The speed of Mercury around the Sun in kilometers/second is 48 kilometers/second.
In 2 seconds, Mercury will travel 96 kilometers.
What is the speed of an object?The speed of an object is the ratio of the distance travelled by the object to the time taken by the object to travel that distance.
Given, the speed of Mercury around the Sun is 30 miles/second.
Therefore, the speed of Mercury around the Sun in kilometers/second
= (30 × 1.6) kilometers/second
= 48 kilometers/second
Now, in 2 seconds, Mercury will travel
= 48 × 2 kilometers
= 96 kilometers
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py+7=6y+q solve for y
We know that we are solving for y.
This is a step by step procedure to get the value of y.
First: Move all terms to the left side and set equal to zero.
Second: Then set each factor equal to zero.
The application is:
Given: py+7=6y+q
-6y -7 -6y -7 = 0
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)
Answer is y = (q – 7) / (p – 6)
The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
We have to given that,
An expression is,
⇒ py + 7 = 6y + q
Now, We can simplify the expression for y as,
⇒ py + 7 = 6y + q
Subtract 6y both side,
⇒ py - 6y + 7 = 6y + q - 6y
Subtract 7 both side,
⇒ py - 6y = q - 7
⇒ y (p - 6) = (q - 7)
Divide both side by (p - 6);
⇒ y = (q - 7) / (p - 6)
Therefore, The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
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2x+5=10
Solve for x
Round 754 to the nearest ten
8x__=2
10x__= 5
—
2
6x__= 3
—
2
?? Can you fill in the blanks?
i need help 7th grade 13 + p + - 4 3
pre cal/cal master needed
g(x)={ ax-3, x<-2
{ x^2 -2x, x>-2
What value would the function g(x) have point discon. at x=-2 how to find?
The following data pairs represent the average temperature x (in degrees Fahrenheit) and electricity costs y (in dollars) for different homes: (65, 147), (59, 141), (71, 176), (78, 189), (82, 183), (85, 211), (88, 231), (91, 227), (84, 198), (79, 188), (63, 152), (59, 126) Which of the following values is most likely the closest to the correlation coefficient of the data?
The correlation coefficient of the given data pairs is most likely closest to 0.8694.
Explanation:The correlation coefficient measures the strength and direction of the relationship between two variables. To find the correlation coefficient, you can use the formula:
r = [n(Σxy) - (Σx)(Σy)] / sqrt{[n(Σx^2) - (Σx)^2][n(Σy^2) - (Σy)^2]}
Using this formula, you can calculate the correlation coefficient for the given data pairs. The closest value to the correlation coefficient will be 0.8694, option d.
The answer closest to the correlation coefficient of the data is 0.835.
To find the correlation coefficient of the given data pairs, we can use the formula:
r = (Σxy - (Σx)(Σy)/n) / sqrt((Σx^2 - (Σx)^2/n)(Σy^2 - (Σy)^2/n))
where Σ represents the sum, n is the number of data pairs, x is the average temperature, y is the electricity cost, and xy is the product of x and y.
To calculate the correlation coefficient, we first need to find the sums and products of the data pairs:
Σx = 65 + 59 + 71 + 78 + 82 + 85 + 88 + 91 + 84 + 79 + 63 + 59 = 924
Σy = 147 + 141 + 176 + 189 + 183 + 211 + 231 + 227 + 198 + 188 + 152 + 126 = 2259
Σxy = (65*147) + (59*141) + (71*176) + (78*189) + (82*183) + (85*211) + (88*231) + (91*227) + (84*198) + (79*188) + (63*152) + (59*126) = 219907
Using these values, we can calculate the correlation coefficient:
r = (219907 - (924*2259)/12) / sqrt((Σx^2 - (Σx)^2/12)(Σy^2 - (Σy)^2/12))
Calculating the remaining sums:
Σx^2 = (65^2) + (59^2) + (71^2) + (78^2) + (82^2) + (85^2) + (88^2) + (91^2) + (84^2) + (79^2) + (63^2) + (59^2) = 73482
Σy^2 = (147^2) + (141^2) + (176^2) + (189^2) + (183^2) + (211^2) + (231^2) + (227^2) + (198^2) + (188^2) + (152^2) + (126^2) = 827259
Plugging in the values:
r = (219907 - (924*2259)/12) / sqrt((73482 - (924^2)/12)(827259 - (2259^2)/12))
After performing the calculations, the correlation coefficient is approximately 0.835.
Therefore, the answer closest to the correlation coefficient of the data is 0.835.
I need help I am trying to find ft
1 foot = 12 inches
divide 69 by 12
69/12 = 5.75 feet
What is n in a(n-5)+6=bn.(You can use variables in the answer). Please explain, if you can.
Bill gates makes approximately $12 billion a year. On average, how much does he make per minute
Bill Gates makes approximately $22,831.05 per minute, calculated by dividing his annual earnings of $12 billion by the number of minutes in a year (525,600).
Explanation:To calculate how much Bill Gates makes per minute, we need to start by determining how much he makes per year. According to the question, Bill Gates makes approximately $12 billion a year. To find out how much that is per minute, we need to follow these steps:
Therefore, on average, Bill Gates makes $22,831.05 per minute.
