For the values 44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8, the mean of the data set is 49.52. The Mean Absolute Deviation (MAD) of the data set is 4.83.
To find the mean of the given data set, we add up all the values and divide by the number of values:
Mean = (44.4 + 43.8 + 45.6 + 45.9 + 44.1 + 45.6 + 44.0 + 44.9 + 45.8) / 9 = 445.7 / 9 = 49.52
So, the mean of the data set is 49.52.
To find the Mean Absolute Deviation (MAD), we first find the absolute difference between each value and the mean, and then find the mean of these absolute differences:
Absolute Difference = |44.4 - 49.52|, |43.8 - 49.52|, ..., |45.8 - 49.52|
MAD = (Absolute Difference1 + Absolute Difference2 + ... + Absolute Difference9) / 9
Calculating the MAD gives:
MAD = (5.12 + 5.72 + 3.92 + 3.62 + 5.42 + 3.92 + 5.52 + 4.62 + 5.32) / 9 = 43.5 / 9 = 4.83
So, the Mean Absolute Deviation (MAD) of the data set is 4.83.
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Find each exact value if 0
Cos (x + y) if sin x = 5/13 and sin y = 4/5
The exact value of the given trigonometry expression is 16/65
Trigonometry expression involving sine and cosineGiven the following trigonometry expressions
Cos (x + y)
sin x = 5/13 and:
sin y = 4/5
We need to find the exact value of cos(x+y)
According to the trigonometry identity
cos(x+y) = cosxcosy - sinxsiny
If sinx = 5/13, then cosx = 12/13. Also, if siny = 4/5, then cosy = 3/5
Substitute to have:
cos(x+y) = 12/13(3/5) - 5/13(4/5)
cos(x+y) = 36/65 - 20/65
cos(x+y) = 16/65
Hence the exact value of cos(x+y) is 16/65
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Use substitution. What is the solution of the system of equations?
\large y=\frac{1}{2}x+2 and \large 2y=x+4
The solution of the system of equations include the following:
(0, 2)
(-4, 0).
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the above, we can logically deduce the following system of equations:
y = 1/2(x) + 2 .......equation 1.
2y = x + 4 .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
2(1/2(x) + 2) = x + 4
x + 4 = x + 4
x - x = 4 - 4 (no solution).
However, we would solve the system of equations graphically in order to determine the solutions as shown in the image attached below.
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A surveyor wants to know the length of a tunnel built through a mountain. According to her equipment, she is located 243 meters from one entrance of the tunnel, at an angle of 47 degrees to the perpendicular. Also according to her equipment, she is 186 meters from the other entrance of the tunnel, at an angle of 27 degrees to the perpendicular. Based on these measurements, find the length of the entire tunnel.
Do not round any intermediate computations. Round your answer to the nearest tenth
The length of the tunnel is approximately 205.6 meters to the nearest tenth.
What is Pythagoras Theorem?
Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a²+b²=c²
Here's one way to find the length of the tunnel:
1) Draw a diagram to represent the situation
2) Draw the perpendiculars from the surveyor to each entrance, and label the height of the triangle formed by each entrance and the surveyor as h1 and h2, respectively
3) Use trigonometry to find h1 and h2:
h1 = 243 * sin(47) = 160.1
h2 = 186 * sin(27) = 105.8
4) Find the horizontal distance between the two entrances, which is the length of the tunnel, by using the Pythagorean theorem:
[tex]d = \sqrt{(h1^2 + h2^2) }\\\\ d = \sqrt{(160.1^2 + 105.8^2)}\\\\ d = 205.6[/tex]
So, The length of the tunnel is approximately 205.6 meters to the nearest tenth.
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find the inverse function of p(x)= 50x - 400
The inverse function of p(x) = 50x - 400 is p⁻¹(x) = x/50 + 8.
What is the inverse of the given function?Given the function in the question;
p(x) = 50x - 400
To determine the inverse, replace p(x) with y.
p(x) = 50x - 400
y = 50x - 400
Now, interchange the variables y and x.
x = 50y - 400
Solve for y
Add 400 to both sides
x + 400 = 50y - 400 + 400
x + 400 = 50y
Reorder the equation
50y = x + 400
Divide both sides by 50
50y/50 = x/50 + 400/50
y = x/50 + 400/50
y = x/50 + 8
Replace y with p⁻¹(x)
p⁻¹(x) = x/50 + 8.
Therefore, the inverse is x/50 + 8.
