The distances travelled in each hour for both part are given as 5760 m and 5.76 km respectively.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given problem can be solved by ratio method as follows,
(A) The average walking rate is 1.6 m/s
The speed in meter per hour is calculated as,
1 second = 1/3600 hour
Take the ratio of 1.6 and 1/3600 as follows,
1.6 ÷ 1/3600
= 3600 × 1.6
= 5760
(B) The average walking rate is 1.6 m/s
It implies that 1.6 m in 1 second.
Now, 1 m = 1/1000 km
=> 1.6 m = 1.6/1000 km
And, 1 second = 1/3600 hour
Thus, the distance travelled in kilometer per hour can be evaluated by taking the ratio as follows,
1.6/1000 ÷ 1/3600
= (3600 × 1.6)/1000
= 5.76
Hence, the distances travelled per hour in meter and kilometer are given as 5760 m and 5.76 km respectively.
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Matthew and some friends are going to a concert. They hire a car service for $75 to drive them to a
restaurant for dinner and then the concert. They divide the $60 cost of the dinner equally. However, since
Matthew's dad provided concert tickets for the group, the friends agree that Matthew doesn't have to help pay
for the car service. The friends divide this cost equally among themselves. If each friend spends a total of $25,
how many friends went to the concert with Matthew?
n represents the number of friends, there must have been 2 friends with Matthew at the concert.
What is the arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Let's call the number of friends n. The cost of the car service for the friends is 75 - 25 = 50 dollars. Since this cost is divided equally among the friends, each friend pays 50/n dollars.
The total cost for each friend, including the cost of the car service and the cost of dinner, is 25 dollars. Therefore, the cost of dinner for each friend is 25 - 50/n dollars.
Since the cost of dinner was divided equally among the friends, each friend paid 60/n dollars for dinner. Therefore, 25 - 50/n = 60/n.
Solving this equation for n, we get:
25 - 50/n = 60/n
50/n - 60/n = -25
10/n = 25
n = 2.5
Hence, n represents the number of friends, there must have been 2 friends with Matthew at the concert.
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Question 1Mutple Choice Worth 2 points)
(Angle Relationships MC)
One angle measures 24", and another angle measures (7d-4). If the angles are complementary, what is the value of off
Od=80
Od=17
Od=10
Od=3
As two angles are Complementary Angles they sum up to 90.
So value of d is 10.
What are Complementary angles?Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.
If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.
60° + 30° in the figure below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,
The opposite of 30° is 60°.
The opposite of 60° is 30°.
Calculation:Given;
24,(7d-4) are complementary angles
So, 24°+7d-4 =90°;
⇒7d-4=90-24;
⇒7d-4=66;
⇒7d=70;
⇒d=10.
As two angles are Complementary Angles they sum up to 90.
So value of d is 10.
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Please give an answer, and thinking. Thank you.
Answer:
see explanation
Step-by-step explanation:
- 1x + 4y = 12 , that is
- x + 4y = 12 ( add x to both sides )
4y = 12 + x ( divide each term by 4 )
y = 3 + [tex]\frac{1}{4}[/tex] x
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
(4,-10)
Step-by-step explanation:
Graphing calculator
A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water. What is the velocity of the boat relative to shore?
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Define velocity.The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity. Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.
Given
A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Velocity,
v = √(1.65)² + (10.7)²
v = √2.722 + 114.49
v = √117.212
v = 10.82
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
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what is the answer for 3(m+5)-2(-9+m)=29
solving for m
distribute into parentheses
3m + 15 + 18 -2m = 29
simplify
m + 33 = 29
subtract
m = -4
verify
3(-4+5) -2(-9-4) = 29
3 + 26 = 29
29 = 29
true
m = -4
hope this helps :)
jeron
Convert the quadratic function from vertex form to standard form: g(x)= 1/2 (x+2)^2-8
Answer:
y = 1/2x² - 2x - 6
Consider the following regression model: yi = B0 +B 1xi + ui. If the first four Gauss-Markov assumptions hold true, and the error term contains heteroskedasticity, then _____.a. Var(ui|xi) = 0b. Var(ui|xi) = 1c. Var(ui|xi) = Θi2d. Var(ui|xi) = Θc. Var(ui|xi) = Θi2
If the first two Gauss-Markov assumptions are met and heteroskedasticity exists in the error term, Var(ui|xi) = i2.
