Answer:
The value of the book after 11 years is $103.11
The equation should be 258*0.92, 11 times repeating.
The answer should be 103.106443494, but if you round it the answer is 103.11
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &258\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &11\\ \end{cases} \\\\\\ A = 258(1 - 0.08)^{11} \implies A=258(0.92)^{11}\implies A \approx 103.11[/tex]
ABCD is rhombous wi4h M(<ADC)=135 find m(<BAD) and m(<ADC)
In the given figure of Rhombus, Angle ∠BAD is 0°. In summary: angle ∠ABC = 135°
angle ∠ADC = 135°
angle ∠BAD = 0°
What is rhombus?
A rhombus is a quadrilateral (four-sided) geometric shape with equal-length sides. Since it has two sets of opposite equal acute angles and opposite equal obtuse angles, it is also known as a diamond form. In other words, the opposite angles and the neighbouring sides of a rhombus are congruent. A rhombus has two equal-length diagonals that are right angles to one another. A rhombus's area is equal to the product of its diagonal lengths.
by the question.
In a rhombus, opposite angles are equal, so we know that:
angle ∠ABC = angle ∠ADC (opposite angles of rhombus)
angle ∠BCD = angle ∠BAD (opposite angles of rhombus)
We are given that angle ∠ADC is 135°. Therefore, angle ∠ABC is also 135°.
To find angle ∠BAD, we can use the fact that the angles of a quadrilateral sum to 360°. Since we know three of the angles (∠ABC, ∠BCD, and ∠ADC), we can find the fourth angle (∠BAD) by subtracting their sum from 360°:
∠BAD = 360° - (∠ABC + ∠BCD + ∠ADC)
= 360° - (135° + 90° + 135°)
= 360° - 360°
= 0°
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a recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by peterbilt. find a 95% confidence interval for those who shop at this dealership that will purchase a peterbilt truck. identify the correct population parameter.
The correct population parameter for shop at this dealership that will purchase a Peterbilt truck is p that is option C.
In statistics, a population parameter characterises an individual or population. A population parameter describes the distribution of all values within a group and is a fixed but unknowable property. The parameters used in other sorts of maths should not be confused with this. These are the parameters of a mathematical function that never change. An indicator of the population is not a statistic. This information only applies to a portion of a certain demographic. You can determine the genuine population value with the aid of a well-designed research.
Statistics and parameters share many similarities. Both express a characteristic of the group, such as the fact that 20% of M&Ms are red. Yet, the fundamental distinction is in who and what they are describing. The entire population is referred to by parameters. The part or sample that was examined in a study is referred to as the statistic.
You might count the quantity of red M&Ms in the aforementioned example's various packs. Your statistic will be provided by this. If your study was well-designed, the statistic you obtain should precisely reflect the population parameter.
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Complete question:
A recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by Peterbilt. Find a 95% confidence interval for those who shop at this dealership that will purchase a Peterbilt truck. Identify the correct population parameter.
μ
х
р
p^
[tex]\mu_1 - \mu_2[/tex]
Xi – X2
î
Pi – P2
If f(x) = x3, what is the equation of the graphed function?
A. y = f(x − 3) − 2
B. y = f(x + 3) – 2
C. y = f(x + 2) − 3
D. y = f(x − 2) + 3
Answer:
B. y = f(x + 3) – 2
Step-by-step explanation:
We need move point (0,0) to point (-3,-2).
(-3,-2)=(a,b)
y=f(x-a)+b
y=f(x-(-3))-2
y=f(x+3)-2
Answer:
f(x) = (x+3)^3
I think this is the right answer...
g suppose an unknown radioactive substance produces 2800 counts per minute on a geiger counter at a certain time, and only 700 counts per minute 15 days later. assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance. the radioactive substance has a half-life of days.
The half-life of the radioactive substance is 7.5 days. This means that, after 7.5 days, half of the radioactive atoms will have decayed and the count per minute will be reduced by half
The half-life of a radioactive substance is the amount of time it takes for half of its radioactive atoms to decay. In this case, you are given the initial count per minute of 2800 and the count per minute after 15 days of 700. We can use this information to calculate the half-life of the radioactive substance. First, divide the initial count per minute (2800) by two. This gives us the count per minute that we need to find, which is 1400.
We then subtract the count per minute after 15 days (700) from the count per minute we need to find (1400). This gives us the difference in count per minute, which is 700. Now, we need to determine how much time it would take for the count per minute to decrease by 700. To do this, we divide the difference in count per minute (700) by the initial count per minute (2800). This gives us a decimal, which we then multiply by the number of days (15). The result is the half-life of the radioactive substance in days, which is 7.5 days.