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a snack food company is developing a new flavor for crackers and asks customers to text their preference between two possibilities. what kind of sampling is being used
The kind of sampling that is being used by the snack food company, which is developing a new flavor for crackers and which asks customers to text their preference between two possibilities, is known as non-probability sampling.
Non-probability sampling refers to a sampling technique where a researcher selects samples that are based on the subjective judgment of the researcher rather than random selection. This kind of sampling is a less stringent method, and the method depends heavily on the expertise of the researchers.
Non-probability sampling is carried out by observation, and it is used widely for qualitative research.
Since the food company selects only samples that the company would like (the samples being the company's own customers), the company uses non-probability sampling.
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can someone please help me(20 points will give brainliest!!!)
Answer: ez question, the answer is F = 200, and V = 8
Step-by-step explanation:
how to solve using the quadratic formula
For a quadratic equation:
a*x^2 + b*x + c = 0
The quadratic formula is just:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
How to solve using the quadratic formula?For a general quadratic equation:
a*x^2 + b*x + c = 0
The quadratic formula is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
So for example, let's assume that we have the quadratic equation:
3x^2 + 7x - 12 = 0
Here we have the values:
a = 3
b = 7
c = -12
Now you could just replace them in the quadratic formula and you will get:
[tex]x = \frac{-7 \pm \sqrt{7^2 - 4*3*-12} }{2*3}[/tex]
And if you simplify that you will get the two solutions.
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Preform the multiplication. Simplify your answer if possible
(5 √(3) + √(15)) × (3 √(5) + √(15))
According to square root and multiplication, the simplified answer is 126.54.
Rewriting the equation first to perform multiplication and simplify the equation -
Equation = (5✓3 + ✓15) × (3✓5 + ✓15)
Firstly multiplying the possibile entities in the equation
Equation = 15✓15 + 5✓3×✓15 + 3✓5×✓15 + 15
Keep the value of ✓3 and ✓15 in the equation
✓15 = 3.9
✓3 = 1.7
Equation = 15×3.9 + 5×1.7×3.9 + 3×1.7×3.9 + 15
Performing multiplication on Right Hand Side of the equation
Equation = 58.5 + 33.15 + 19.89 + 15
Performing addition on Right Hand Side of the equation
Equation = 126.54
Thus, the simplified form of equation is 126.54.
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what is equivalent to 4(5x8+7)
Answer:20x^8+28
Step-by-step explanation:multiply both terms by 4
Let G be the sales (in millions of dollars) of football jerseys. Let H be the sakes (in millions of dollars) of baseball jerseys. During a 5-year period, G and H can be modeled by the following equations, where t is the time (in years).
G = 15t^4 + 13t^3 + 10t^2 - 10t + 750
H - 11t^4 + 13t^3 + 9t^2 + 8t + 650
a. Find a polynomial function A for the total sales of football and baseball jerseys.
A = ?
b. Is the function A even, odd, or neither? Explain.
A. A polynomial function A for the total sales of football and baseball jerseys is 26t^4 + 26t^2 + 760
B. The function A is neither even nor odd
How did we get the value?a. To find a polynomial function for the total sales of football and baseball jerseys, we simply add the two functions:
A = G + H = 15t^4 + 13t^3 + 10t^2 - 10t + 750 + 11t^4 - 13t^3 + 9t^2 + 8t + 650 = 26t^4 + 26t^2 + 760
b. The function A is neither even nor odd. An even function is one that is symmetrical around the y-axis and an odd function is one that is symmetrical around the origin. The polynomial function A has no symmetry around either the y-axis or the origin, so it is neither even nor odd.
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I need help with this question
The algebraic expression for this problem is given as follows:
2C - D = -2x² + 2x + 11.
How to obtain the algebraic expression?The definition for C in this problem is given as follows:
C = x + 3.
We applying the distributive property to multiply by 2 as follows:
2C = 2(x + 3) = 2x + 6.
The definition for D in this problem is given as follows:
D = 2x² - 5.
The subtraction is then obtained as follows:
2C - D = 2x + 6 - (2x² - 5)
2C - D = 2x + 6 - 2x² + 5
2C - D = -2x² + 2x + 11.
Meaning that the second option is correct.
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y - 6x = 12
y = 6x + 5
Answer:
there is no question. but these are two of the same lines with different Y-intercepts.
1. mCB=
4. m/FOB =
7. m/FIG=
10. MAE=
13. m/COF=
N
The Biggest Circle Puzzle
You are given the following information:
B
2. mZAJC=
5. mFG=
8. MFI =
11. m/ELD =
14. mFM
M
O is the center of the circle.
