You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)
To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,
y = -2,200(3) + 22,000 = $15,000which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be
y = -2,200(5) + 22,000 = $11,000which is the average value of the used car at that age.
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Complete Question:
Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:They likely had an average price of around $22,000 when new.They typically lose $2,200 of value per year.At 5 years old, they had an average value of around $11,000.Express sin T as a fraction in simplest terms
Solving the provided question, we can say that by Pythagoras theorem VT² = 18² + 24² = 900 => VT = [tex]\sqrt{1900} = 30[/tex]
what is Pythagorean theorem?The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.
Pythagoras theorem
VT² = 18² + 24² = 900
VT = [tex]\sqrt{1900} = 30[/tex]
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A (4,0).B (1.5), and C(-3,-5) are three vertices of a parallelogram ABCD. What is the ordered pair for D, the fourth vertex of the parallelogram?
Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.
Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:
AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)
BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)
Next, we subtract these vectors to find the vector for CD:
CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)
Finally, we add the vector CD to vertex C to find vertex D:
D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)
So, the ordered pair for vertex D is (-5, -10).
Step-by-step explanation:
Raul is choosing from two plans at his gym. He can either pay a set price
for each visit, or he can buy a membership, which would have a lower
price per visit in addition to a membership fee. Which model could be
used to determine which plan would be less expensive based on the
number of visits he makes?
The linear model that could be used to determine which plan would be less expensive based on the number of visits he makes is given as follows:
Second graph (top right graph, where the two lines intersect).
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.For the plan with the set price, we have that:
The slope is greater than for the other plan.The intercept is of zero.Hence it costs less for a lower number of visits.
For the plan with the set price plus the fee, we have that:
The slope is less than for the other plan.The intercept is greater than zero.Hence it costs less for a higher number of visits.
Meaning that the second graph is the correct graph in this problem.
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Evaluate 2 + y + 1, when y = 12
Answer:
Step-by-step explanation:
Simply substitute for y in the equation if y = 12.
2 + y + 1 -> 2 + (12) + 1 = 15
a hand woven rectange rug measures x feet long and 2 4/5 feet wide. write an expression to represent the perimeter of the rug
Answer:
see below
Step-by-step explanation:
(x+ 2 4/5) * 2 = perimeter
so perimeter = 2x + 5.6
Read the problem.
There are 60 students in the Geneva Middle School marching band. 20% of those
students play the trombone.
Shade the grid to show the percent of students in the marching band who play the trombone.
How many students in the marching band play the trombone? You can use your model to
help.
Answer: If 20% of the 60 students in the Geneva Middle School marching band play the trombone, then 60 * 20% = 12 students play the trombone. To shade the grid to show the percent, you can shade 20 out of 100 squares on the grid, or 1/5 of the total number of squares.
Step-by-step explanation:
$1.76 Red Kidney Beans 400g, Can 1. $1.89 Red Kidney Beans 420g, Can 2. $1.00, Red Kidney beans, 125 g, Can 3. $2.40, Red Kidney Beans, 500g, Can 4. Which can of red kidney beans costs the least per gram?
Answer:
Can 3. $2.40, Red Kidney Beans, 500g, Can. This can costs $0.0048 per gram.
Laura has saved $1800 to use as a down payment on a new car. If she wants to continue saving $150 a month, which equation will determine how much money, y, Laura can save in x months?
1800 + 150x = y
150x is the money she makes a month
Y is the total
enjoy :D
justify your reasons by determining the postulates, definitions, theorems, and properties used
By alternating internal angles, angles 1 and 2 are equivalent.
What does the triangle's angle sum property entail?
According to the triangle's "angle sum property," the inner angles of a triangle add up to 180 degrees.
1. Angles 1 and 2 complement one another. Angles 2 and 3 compliment one another.
These angles are linear, hence their sum is 180 degrees.
2.m angle
Angle 1 + m2 Equals 90° Angle m2 + m3 = 90°
Equals makes a straight angle
3. m angle1 plus m angle2 equals m angle2 plus m angle3
= 180 degrees when the total of the two sides
4. m angle2 equals m angle
= The total of the two sides is equal
5. m angle1 = m angle3
= The total of the two sides is equal
6.Angle1 and Angle3 are congruent.
Alternate interior angles are what they are.
Angle 1 and Angle 3 are therefore equivalent based on the triangle's characteristics.
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Find the value of x.
5
4
3
12
X
a. 24
b. 36
c. 40
d. 45
By the 1/3 ratio, the value of x for the given figure is 33 units.
What is ratio?A ratio is an ordered pair of integers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls). A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Here,
4/12=3/x1=5/x2
1/3=3/x1
x1=9 units
1/3=5/x2
x2=15 units
12+15+9=33 units
The value of x for the given figure is 33 units by the ratio of 1/3.
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solve for x please and thank you
Step-by-step explanation:
this is the process and figure is cointerior
a) A wall has a length of 15m and breadth 7cm. The wall also has a square shaped window of length 4m. What is the cost of coloring the wall at Rs. 15 per meter square? 11
Using the formula of area of rectangle and square, the cost of painting is Rs. 1335
What is Area of RectangleThe area of a rectangle is equal to the product of its length and width. Mathematically, it can be represented as:
Area = Length × Width
In this problem, we need to substitute the values and calculate the area of the rectangular wall and then subtract the area of the window from it.