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help me with this please hurry
Answer: Its A
Ive took this test :3
How to solve it and what the answer
Answer:
34.56 in
Step-by-step explanation:
2.4*2.4*6=34.56
A vehicle purchased for $ 29800depreciates at a constant rate of 9% per year. Determine the approximate value of the vehicle 15 years after purchase.
Answer:
The value of the vehicle would be $7,242
Step-by-step explanation:
Given,
The original value of the vehicle, P = $29,800,
Rate of depreciation, r = 9% = 0.09
Time, t = 15 years,
Thus, the value of the car after 15 years,
[tex]A=P(1-r)^t[/tex]
[tex]=29800(1-0.09)^{15}[/tex]
[tex]=29800(0.91)^{15}[/tex]
[tex]=7241.64363066[/tex]
[tex]\thickapprox \bold{\$ 7,242}[/tex]
100 POINTS AND BRAINLIEST Please help solve at least 1 of these problems and show your work because I don’t know how to solve these
Step-by-step explanation:
Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.
a)
n = 6 : 2
n = 3
m = √(6²+3²)
m = √45
b)
x = 10 x 2 = 20
y = √(20²-10²)
y = √300
c)
a = √(5²+5²)
a = √50
the answers are in simple radical form as requested
Ms. Kent measures the perimeter of a common shape. One of the sides is 7 centimeters, and the perimeter is
21 centimeters. If all of the sides are the same length, what shape does Ms. Kent measure? Explain.
Answer:
Step-by-step explanation:
If the perimeter of a shape is 21 centimeters and one side is 7 centimeters, then we can find the total number of sides by dividing the perimeter by the length of one side:
Number of sides = Perimeter / Length of one side
Number of sides = 21 cm / 7 cm
Number of sides = 3
This means that the shape has 3 sides, which makes it a triangle.
Since all sides of the triangle have the same length, we can call it an equilateral triangle. In an equilateral triangle, all sides have the same length, and all angles are 60 degrees.
The gas mileage m(x) (in mpg) for a certain vehicle can be approximated by m(x) = -0.026x^2 + 2.593x - 35.023, where x is the speed of the vehicle in mph. What is the maximum/mph.
Answer:
To find the maximum gas mileage, we need to find the vertex of the parabola representing the gas mileage function.
The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c is given by -b/2a.
In this case, the gas mileage function is m(x) = -0.026x^2 + 2.593x - 35.023, so a = -0.026 and b = 2.593.
The x-coordinate of the vertex is therefore:
x = -b/2a = -2.593/(2*(-0.026)) = 49.9 (rounded to one decimal place)
This means that the maximum gas mileage occurs at a speed of 49.9 mph.
To find the maximum gas mileage, we can substitute x = 49.9 into the gas mileage function:
m(49.9) = -0.026(49.9)^2 + 2.593(49.9) - 35.023 ≈ 36.1 mpg
Therefore, the maximum gas mileage is approximately 36.1 mpg.
Step-by-step explanation:
The radius of a circle is 18 cm. Find its area in terms of π
Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?
A.{x | x R, x < 5}
B.{x | x R, x > 5}
C.{x | x R, x ≤ 5}
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
What exactly is a set?
In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.
Now,
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.
In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.
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I don't understand this, can someone please help me?
Answer: You'll have to plug each function into a calculator and match the corresponding ones with each other.
for example Sin45° = B cos 45°
Step-by-step explanation:
9e^2 f=49 solve for e
For given expression e will be 7/3.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a single value.
Expressions can be simple or complex, and they can involve arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.
Now,
We can solve for e by setting the given value of f equal to 49 and then solving for e.
f = 9e²
When f = 49, we have:
49 = 9e²
Dividing both sides by 9, we get:
49/9 = e²
Taking the square root of both sides, we get:
±√(49/9) = ±(7/3) = e
So the solutions for e are e = 7/3 or e = -7/3. However, since e is a measure of distance and cannot be negative, the only valid solution is e = 7/3.
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Correct Question:-
Function f=9e² , If f=49 then solve for e.
On three of the first four math tests, Daniel earned the following scores: 84, 92 and 88. If Daniel’s
average for all four tests is 87.5, what score did Daniel earn on his fourth test?
Answer: 86
Step-by-step explanation:
let x be the unknown
(84+92+88+ x)
----------------------- = 87.5
4
then cross multiply
(84+92+88+ x )= 87.5 times 4
84+ 92+ 88 + x= 350
add the left side
264+ x=350
subtract 264 from both sides
264 - 264 + x= 350 - 264
therefore x= 86.
Match the example on the left with corresponding property on the right 1. x+y+z=z+y+x
Answer:
Commutative property of addition.
Step-by-step explanation:
The given expression is:
x + y + z = z + y + x
To match the example with the corresponding property, we need to simplify the expression using the commutative property of addition.