AB, CD, and EF are diameters.
3. mCG=
6. m/FPC=
9. m/IKF =
12. mCD-
15. m/FNB =
mGB = 26
mZOAH = 50
m/IGA=24
PI = 4.5
CM = 10
'E
H
m/AOC = 30
m/AHF = 65
IF = 10.5
PC = 3.4
HM = 7.5
LD and LE are tangent to the circle.
HELP PLEASE, SHOW WORK
The radius of the circle is equal to the distance between the two points, or LD and LE.
What is circle?A circle is a safe consisting of all points in a plane that are given distance from a given point the centre the distance from the centre to any point on the circle is known as the radius is alkal is no slider corners and all points along the circle are equidistant from the centre.
mCB= Circumference of the circle is the distance around the outside of the circle.
m/FOB= The formula for finding the circumference of a circle is C=2πr, where C is the circumference, π is 3.14, and r is the radius of the circle.
m/FIG= The formula for finding the area of a circle is A=πr2, where A is the area of the circle, π is 3.14, and r is the radius of the circle.
MAE= Mean Average Error (MAE) is used to measure the accuracy of a model or an algorithm by calculating the average difference between the predicted values and the actual values.
m/COF= The coefficient of friction (COF) is a measure of the resistance of a surface to sliding. It is usually expressed as a ratio of the force of friction to the normal force.
mZAJC= Distance between O and A is the same as the distance between J and C, or mZAJC.
mFG= The length of the arc FG is equal to the product of the central angle and the radius of the circle, or mFG.
MFI= The length of the arc FI is equal to the product of the central angle and the radius of the circle, or MFI.
m/ELD= The length of the line segment ED is equal to the difference between the lengths of the two arcs, or m/ELD.
mFM= The length of the arc FM is equal to the product of the central angle and the radius of the circle, or mFM.
m/AOC= The length of the line segment OC is equal to the difference between the lengths of the two arcs, or m/AOC.
m/AHF= The length of the line segment HF is equal to the difference between the lengths of the two arcs, or m/AHF.
IF= The length of the arc IF is equal to the product of the central angle and the radius of the circle, or IF.
PC= The length of the line segment PC is equal to the difference between the lengths of the two arcs, or PC.
HM= The length of the line segment HM is equal to the difference between the lengths of the two arcs, or HM.
LD and LE are tangent to the circle. This means that the radius of the circle is equal to the distance between the two points, or LD and LE.
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The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
Black 9 36 63 90
White 13 52 91 130
Black 10 36 63 90
White 13 52 91 117
Black 9 36 63 90
White 13 39 91 117
Black 3 36 63 90
White 13 65 91 104
The table with the correct values for A, B and C are,
Black 9 36 63 90
White 13 52 91 130
What is a proportional relationship?A proportional relationship is defined as follows:
⇒ y = kx.
In which k is the constant of proportionality.
Here, The input and output variables for this problem are given as follows:
Input: number of black keys.
Output: number of white keys.
Hence, The constant k is obtained as follows:
91 = 63k
k = 91/63
k = 13/9.
So, The equation is,
⇒ y = 13x/9.
Hence, the values are given as follows;
For A:
when x = 9,
y = 13 × 9 / 9
y = 13
For B:
when x = 36,
y = 13 x 36/9
y = 52.
For C:
when x = 90,
y = 13 x 90/9 = 130.
Thus, First table is correct.
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A Ferris wheel has a diameter of 150 ft. Passengers ride in a carriage around the Ferris wheel. About how far does a carriage of passengers travel during one rotation of the wheel? Round to the nearest tenth. Show or explain your thinking.
Therefore, the distance covered by a passenger vehicle during one turn of the wheel is roughly 471.2 feet (rounded to the nearest tenth).
Diameter and circumference are what?The ratio of a circle's circumference to width serves as the basis for the traditional meaning of Pi (). The diameter or extent of a circular is its circumference. A straight line connecting a spot on one point of the circular to a point at the other end, going through the middle, is the diameter.
The following algorithm determines a circle's circumference:
C = πd
where d is the diameter of the circle. In this case, the diameter of the Ferris wheel is 150 ft, so its circumference is:
C = π(150) ≈ 471.2 ft
This indicates that a full rotation of the Ferris wheel is equal to a passenger vehicle moving about 471.2 feet.
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you use a garden hose to fill a wading pool. if the water level rises 15 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? use slope to justify your answer.
