After 5 year term, the distance covered is 140000 km, the charge paid is, $1200
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
Given that,
In lease agreement, the distance allowed 25000 km per year for free
After that the charge will be $0.08 per km
After 5 year term, you drove a total of 140000 km
The owed amount = ?
So, in 5 year term the distance which is free according to agreement,
⇒ 5 × 25000
⇒ 125000
Now, the distance for which charge has given
⇒ 140000 - 125000
⇒ 15000
Charged amount = $0.08 per km
The owed amount = 0.08 × 15000
= $1200
Hence, the amount owed is $1200
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Which expression is equivalent to (2x^2 + 4x – 7)(x – 3)?
A. x(2x^2 + 4x – 7) + 3(2x^2 + 4x – 7)
B. x(2x^2 + 4x – 7) – 3
C. –3x(2x^2 + 4x – 7)
D. (2x^2 + 4x – 7)(x) + (2x^2 + 4x – 7)(–3)
The expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= (2x² + 4x – 7)(x – 3)
After using the distributive property:
= (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3)
Distributed the whole term (2x² + 4x – 7) with (x - 3)
Thus, the expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
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The sum of three consecutive odd integers is 207. What are the integers?
Which of the following is a key property of the linear parent function
A it is in quadratic ll and lV
B is has a slope of 1
C it is a curved line
D it does not go through the origin
Answer:
The correct option is B.
Step-by-step explanation:
The equation of linear parent function is
[tex]y=x[/tex]
Key property of the linear parent function are:
1. It is in quadratic l and lII.
2. It has a slope of 1.
3. It is a straight line.
4. It passes through the origin.
The graph of parent function is shown below.
In the given options only the statement " It has a slope of 1" is true.
Therefore the correct option is B.
I really need help :(...............
Stan and hilda can mow the lawn in 30 min if they work together. if hilda works twice as fast as stan, how long does it take stan to mow the lawn alone?
If a cone and a sphere have the same radius and the same height what is the relationship among the volumes of the two shapes
Answer:
the volume of the sphere will be 4 times the volume of the cone;
Step-by-step explanation:
The question is on volume comparison
Volume of a sphere=4/3 ×r³
Volume of a cone= /3×r²h
where r is the radius and h is the height
Apply the condition
If r=h=1 unit
Then volume of sphere will be= 4/3 × ×1³ = 4/3
And volume of the cone will be= /3 ×1²×1 =/3
We can see the volume of the sphere will be 4 times the volume of the cone;
4/3 = 4×/3
The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point C? Explain how you find your answer
To find the coordinates of point C which divides line AB into a 2:5 ratio, use the section formula. Therefore, the coordinates are (-4/7, -11/7). This provides point C's location on the line segment AB.
Explanation:The coordinates of C are determined through the section formula, which finds the coordinates of a point dividing a line segment into a specific ratio. In this case, the ratio is 2:5. To solve for the x-coordinate of C, the formula [(m*x2) + (n*x1)] / (m+n) is used, where m and n are the ratio values, x1 and x2 are the x-coordinates of points A(-2, -3) and B(3, 2). Using these, the x-coordinate of C is found to be (2*3 + 5*(-2)) / (2+5) = -4/7.
Similar calculations apply to solving for the y-coordinate of C: [(m*y2) + (n*y1)] / (m+n) = (2*2 + 5*(-3)) / (2+5) = -11/7.
Therefore, the coordinates of point C are (-4/7, -11/7). This is the point C on the line segment AB that is 2/5 of the way from point A to point B.
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Why is 8.8 classified as a rational number?
.........simplify 3^2*3^5
8y - 1 = x 3x = 2y Solve the system of equations by substitution.
Help with these three problems? Please
6. add the averages then take that average
50+74 = 124, 124/2 = 62
answer: 62
8. first put all the numbers in order
4, 5 ,6 ,8 11, 12,14, 15, 23 ,23
Find the middle number, since there are 10 numbers find the average of the 2 middle numbers
11+12 =23/2 =11.5
Lower half data = 4, 5, 6, 8, 11
The middle number of that set is Q1,
Q1=6
9
9, find q3
1, 2, 3, 5, 5, 6, 9
Find middle number (5)
upper half data = 5, 6, 9
Q3= 5 , 6, 9 = 5+10 +15 = 30
so answer is $30
The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing
divide the discount by the percentage off
so:
99.90/0.27 = 370
the original price was 370 dollars
Jacob and Isaiah are brothers. Their combined ages are 63. Jacob is 7 years older than Isaiah. How old are each of the boys?