According to the commutative property of addition, the order of the terms in an addition expression does not affect its value. That is:
a + b = b + a
Using this property, we can rewrite the given expression as:
x + y + z = x + y + z
we see that both sides of the equation are identical. This means that the expression is true, regardless of the values of x, y, and z.
Therefore, the example "x + y + z = z + y + x" matches with the commutative property of addition.
Divide then show a model
Select the equivalent expression
Answer:
Step-by-step explanation:
The school is located at (0, 0) on a coordinate plane. Mary lives 2 miles north of the school. Her classmate Roger lives 3 miles west of the school. What is the
distance between Mary's and Roger's houses? Round your answer to the nearest tenth of a mile.
Answer:
Step-by-step explanation:
that would be 5 miles bc 3+2 is 5
The distance between Mary's and Roger's houses is approximately 3.6 miles.
What are coordinates?
A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
We can use the Pythagorean theorem to find the distance between Mary's and Roger's houses since they form a right triangle with the school at the vertex:
Let A be the school (0, 0), B be Mary's house (0, 2), and C be Roger's house (-3, 0).
Then the length of AB is 2 miles and the length of AC is 3 miles.
The distance between Mary's and Roger's houses is the length of the hypotenuse BC.
Using the Pythagorean theorem, we have[tex]BC^2 = AB^2 + AC^2 = 2^2 + 3^2 = 13.[/tex]
Taking the square root of both sides, we get[tex]BC = \sqrt{(13)} = 3.6[/tex] miles.
Therefore, Between Mary and Roger's homes, there are roughly 3.6 miles.
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a faulty car odometer proceeds from digit $3$ to digit $5$, always skipping the digit $4$, regardless of position. for example, after traveling one mile the odometer changed from $000039$ to $000050$. if the odometer now reads $002005$, how many miles has the car actually traveled?
The car has actually travelled 1745 miles, even though the odometer reads 2005. This is because the odometer skips the digit 4, so the number of valid readings must be counted and subtracted from the odometer reading.
We can approach this problem by counting the number of valid readings on the odometer between 3000 and 5000. We can then subtract the number of invalid readings (i.e., readings that contain the digit 4) to determine the actual number of miles the car has travelled.
The valid readings between 3000 and 5000 are: 3001, 3002, 3003, 3005, 3006, 3007, 3008, 3009, 3010, ..., 4997, 4998, 4999, 5000.
There are a total of 2001 valid readings in this range.
However, we need to subtract the number of invalid readings, which are the readings that contain the digit 4. Since the odometer skips the digit 4, we can think of each valid reading as having four possible digits (0, 1, 2, or 5) for each of its four places. Therefore, the number of invalid readings is 4 x 4 x 4 x 4 = 256.
So the actual number of miles the car has travelled is 2001 - 256 = 1745.
Therefore, the car has actually travelled 1745 miles.
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Help I dont know this but it has to be done Anyone help ?
Answer:
C- 80 degrees Celsius
Step-by-step explanation:
If you followed the formula by subtracting 176 by 32 you would get 144 multiplied by 5/9 = 80 degrees
His is a question need answering
Answer:it’s wrong if so then 5 would’ve been in c’s place
Step-by-step explanation:
what is the probability that the first white ball drawn in powerball will not be an 18? round your answer to 3 decimal places.
The probability that the first white ball drawn in powerball will not be an 18 is 0.985.
Concept used:
Probability of an event = number of favorable outcomes / total number of outcomes.
We have 69 balls, out of which 1 is an 18. Thus, there are 68 balls that are not 18.
Therefore, the probability of the first white ball drawn in powerball will not be an 18 is given by,
P(event)= number of favorable outcomes / total number of outcomes= 68/69 = 0.985 (approx)
Thus, the required probability that the first white ball drawn in powerball will not be an 18 is 0.985, rounded to three decimal places.
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Write a equation and solve.
A car moves 660 feet every 10 seconds. How far does it go if it moves for 10 sec, 20 sec, and 30 sec
Answer: 10sec 660 feet, 20sec = 1320 feet, 30 sec = 1980 feet.
Step-by-step explanation:
It states that a car moves 660 feet in 10sec.
10sec = 660 feet
20sec: 660+660=1320f
30sec: 660+660+660=1980f
10 Points
What is 9 < 3 x = 8
The equation has no solution that satisfies the inequality.
How to explain the InequalityThis equation doesn't have a unique solution because it's contradictory. It should be noted that to see why, we can simplify the equation by subtracting 9 from both sides:
3x = 18 - 9
which simplifies to:
3x = 9
Now we can solve for x by dividing both sides by 3:
x = 3
However, if we substitute x = 3 back into the original equation, we get:
9 < 3(3) = 9
This isn't true. Therefore, the equation has no solution that satisfies the inequality.