Area of rectangle = 15 * 7 = 105m²
The area of the window is calculate by using the formula of area of square.
Area of square = 4 * 4 = 16m²
Area of wall painted = 105 - 16 = 89m²
The cost of painting one square meter = Rs. 15
1m² = Rs. 15
89m² = x
x = 15 * 89
x = Rs. 1335
The cost is Rs. 1335
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Hi can somebody please explain the second question and how you got it?
Thank you in advance!
Nice work on getting part (a) correct.
The 261% falls in the "250-300%" range, so they pay 8.5% of their yearly income toward health insurance.
8.5% of $65,500 = 0.085*65500 = 5567.50
That represents the yearly contribution. Divide that by 12 to find the monthly contribution.
5567.50/12 = 463.95833 = 463.96 approximately
Then round to the nearest dollar to get 464
Answer to part (b) is 464a library has 2500 books.40% of the books are fiction.How many books are not fiction books
A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.
A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
Total amount of book in library are 2500 ,
Out of that 40% are fiction so the number of the non fiction books are 60%
so 60% of 2500 will give us the value of non fiction books,
Number of non fiction = 2500 x 60%
= 2500 x 60/100
= 25 x 60
= 1500
Therefore, Number of non fiction books are 1500.
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explain why it is necessary to consider variability around the mean or nominal dimension as a measure of quality.
Variability around the mean or nominal dimension is a measure of quality because it helps to quantify the spread of data and the degree to which it deviates from the expected value.
By considering variability, manufacturers and designers can identify areas for improvement, determine tolerances for product specifications, and ensure consistency in production. Additionally, it helps to identify outliers and inconsistencies in the data which can be indicative of defects or issues in the production process. Furthermore, considering variability helps to assess the risk of non-conformance and predict the performance of a product in real-world scenarios. In short, considering variability helps to improve the overall quality of products and ensure they meet customer expectations.
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Convert each rate to a unit rate. $4.25 for 64 fluid ounces 297 miles on 11 gallons of gas 124 feet in ten seconds
Answer:
$4.25 for 64 fluid ounces = $0.06640625 per fluid ounce
297 miles on 11 gallons of gas = 27 miles per gallon
124 feet in 10 seconds = 12.4 feet per second
Step-by-step explanation:
Help me please i just want to get ALEKS done for school :( PLEASE HELP
The measure of the side of the partial rectangle is 7 cm
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangular figure be represented as P
Now , the equation will be
The length of the rectangle 1 = 12 cm
The width of the rectangle 1 = 6 cm
The length of the rectangle 2 = 15 cm
The width of the rectangle 2 = 5 cm
Now , let the unknown length be represented as A
And , A = length of the rectangle 1 - width of the rectangle 2
Substituting the values in the equation , we get
The unknown length A = 12 cm - 5 cm
On simplifying the equation , we get
The unknown length A = 7 cm
Hence , the unknown length of the rectangle is A = 7 cm
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A bouncy ball is dropped such that the height of its first bounce is 6.75 feet and each
successive bounce is 74% of the previous bounce's height. What would be the height
of the 6th bounce of the ball? Round to the nearest tenth (if necessary).
The graph below shows a system of equations:
Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5, 0. Draw a line labeled y equals x minus 1 by joining the ordered pairs negative 1, negative 2 and 5, 4
The x-coordinate of the solution to the system of equations is
___ (5 points)
The x-coordinate of the solution to the system of equations is 3.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Two lines are labeled on x-y coordinate y = - x + 5 and y = x - 1.
Now, Adding these two equations we have,
2y = 4. (x and - x cancells).
y = 2.
Now, Putting the value of 'y' in any of the equations we have,
2 = - x + 5.
x = 5 - 2.
x = 3.
so, The x-coordinate of the solution is 3.
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Find a formula for the tenth term in this arithmetic sequence: a1=28 a2=21 a3=14 a4=7
Answer:
an = - 7n+35
Step-by-step explanation:
In an arithmetic sequence, the difference between consecutive terms is constant. To find this difference, we can subtract the first term from the second term and the second term from the third term, etc.
a2 - a1 = 21 - 28 = -7
a3 - a2 = 14 - 21 = -7
Since the difference between consecutive terms is the same, we can conclude that the difference is -7.
The nth term in an arithmetic sequence can be found using the formula: an = a1 + (n-1)d, where d is the common difference.
For this sequence, the nth term can be found as: an = 28 + (n-1)(-7) = 28 - 7(n-1) = 28 - 7n + 7 = 35 - 7n.
So, the formula for the nth term in this arithmetic sequence is an = - 7n+35
a piece of wire 22cm long is sent into an arc of a circle of radius 4cm . what angle does the wire subtend at the centre of the circle
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=22\\ r=4 \end{cases}\implies 22=\cfrac{\theta \pi (4)}{180}\implies 22=\cfrac{\theta \pi}{45} \\\\\\ (22)(45)=\theta \pi \implies \cfrac{(22)(45)}{\pi }=\theta \implies 315.13\approx \theta[/tex]
Brian pays £466.98 a year on his car insurance.