The value of y is 45.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Given that, water level rises 15 centimeters every 7 minutes.
Water level in 7 minutes = 15 cm
Water level in 1 minute = 15/7 cm
So the rate of change of the water rising is 15/7 cm per minute.
That is the point is (1, 15/7).
Let x represent the time and y represent the rise of water.
You have to calculate y of the point (21, y).
Water level rise in 21 minutes = 21 × (15/7) = 45 cm
Value of y is 45.
Slope of a line with two points (x, y) and (x', y') is,
Slope = (y' - y) / (x' - x)
We have slope = 15/7 since it is a proportional relationship.
Take the points (1, 15/7) and (21, y).
(y - 15/7) / (21 - 1) = 15/7
(y - 15/7) / 20 = 15/7
(7y - 15) / (20 × 7) = 15/7
7y - 15 = 15/7 × (20 × 7)
7y - 15 = 300
7y = 315
y = 45
Using slope, it is justified.
Hence the value of y is 45.
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a coin jar contains a combination of nickels and quarters. If there 60 total coins in the jar worth $7.20, how many nickels are there?
There are 39 nickel coins in the jar.
What is a linear equation?
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given a coin jar contains a combination of nickels and quarters,
let the number of nickels be x,
number of quarters be y,
total coins = 60
x + y = 60
y = 60 - x.........(1)
and total coins in the jar worth = $7.20
we know the value of a nickel coin = $0.05
value of quarters coin = $0.25
so, 0.05x + 0.25y = 7.20
substitute the value from equation 1
0.05x + 0.25(60 - x) = 7.20
0.05x + 15 - 0.25x = 7.20
-0.2x = 7.20 - 15
x = 7.8/0.2
x = 39
Hence there are 39 nickel coins.
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F If RV = x + 6. US = 5x - 9, and RS = 11,
find VT and ST
The value of VT is 13 units and the value of ST is 23.56 units
Consider the following diagram of rectangle RSTU
We know that the diagonals of rectangle bisect each other, intersect at right angles.
For rectangle RSTU,
2RV = RT
But RT = US
So, 2RV = US
2(x + 6) = 5x - 9
2x + 12 = 5x - 9
12 + 9 = 5x - 2x
3x = 21
x = 7
So, RV = 7 + 6
RV = 13 units
But RV = VT
So, VT = 13
Now we find the value of ST using Pythagoras theorem.
RT² = ST² + RS²
ST = [tex]\sqrt{RT^2 - RS^2}[/tex]
ST = 23.56 units
Thus, VT = 13 and ST = 23.56
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Which is a stretch of an exponential growth function?
The width of a rectangle is 5 units less than the length. If the area is 150 square units the find the dimensions of the rectangle
Answer:
Step-by-step explanation:
width is 10 length is 15.
You pick a card at random.
2
3
4
5
What is P(3 or even)?
Write your answer as a fraction or whole number.
The Probability of (3 or even) = 3/4
What is probability?
Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
From the question;
The p(3) = 1/4
The P(even) = 2/4 =1/2
P(3 or even) = 1/4 + 1/2
P(3 or even) = 6/8
Reducing to the lowest terms
P(3 or even) = 3/4
Hence, 3/4 is the Probability of (3 or even) of picking a card at random
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9 and 10 please show work
The value of x in triangle HJK is 5 √2, So correct option is (A). The value of x in triangle ABC is 25√3, So correct option is (H).
What do you mean by Pythagorean Theorem?The Pythagorean Theorem is a fundamental theorem in mathematics that relates the lengths of the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, the Pythagorean Theorem can be expressed as:
a² + b² = c²
where "a" and "b" are the lengths of the two sides of the right triangle and "c" is the length of the hypotenuse.
The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is a widely used theorem in mathematics and has numerous applications in many fields, including geometry, trigonometry, engineering, physics, and computer graphics.
For example, in geometry, the Pythagorean Theorem can be used to find the distance between two points in two-dimensional space. In trigonometry, it can be used to find the sine, cosine, and tangent of an angle. In physics, it can be used to calculate the force required to accelerate an object, or to determine the velocity of an object at a given time.
Overall, the Pythagorean Theorem is an important theorem that provides a simple and elegant solution to many problems involving right triangles and is widely used in mathematics and science.
