, then they are using 9/10 * 5/5 = 9/10 bags of dog food per day. If we divide 1 4/5 bags of dog food by 9/10 of a bag per day, we get (1 4/5) / (9/10) = (18/5) / (9/10) = 18/5 * 10/9 = 20/9 days. Therefore, 1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.
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A group of researchers is studying the relationship between cortisol (stress hormone) levels and memory, and they want to see if a sample of 25 adults that has been recruited is a good representation of the population it came from, before they conduct additional research. The population has been found to have an average cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have an average cortisol level of 15 mcg/DL, with a standard deviation of 3 mcg/dL. For this assignment, construct a confidence interval to determine if this sample mean is significantly different from the population mean. Explain how you know, based on the confidence interval, and specific the confidence level you used. Be sure to show your work and calculations. This can be tricky with Word, so if necessary you may take a photo of your hand calculations and add it to the Word document
The sample mean is significantly different from the population mean. The confidence level used was 95%.
To build a confidence interval to decide whether this example mean is fundamentally not the same as the populace mean, there are a few stages that should be taken.
To begin with, work out the standard error of the mean (SEM) for the example, which is the standard deviation separated by the square base of the example size (SEM = σ/√n). For this situation, the SEM is 3/5 = 0.6 mcg/dL.
Then, compute the critical value for the confidence interval picked by increasing the SEM by the t-esteem from the t-dissemination for the given confidence interval. For instance, in the event that a 95% confidence interval is picked, the t-esteem is 1.96. This provides us with a basic worth of 0.6 x 1.96 = 1.176 mcg/dL.
At last, build the certainty span utilizing the example mean and the basic worth. The certainty span is (15 - 1.176, 15 + 1.176), or (13.824, 16.176). This implies that we are 95% sure that the genuine populace mean exists in this reach.
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What is 2 1/5 + 1 5/6??
A bone fragment has 10% of the parent Pb-210 remaining. The half-life of Pb-210 is 22 years.
How old is the bone fragment?
A bone fragment that has 10% of the parent Pb-210 remaining with half-life of Pb-210 is 22 years, the bone fragment is approximately 51 years old.
To determine the age of the bone fragment, you need to calculate the number of half-lives that have elapsed since the bone was formed. The age of the bone can be calculated using the formula:
age = number of half-lives * half-life
To calculate the number of half-lives, you need to determine how much of the original Pb-210 has decayed. If a bone fragment has 10% of the parent Pb-210 remaining, then 90% has decayed.
You can calculate the number of half-lives by taking the natural logarithm of the ratio of the remaining amount of Pb-210 to the original amount:
number of half-lives = ln(0.10) / ln(0.5)
Using the half-life of Pb-210, which is 22 years, you can now calculate the age of the bone fragment:
age = number of half-lives * 22 years
Substituting the values and calculating the number of half-lives and the age of the bone fragment, you get:
number of half-lives = ln(0.10) / ln(0.5) = 2.302
age = number of half-lives * 22 years = 51.064 years
So, the bone fragment is approximately 51 years old.
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Find an equation of the line L.
L is perpendicular to y = - 2x.
4
On solving the provided question, we can say that the new equation of the line is = (y +6) = 1/2(x-3) => x - 2y = 9
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
coordinates are (3, -6)
the perpendicular equation is y = -2x
so, m. the slope = 1/2
the new equation of the line is = (y +6) = 1/2(x-3)
2y + 12 = x = 3
x - 2y = 9
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Which property is demonstrated below?
A. associative property
B. distributive property
C. commutative property
D. identity property
The property which is demonstrated by this expression 6 + 7 = 7 + 6 include the following: C. commutative property.
What is the Commutative Property of Addition?In Mathematics, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.
Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.
By applying the Commutative Property of Addition, we have the following;
6 + 7 = 7 + 6
13 = 13
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Complete Question:
Which property is demonstrated below?
6 + 7 = 7 + 6.
A. associative property
B. distributive property
C. commutative property
D. identity property
slice for x please and thank you
Answer:
x = 45
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360
x + 3x + 90 + 90 = 360
4x + 180 = 360 ( subtract 180 from both sides )
4x = 180 ( divide both sides by 4 )
x = 45
mike estimated the difference of 79.44 and 6.7 by rounding to the nearest whole.
We can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.
What is rounding off?A number is simplified when it is rounded off, preserving its value while moving it closer to the next number.
It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.
When numbers are rounded off, the important numbers are kept.
To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up.
So, Mike determined 79 to be 79.44 and 7 to be 6.7, so he determined the difference as follows:
79 - 7 = 72
Actual numbers that vary are:
79.44 - 6.7 = 72.74
Therefore, we can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.
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Correct question:
Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be. The actual difference is __.
5-8(3+x) simplified expression
Answer: -8x - 19
Step-by-step explanation:
Distribute: 5-8(x+3) = 5-8x-24
5-8x-24= -19 - 8x
= -8x - 19
Answer:
-8x - 19
Step-by-step explanation:
1. Rearrange terms: 5 - 8 (3 + x)
2. Distribute terms: 5 - 8 ( x + 3) = 5 - 8x - 24
3. Subtract the numbers: 5 - 8x - 24 = -19 - 8x
4. Rearrange terms again: -19 - 8x to -8x - 19
5. Here's your answer! Hope this helped :)
What is the circumference, in centimeters, of the circle? Use 3. 14 for π. Enter your answer in the box. Cm
the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.
94.68 cm
The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, to find the circumference of the circle, we need to first calculate the radius.
The area of the circle is given as A = πr2.