The insurance company increases the price by 3.2%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.
Answer:
£481.02
Step-by-step explanation:
To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:
£466.98 * 1.032 = £480.9936
£480.9936 + £466.98 = £481.02
Rounding to 2 decimal places, the answer is £481.02.
f 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? 5 if 6 bottles are randomly selected, what is the probability that all of them are the same variety?
The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.
The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.
The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.
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A Christian school had 25 students in the senior class. A total of 80% of these students went to college. How many students went to college?
Answer:
20 students went to college.
Step-by-step explanation:
In order to find a percent of a number you must do the number multiplied by the percent divided by 100. For example, the formula is (x*%) divided by 100. 25*80 = 2000. 2000/100 = 20 students. Hope I helped!
Answer:
80% of 25 students
80÷100 × 25 = 20
therefore , 20 students went to college.
Boden's account has a principal of $600 and a simple interest rate of 3.9%. Complete the number line. How much money will be in the
Answer:
Step-by-step explanation:
If Boden's account has a principal of $600 and a simple interest rate of 3.9%, then the interest he earns each year can be calculated as follows:
Simple Interest = Principal * Rate * Time = $600 * 3.9% * 1 = $23.40
So, after one year, the amount of money in the account will be $600 + $23.40 = $623.40
This process can be repeated for multiple years to find the amount of money in the account for a specific time period.
Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of C′ if the preimage is reflected across y = 4.
C′(−3, 6)
C′(−3, 14)
C′(−1, 6)
C′(−1, 14)
Answer:
(d) C'(-1, 14)
Step-by-step explanation:
You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.
ReflectionReflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.
The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...
(C +C')/2 = (-1, 4)
C +C' = 2(-1, 4) = (-2, 8) . . . . .multiply by 2
C' = (-2, 8) -C
C' = (-2, 8) -(-1, -6) = (-1, 8+6)
C' = (-1, 14)
__
Additional comment
Effectively, the reflection across the line y=4 is the transformation ...
(x, y) ⇒ (x, 8 -y)
Answer:
C'(-1, -6).
Step-by-step explanation:
the reflection across y = 4 for point C(-1, -6).
When reflecting a point across a horizontal line like y = 4, the y-coordinate remains the same, and the x-coordinate is inverted with respect to the line of reflection.
For point C(-1, -6), the y-coordinate remains -6, and the x-coordinate is inverted across y = 4:
New x-coordinate = -1
So, the reflected image of point C across y = 4 is C'(-1, -6).
None of the provided options match this reflection, so it seems there might be an error in the given answer choices. The correct reflection of point C(-1, -6) across y = 4 is C'(-1, -6).
PLEASE HELP (will mark as brainlest)
The solution to the monomial in standard form is 0.04b^19.
What is a standard form of a polynomial?The term "polynomials in standard form" can also refer to a polynomial written in the decreasing order of the degree of the variable.
The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.
Given that:
= (-0.2b^6)^3*5b
Rewrite using the commutative property of multiplication
= 5(-0.2b^6)^3b
Apply the product rule to −0.2b^6
= 5(-0.2^3)(b^6)^3b
= 5(-0.008b^18)b
= 5(-0.008^19)
= 0.04b^19
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In investing $5,750 of a couple's money, a financial planner put some of it into a savings account paying 2% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 12% annual simple interest. The combined interest earned for the first year was $475. How much money was invested at each rate?
$2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned amount for the first year was $475.
The financial planner invested $5,750 of the couple's money. Let x be the amount of money invested in the savings account paying 2% annual simple interest and y be the amount of money invested in the riskier mini-mall development plan paying 12% annual simple interest. Since the combined interest earned for the first year was $475, we can write the equation 2x + 12y = 475. Since the total amount of money invested was $5,750, we can add the equation x + y = 5,750 to our system of equations. Solving the system of equations yields x = 2,250 and y = 3,500. Thus, $2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned for the first year was $475.
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Pedro tiene 42 años y 3 hijos. Las edades de sus hijos son divisores de su edad. Sabemos que la edad del mayor es un numero compuesto impar. La del segundo es un numero compuesto par que no es multiplo de 3 y la edad del tercero es un numero primo impar que es divisor del segundo. ¿Que edad tiene cada hijo?
Answer:
No se puede determinar la edad de cada hijo con la información proporcionada.
Step-by-step explanation:
ASAP I NEED THIS ASAP
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Based on the information in the graph, the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.
How to find the side length DF?To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:
a² + b² = c²7² + b² = 8²49 + b² = 64b² = 15b = 3.87How to calculate side XF?To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:
a² + b² = c²3² + 3.87² = c²9 + 14.97 = c²23.97 = c²4.89 = cThe point 2cm from E would lie on the line EX at 2cm from E and 5cm from X.
What is the angle of D?To calculate the angle of D we can use a compass, in this case, we know that the angle of X is 90°, so the other 90° that make up the triangle are distributed between point F and D. However, we know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.
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