PLEASE ASAP
Trapezoid W ′ X ′ Y ′ Z ′ is the image of trapezoid WXYZ under a dilation through point C. What scale factor was used in the dilation?
− 7/3
− 3/7
3/7
7/3
what is 28.5 divided by 5
Give A={a,b,c},how many subsets does A have including 0?
the point (1,1) is the image under the image under rhe translation (x,y) (x+3,y-3)
The pre-image of the point (1, 1) under the translation (x, y) -> (x+3, y-3) in a coordinate system is the point (-2, 4).
The student's question relates to a translation transformation in mathematics. A translation moves every point of a figure or a space by the same distance in a given direction. In this case, the student has provided a specific translation transformation, which is represented by the formula (x, y)
ightarrow (x+3, y-3). This transformation means that for any point with coordinates (x, y), the translated point will have coordinates where 3 is added to the x-coordinate and 3 is subtracted from the y-coordinate.
If the point (1,1) is an image under this translation, you can find its pre-image by reversing the translation. Thus, subtracting 3 from the x-coordinate of the image and adding 3 to the y-coordinate of the image gives the pre-image coordinates:
Pre-image x-coordinate: 1 - 3 = -2Pre-image y-coordinate: 1 + 3 = 4Therefore, the pre-image of the point (1, 1) under the given translation is (-2, 4).
Slope formula question (Algebra 2)
A kite flying in the air has a 12 ft line attached to it. Its line is pulled taut and casts an
11 ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
A factory makes an oil mixture by mixing oils of grades A and B as follows. For every 2.3 liters of grade A oil, 1.2 liters of grade B oil are mixed in. How many liters of grade A oil and grade B oil will the factory need to make 1000 liters of their oil mixture? Explain your solution.
There is 3/4 of a box of cereal remaining. You eat 2/5 of the remaining cereal. What fraction of the box do you eat?
How do you write 7/20 as a percentage??
Find the quadratic function that is the best fit for f(x) defined by the table below
The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
How to determine the function?A quadratic function is represented as:
f(x) = ax^2 + bx + c
Using the table of values, we have:
a(0)^2 + b(0) + c = -1.55
This gives
c = -1.55
Also, we have:
a(2)^2 + b(2) + c = 17.29
4a + 2b -1.55 = 17.29
This gives
4a + 2b = 18.84
Divide through by 2
2a + b = 9.42 --- (2)
Also, we have:
a(4)^2 + b(4) + c = 54.93
16a + 4b -1.55 = 54.93
This gives
16a + 4b = 56.48
Divide through by 4
4a + b = 14.12 ---- (3)
Subtract (2) from (3)
2a = 4.7
Divide by 2
a = 2.35
Substitute a = 2.35 in 4a + b = 14.12
4*2.35 + b = 14.12
Evaluate
b = 4.72
Substitute values for a, b and c in f(x) = ax^2 + bx + c
f(x) = 2.35x^2 + 4.72x -1.55
Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
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use properties to find 4 times 23 times 25
Answer:
2300
Step-by-step explanation:
You are building a new house on a cartesian plane whose units are measured in miles.
Your house is to be located at the point (6,0). Unfortunately, the
existing gas line follows the curve y=√16x^(2)+6x+19.
It costs 300 dollars per mile to install new pipe connecting your house to the existing line.
What is the least amount of money you could pay to get hooked up to the system?
How are the values of the eights in 880 relared
The difference between two positive integers is 4. If the smaller is added to the square of the larger, the sum is 68. Find the integers.
Two positive integers x and y
x - y = 4
x² + y = 68
Findx and y
SolutionAdd the two equations together.
... (x - y) + (x² + y) = (4) + (68)
... x² + x = 72
Rearrange to standard form and factor.
... x² + x - 72 = 0
... (x + 9)(x - 8) = 0
Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.
... x + 9 = 0 ⇒ x = -9
... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution
Then we can find y from
... 8 - y = 4
... y = 4 . . . . . . . add y-4 to the equation
The two positive integers are 8 and 4.
To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.
Explanation:The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.
Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.
Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.
Therefore, the two positive integers are 4 and 8.
what is 25.6 divided by 0.5 =
What is 36 divided by 3/4?
The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing
Answer:
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Step-by-step explanation:
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Here, we have,
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
scale = length in drawn/actual length
scale = length in drawn : actual length
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
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how many integers from 1 to 700 are divisible by 2, 5 and 7
There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.
Explanation:The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.
To find the number of multiples of 70 in that range, you can use the following steps:
Divide the largest number in the range (700) by 70 to find the highest multiple within the range. ∑(700 ÷ 70 = 10).Since we started from 1 and 70 is the first multiple, the total count is the result of the division.Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.
What is the vertex of the graph of y+2x+3 = -(x+2)^2 + 1?
A. (-3,-33)
B. (-3,3)
C. (3,-24)
D. (3,21)
How do I solve this equation? I need a refresher on Algebra.
Final answer:
To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.
Explanation:
To solve an algebraic equation, follow these systematic steps:
Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.
Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.
Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.
Substitute the known values into the equation.
Solve for the unknown and make sure to include units where necessary.
Finally, always check your answer to see if it is reasonable and makes sense.
These steps should yield a solution that is both accurate and verifiable.