Final answer:
To solve this problem, set up a system of equations and solve for the variables. Isaiah is 28 years old and Jacob is 35 years old.
Explanation:
To solve this problem, we can set up a system of equations.
Let's say Isaiah's age is represented by x. Jacob's age is then represented by x + 7, since he is 7 years older than Isaiah.
We know that the sum of their ages is 63, so we can set up the equation: x + (x + 7) = 63.
Simplifying the equation gives us: 2x + 7 = 63.
Subtracting 7 from both sides of the equation gives us: 2x = 56.
Dividing both sides of the equation by 2 gives us: x = 28.
So, Isaiah is 28 years old, and Jacob is 28 + 7 = 35 years old.
the question is............
A worker produced a total of 198 mousetraps during a 6 hour run with no rejects and no downtime. A report states that this worker produced at a rate of 2 mousetraps per minute. Based on the actual production, is the rate of 2 mousetraps per minute accurate?Exit Test
Based on the actual production, the rate of 2 mousetraps per minute is not accurate.
What is Rate?Rate of a quantity is the amount of that quantity with respect to some amount of another quantity.
If the quantity with respect to which the rate is measured is taken as single unit or one unit, then the rate is called unit rate.
Production of mousetraps by the worker in 6 hours = 198
Production of mousetraps by the worker in 1 hour = 198/6 = 33
That is, production of mousetraps by the worker in 60 minutes = 33
Production of mousetraps by the worker in 1 minute = 33/60 = 0.55
The worker produced mousetraps at a rate of 0.55 mousetraps per minute.
But the report states that this worker produced at a rate of 2 mousetraps per minute, which is not correct.
Hence the statement of report that the worker produced at a rate of 2 mousetraps per minute is not accurate, because he is only producing 0.55 mousetraps per minute.
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2x^3y + 18xy - 10x^2y - 90y Part A: Rewrite the expression so that the GCF is factored completely. (3 points)
To factor 2x^3y + 18xy - 10x^2y - 90y, find the GCF of the terms, rewrite the expression, factor out the GCF from the terms inside the parentheses, and simplify the expression.
Explanation:To factor the expression 2x^3y + 18xy - 10x^2y - 90y, we can begin by finding the greatest common factor (GCF) of the terms. The GCF of the coefficients is 2, and the GCF of the variables is y.
So, we can rewrite the expression as 2y(x^3 + 9x - 5x^2 - 45).
Next, we can factor out the GCF from the terms inside the parentheses. The GCF of x^3, 9x, -5x^2, and -45 is x. Factoring out x, we get x(x^2 + 9 - 5x - 45).
Finally, we simplify the expression inside the parentheses. Rearranging the terms, we have x(x^2 - 5x + 9 - 45). Combining like terms, we get x(x^2 - 5x - 36).
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What is the measure of an exterior angle of a regular 11-sided polygon?
The measure of an exterior angle of a regular 11-sided polygon is 32.73°.
The measure of an exterior angle of a regular 11-sided polygon can be calculated using the formula:
60° divided by the number of sides.
In this case, for an 11-sided polygon, each exterior angle would measure 360° / 11 = 32.73°.
PLEASE ANSWER ASAP!!! WORTH 13 POINTS! I need help D:
Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
A) |c − 450| less than or equal to 45
B) |c + 450| greater than or equal to 45
C) |c − 45| less than or equal to 450
D) |c − 45| greater than or equal to 450
Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. How much money will she have in her account 4 years later if she does not make any deposits or withdrawals (round to the nearest dollar)?
A) $1,257
B) $1,557
C) $1,559
D) $2,341
Answer:
$4236.
Step-by-step explanation:
We have been given that Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. We are asked to find the total amount Jamie will have in her account after 4 years.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
t = Number of years.
Let us convert our given rate in decimal form.
[tex]3.8\%=\frac{3.8}{100}=0.038[/tex]
Since the we have been given monthly interest rate, so we will convert the given rate to annual interest rate by multiplying 0.038 by 12.