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I need help with this.
thx
We can conclude after answering the provided question that In order to slope make at least $225.00 in sales, we must solve for m:
[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]
what is slope?Slope is the downward movement of a near - constant basis in mathematics. It is a test of how much the y-value of an activity appears to vary when the x-value changes. The curve of a line is ordinarily indicated by the letter m and can be determined using the equation: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 things on the line. A line's slope can be positive, negative, zero, or unknown. A positive slope indicates that the line moves up from left to right, whereas a decreasing trend indicates that the line descends from left to right.
a. Because the relationship between the two variables is proportional, the function that connects the sales (s) and the number of muffins (m) is a linear function. The slope of the line can be calculated by dividing the change in sales by the change in the number of muffins:
slope = (2400 - 1800) / (12 - 4) = 600 / 8 = 75
The equation line is as follows:
s = 75m + b
To find the y-intercept (b), we can substitute one of the data points:
[tex]1800 = 75(4) + b\sb = 1800 - 300\sb = 1500[/tex]
As a result, the function that connects sales and the number of muffins is:
s = 75m + 1500
b. In order to make at least $225.00 in sales, we must solve for m:
[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]
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How do I prove that the sum of exterior angles of any polygon is equal to 360 degrees?
To prove that the sum of the exterior angles of any polygon is equal to 360 degrees, the Sum of interior angles = (n - 2) x 180 degrees.
we can use the following steps:
Draw any polygon and mark a point outside the polygon for each vertex.
Draw a line segment connecting each vertex to the point outside the polygon that corresponds to it, creating an exterior angle at each vertex.
Measure each exterior angle using a protractor and record the measurements.
Sum all the exterior angles together and observe the result.
We can see that the sum of all the exterior angles is always equal to 360 degrees, regardless of the number of sides or the shape of the polygon. This can be written as:
The sum of exterior angles = 360 degrees
To prove this algebraically, we can use the fact that the sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon. Each exterior angle is supplementary to the corresponding interior angle, so we can write:
The sum of exterior angles = Sum of interior angles (supplementary angles)
Substituting the formula for the sum of interior angles, we get:
Sum of exterior angles = (n - 2) x 180 degrees (supplementary angles)
= 180n - 360 degrees
= 360 degrees - 360 degrees + 180n
= 360 degrees - Sum of interior angles
= 360 degrees - (n - 2) x 180 degrees
= 360 degrees - 180n + 360 degrees
= 720 degrees - 180n
Since the sum of the exterior angles must be a positive value, we can take the absolute value and simplify:
|Sum of exterior angles| = |720 degrees - 180n|
= 180|4 - n|
Since n is always a positive integer greater than or equal to 3 (since a polygon must have at least three sides), we know that 4 - n is always a negative integer between -1 and -n+1. Therefore, |4 - n| is equal to n - 4. Substituting this into the equation above, we get:
|Sum of exterior angles| = 180|n - 4|
= 180(n - 4)
= 180n - 720 degrees
= 360 degrees - 360 degrees + 180n - 720 degrees
= 360 degrees - Sum of interior angles
Therefore, we have shown that the sum of the exterior angles of any polygon is equal to 360 degrees.
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What is the volume of this sphere? responses 8π cm³ 8 pi, cm³ 16π cm³ 16 pi, cm³ 27π cm³ 27 pi, cm³ 36π cm³
The volume of a sphere with a radius of 3cm is 113.04 cm³, which is approximately equal to 36π cm³. So, the correct option is D).
The formula for calculating the volume of a sphere, V = 4/3πr³, is used to find the amount of space enclosed by a sphere with a given radius. In this case, the sphere has a radius of 3cm. By substituting this value into the formula, we can solve for the volume of the sphere.
V = 4/3πr³
V = 4/3 × 3.14 × 3³ = 113.04 cm³
= approximately 36π cm³
The result is 113.04 cm³, which is approximately equal to 36π cm³. This calculation is important in many applications, such as engineering, physics, and mathematics. The correct answer is D).
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_____The given question is incomplete, the complete question is given below:
What is the volume of sphere r = 3cm? responses A 8π cm³ 8 pi, cm³ B 16π cm³ 16 pi, cm³ C 27π cm³ 27 pi, cm³ D 36π cm³
I NEED HELP ON THIS ASAP!
Answer:
(-2,4) is quadrant 2, (8,4) is quadrant 1, (6,-2) is quadrant 4
Step-by-step explanation:
20 POINTS.
Solve 4x+2 = 12 for x using the change of base formula
−1. 442114
−0. 207519
2. 55789
3. 79248
Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.
The given equation is 4x+2 = 12.
To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:
4x+2-2 = 12-2
4x = 10
Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.
Rewrite equation:
x = log base 4 of 10
Use the change of base formula, we can present this as:
x = [tex]log base 10 of 10 / log base 10 of 4[/tex]
Simplifying:
x = 1.442114
Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.
In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.
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