9. To find the value of x in triangle HJK, we can use the Pythagorean theorem. Let's call JK = x.
HK² + JK² = KH²
Since Angle HKJ is 60 degrees and Angle KHJ is 90 degrees, we can use the trigonometric ratios to find the length of HK:
HK = JK × tan 60 = JK / √3
Substituting this into the equation above, we get:
JK² / 3 + JK² = 5²
Expanding and solving for JK, we find that:
JK = 5 √2
So, the answer is (a) 5√2.
10. To find x in triangle ABC, we can use similar methods as in question 9. Let's call BC = x. Then, by the Pythagorean theorem, we have:
AC² + BC² = AB²
Since Angle BAC is 60 degrees and Angle ABC is 90 degrees, we can use the trigonometric ratios to find the length of AB:
AB = AC / √3
Substituting this into the equation above, we get:
AC² + BC² = (AC / √3)²
Expanding and solving for BC, we find that:
BC = AC * √3 / 2 = 50 × √3 / 2 = 25√3
So, the answer is (H) 25√3
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3. In addition to the information given in the drawing, which statement is sufficient to prove PORS is a parallelogram? P Q N T S R A. QR = SP B. QP = SR C. Vis the midpoint of PR D. ZOPR ZSRP Ging Wilson (All Things Algebra LLC).201
After answering the provided question, we can conclude that Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).
What is parallelograms?In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of side lengths. A parallelogram is a type of quadrilateral in which both sets of opposite corners are similar and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, geometric shapes, and rhombuses. A quadrilateral is a parallelogram when it has two sets of equal spacing. The opposing sides and angles of a parallelogram are both the same length. The interior angles on each side of the solid line are also angles. The total number of interior angles is 360.
Option C: The fact that V is the midpoint of PR suffices to demonstrate that PORS is a parallelogram.
We know that PV = VR because V is the midpoint of PR. Furthermore, because QR = SP (as shown in the drawing), we can conclude that triangles QRP.
We can deduce from this congruence that angle QRP is congruent to angle SPR, which means that angle POR is congruent to angle PSR (because they are corresponding angles). Angle OPS is also congruent with angle ORP (because they are corresponding angles).
Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).
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The lengths of the sides of a triangle are in the extended ratio 7 : 9 : 10. The perimeter of the triangle is 104cm. What is the length of the sides ?
Answer:
28, 36, 40
Step-by-step explanation:
Add up the numbers in the ratio, giving us 26. Perimeter divided by 26 equals 4. Then, four times each of the numbers in the ratio gives you the lengths
NEED HELP PLS
schoology
Answer:
A=50 B=50 too C=180
5. For the next school year, the new soccer team will need to come up with $600.
a. Suppose the team $500 from the fundraiser at the start of the current school
year, and the money is placed for one calendar year in savings account
earning 0.5% simple interest annually. how much money will the team stilll
need to raise to meet next year's expenses?
Answer:
Step-by-step explanation:
$300
Help quickly its like 12am lol || Which expression can be used to find the number of one-third cup servings in 4 cups?
four times one-third
one-third times four
4 ÷ one third
one third ÷ 4
Answer:
The answer is C). 4 ÷ one third.
Solve the equation below. Show all work.
12 + 7h = 5
Answer: H = -1
Step-by-step explanation:
12 + 7h = 5
7h = -7
H = -1
a motor car drives at an average speed of 106km/h for 2 hours 45minutes.at which constant speed must the car drive to travel the same distance in 2hours and 35minutes?
Answer:
Step-by-step explanation:
Let's start by calculating the distance traveled in the first scenario:
Distance = Average speed x time
First, we need to convert 2 hours and 45 minutes to hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours. Therefore, the total time is:
2 hours and 45 minutes = 2 + 0.75 = 2.75 hours
Now we can calculate the distance:
Distance = 106 km/h x 2.75 hours = 291.5 km
So the car travels 291.5 km in 2 hours and 45 minutes.
To find the constant speed the car must drive to travel the same distance in 2 hours and 35 minutes, we can use the same formula:
Distance = Speed x time
We know the distance is 291.5 km, and the time is 2 hours and 35 minutes. Again, we need to convert the minutes to hours:
2 hours and 35 minutes = 2 + 35/60 = 2.583 hours
Now we can solve for the speed:
Speed = Distance / time = 291.5 km / 2.583 hours ≈ 113 km/h
Therefore, the car must drive at a constant speed of approximately 113 km/h to travel the same distance in 2 hours and 35 minutes.
Surface area 5in 5in 10in 4in 6 in
Answer:
30
Step-by-step explanation:
5 + 5 + 10 + 4 + 6 = 30