Upon substituting our given values in above formula we will get,
[tex]A=\$1500(1+0.038*12*4)[/tex]
[tex]A=\$1500(1+1.824)[/tex]
[tex]A=\$1500(2.824)[/tex]
[tex]A=\$4236[/tex]
Therefore, Jamie will have $4236 in her account after 4 years.
A caterer expects a minimum of 160 but no more than 192 people at a wedding. One fruit tray serves 16 people. The compound inequality represents x, the number of fruit trays the caterer should bring to the wedding.
160 ≤ 16x≤ 192
Which is a possible number of fruit trays the caterer might bring to the wedding?
A. 8
B. 10
C. 14
D. 16
Answer:
b. 10
Step-by-step explanation:
I did the test
Jess observed that 60% of the people at a mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, the number of people who shopped for clothes that day was ______.
Answer:
3750
Step-by-step explanation:
3750
How to tell if there is a horizontal asymptote?
To tell if there is a horizontal asymptote, for rational functions, compare the degrees of the numerator and denominator; if they are equal, the asymptote is the ratio of their leading coefficients. If the numerator's degree is less, the asymptote is at y=0; if greater, there is no horizontal asymptote. Polynomials do not have horizontal asymptotes.
To determine if a function has a horizontal asymptote, we look at the behavior of the function as x approaches infinity (x →∞). For rational functions, the degrees of the numerator and denominator play a crucial role. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. For instance, as x approaches infinity, the term with the highest power dominates and the constant terms become less significant, leading to the horizontal asymptote at y = 1.
In a scenario where the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at y = 0, since the function approaches zero as x increases without bound. Conversely, if the degree of the numerator is greater than the degree of the denominator, no horizontal asymptote exists because the function grows without limit.
Remember, polynomials do not have horizontal asymptotes, as their values continue to increase or decrease indefinitely with x.
a triangle has two sides of lengths 7 and 9.what value could the length of the third side be?
Answer:
13, 10, 8, 5
Step-by-step explanation:
2+7=9 9=9 the requirment is it has to be greater than the third length not equal to
The velocity of a train, measured in meters per second, is described by vector t=(-1,-4). Find the direction the train is traveling using standard position
Answer:
inverse tangent 4/1
75.96 + 180 bc 3rd quadrant which equals 255.96 degrees.
Step-by-step explanation:
round 256 degrees
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer: -3
Step-by-step explanation:
The points (1,1) (2,-2) plugged into slope formula m = y2 - y2/x2 - x1
-2 is y2
1 is y1
2 is x2
1 is x1
Subtract and simplify
If θ is in Quadrant III and cosθ -2/3, then sinθ = _____.
Answer:
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
If θ is in Quadrant III
[tex]\cos\theta=-\dfrac{2}{3}[/tex]
As we know in III quadrant cosine and sine both are negative.
using trigonometry identity
[tex]\sin\theta=-\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=-\sqrt{1-(\frac{2}{3})^2}[/tex]
[tex]\sin\theta=-\sqrt{1-\frac{4}{9}}[/tex]
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Hence, The value of [tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6
To find the equation of a parabola with a vertex at (0,0) and a directrix of y=-6, we determine the focus is at (0,6), leading to the standard form equation of the parabola as y = 1/4x^2.
Explanation:The question asks for the equation of a parabola in standard form given its vertex at (0,0) and directrix as y=-6. In parabolic equations, the standard form is usually y = ax^2 + bx + c for horizontal parabolas, or x = ay^2 + by + c for vertical parabolas. Given the vertex is at the origin (0,0) and the directrix is y = -6, this means the focus is at (0,6) because the distance from the vertex to the focus is equal to the distance from the vertex to the directrix but in the opposite direction.
For a parabola that opens upwards or downwards, the standard form is y = ax^2 (since the vertex is at the origin, b and c are 0). Given that the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 6, the parabola opens upwards, and its focal distance (p) is 6. Hence, the value of 4p = 24, which leads us to conclude that a = 1/4. Therefore, the equation of the parabola is y = 1/4x^2.
Someone help me please !
AE x BE = DE x CE
6x5 = 30
6 x DE = 30
DE = 30/6 =5
DC = DE +CE = 5+6 =11
Answer is C) 11
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
Guys help me out with this one plizz
Getting two 6's in four rolls can happen in 6 ways. 4C2 = 6
The probability of getting two 6's is 1/36. Therefore,
6 times 1/36 = 1/6 or 0.16666666...
Converting to a percent to the nearest tenth is 16.7%