Therefore, we can rearrange this equation to solve for the radius, which is
r = √(A/π)
Plugging in the given area, A = 3.14, we get
r = √(3.14/π) = √(3.14/3.14) = 1
Now, we can use the circumference formula to calculate the circumference, which is
C = 2πr = 2π(1) = 2π × 3.14 = 6.28 × 3.14 = 19.4568
Therefore, the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.
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Enter the interval equivalent to
2
<
x
≤
5
or
x
>
7
2,5
this is how I got the answer
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green, and 1 yellow. What is the probability that you draw one marble that is blue, DO NOT replace it, and draw another marble that is green?
The probability of drawing one blue marble on the first draw is 4/10. Since we do not replace the marble, there are only 9 marbles left in the bag, so the probability of drawing a green marble on the second draw is 2/9.
The probability of drawing one blue marble and one green marble is the product of the probabilities of each event:
(4/10) x (2/9) = 8/90 = 4/45
Therefore, the probability of drawing one blue marble and one green marble is 4/45.
mark as brainliest pls
The ratio of the measures of the sides of a
triangle is 4:7:5. If the perimeter of the
triangle is 128 yards, find the length of the
longest side.
Answer: 56 yards
Step-by-step explanation:
4 + 7 + 5 = 16
128 / 16 = 8 yards
7 is the highest ratio in the set so
7 x 8 yards = 56 yards
What is the 12th term of the sequence -2,-4,-6,...........-100?
pls help
Mr. Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax.
Choose an equation to determine x, the maximum number of bracelets Mr. Gonzales could buy.
The equation to determine the maximum number of bracelets Mr. Gonzales could buy is 29 + 4.50x = 42.50 and the maximum number of bracelets is 3.
According to the question Gonzales has $42.50.
Cost of shirt = $29
Cost of bracelets = $4.50 each.
so, the equation becomes
Total cost = money that Gonzales has.
The cost is $29 + 4.50x, where x is the number of bracelets he can buy.
29 + 4.50x = 42.50
4.50x = 42.50 - 29
x = 13.50/4.50
x = 3
So we have that Mr. Gonzales can buy a total of 3 bracelets.
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Answer: The equation is $29 + x$4.50 = $42.50, and the solution is x = 3
Step-by-step explanation:
The data we have is: Gonzales has $42.50. He wants to buy a shirt that costs $29. SOME bracelets that cost $4.50 each.
The equation that we need to solve is: Total cost = money that Gonzales has. The expression to find the cost is $29 + $4.50x
X represents the number of bracelets he can buy. The equation that we need to solve is: $29 + $4.50x = $42.50
To solve it we must isolate the x
$4.50x = $42.50 - $29 = $13.50x = 13.50/4.50 = 3
So we have that Mr. Gonzales can buy a total of 3 bracelets.
An equestrian club orders magazine subscriptions for new members. Last year, it had 32 new members and spent $576 on subscriptions. Solve the equation 32m = 576 to find the cost of each subscription, in dollars.
Answer:
$ 18
Step-by-step explanation:
To find the cost of each subscriptions, divide the cost of total subscriptions by 32.
32m = 576
m = 576 ÷ 32
m = $ 18
if the work required to stretch a spring 3 ft beyond its natural length is 6 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length?
A total of 2.25 ft-lb work is needed to stretch it 18 in. beyond its natural length.
One foot is equal to 12 inches, so 3 ft is equal to 36 inches. To stretch the spring 18 inches beyond its natural length, we need to perform work on it to stretch it an additional 18/36 = 1/2 of the 3 ft distance. If the work required to stretch it 3 ft is 6 ft-lb, then to stretch it 1/2 of that distance, we would need 1/2 of the work, or 6/2 = 3 ft-lb. The work needed to stretch the spring 18 inches beyond its natural length is 3 ft-lb * 18 inches/12 inches/ft = 2.25 ft-lb.
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Finding the time to reach a limit in a word problem on...
A laptop computer is purchased for $3300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth
$500 or less? (Use the calculator provided if necessary.)
Write the smallest possible whole number answer.
years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 500\\ P=\textit{initial amount}\dotfill &3300\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=years \end{cases}[/tex]
[tex]500 = 3300(1 - 0.75)^{t} \implies \cfrac{500}{3300}=0.25^t\implies \cfrac{5}{33}=0.25^t \\\\\\ \log\left( \cfrac{5}{33} \right)=\log(0.25^t)\implies \log\left( \cfrac{5}{33} \right)=t\log(0.25) \\\\\\ \cfrac{\log\left( \frac{5}{33} \right)}{\log(0.25)}=t\implies 2\approx t\qquad \qquad \textit{to be exact, about 1 year and 131 days}[/tex]
Can anyone help me with the question i circled cuz i couldn't understand them
the equation for the line perpendicular will be y = -5x +11.
What is the equation straight line?
The formula for a straight line is generally expressed as Y = mx + c, where m stands for the slope and c for the y-intercept. In geometry, it is the straight-line version of the equation that is most usually utilised. A straight-line's equation can be expressed in a variety of forms, including point-slope form, slope-intercept form, general form, standard form, etc. An infinitely long straight line has two dimensions and is a geometrical object with two ends. The equations for a straight line that are used the most frequently are y = mx + c and axe + by = c. Point-slope, slope-intercept, standard, general, and other forms are more variations.
The given line is y = x/5 +3
the slope is m = 1/5
So the slope of the perpendicular line will be -5
So the equation of line will be y-3 = m1(x-1)+3
y-3 = -5x+5+3
y = -5x +11
Hence the equation for the line will be y = -5x +11.
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