What is an example of heteroscedasticity?Examples. When there is a significant disparity in the magnitude of the observations, heteroscedasticity frequently develops. An old-fashioned illustration of heteroscedasticity is the relationship between income and food expenses. The variability of eating habits will rise as income does as well.
Does heteroskedasticity make a difference?Because normal regression model (OLS) regression presumes that all royalties are taken from a population with constant variance, heteroscedasticity is a concern (homoscedasticity). The particles ought to have a standard deviation in order to meet the plugs and be capable of relying on the results.
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I have 3 red balls, 3 blue balls and 3 yellow balls in a box. Total of 9 balls. Let's say that I randomly pick 3 balls, what are the chances of having at least 2 red balls in the 3 that I picked?
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.
If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,
P = 3/9
P = 1/3
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
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In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other. PLEASE EXPLAIN WITH WORDS IN TWO SENTENCES I NEED HELP ASAP
Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
(x, y) → (y, x)To determine if f(x) and g(x) are inverses of each other:
Input the x-value of the ordered pair into one function.Input the y-value of the ordered pair as the x-value of the other function.If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
[tex]\implies f(2)=2(2)+5=9[/tex]
Substitute x = 9 into g(x):
[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
12. How much tax would I pay on a Nintendo Wii (cost of $150) if the tax is 8%?
Answer:
$162
Step-by-step explanation:
8% of 150 = 12 + 150
Help pls i need it
Determine which integer will make the inequality 2(n + 1) ≤ 3(n − 2) true.
S:{0}
S:{4}
S:{6}
S:{8}
Solve equation:
-6-3k+8=5
if you solve the equation you get k=-1
Please help you get 100 points and brainly
You have points R(2, 10) and S(6, - 8).
There two ways to construct a right triangle with RS being a hypotenuse.
Please see both ways reflected in the attached.
One triangle is RST and another one is RSU with red or blue legs.
Find the value of x in this equation
Answer:
x = 4
Step-by-step explanation:
7x = 3x + 16
7x - 3x = 16
4x = 16
4/4 x = 16/4
x = 4
kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in., what are the possible lengths of a third rod?
The required length of the third side should be less than the sum of the other two sides or less than 37 in.
As mentioned, Kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in.,
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the length of the third side,
The property of the triangle states that the sum of the two sides of a triangle is always greater than the length of the third side.
So
x < 15 + 22
x < 37
Thus, the required length of the third side should be less than the sum of the other two sides or less than 37.
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Determine whether y = -2x² - 3 is a function.
Answer:yes
Step-by-step explanation:
Use the normal distribution to the right to answer the questions. (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? Standardized Test Composite Scores 1921Score mu equals 19.6 sigma equals 5.3 mu x A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 38 with tick marks at 19 and 21. A normal curve labeled μ = 21.2 σ = 5.4 is centered above the x-axis at 21.2. A vertical line segment labeled μ extends from the normal curve to the x-axis at 21.2. (a) The percent of scores that are less than 19 is nothing %. (Round to two decimal places as needed.) (b) About nothing scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)
a) The percentage of scores that are less than 19 is of: 34.09%.
b) The amount out of the 1500 scores that would be greater than 21 is of: 774.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the scores in this problem are given as follows:
[tex]\mu = 21.2, \sigma = 5.4[/tex]
The proportion of scores that are less than 19 is the p-value of Z when X = 19, hence:
Z = (19 - 21.2)/5.4
Z = -0.41.
Z = -0.41 has a p-value of 0.3409.
Hence the percentage is of 34.09%.
The proportion of scores that are greater than 21 is one subtracted by the p-value of Z when X = 21, hence:
Z = (21 - 21.2)/5.4
Z = -0.04
Z = -0.04 has a p-value of 0.484.
1 - 0.484 = 0.516.
Hence the amount out of the 1500 scores is given as follows:
0.516 x 1500 = 774 scores.
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Find three integer or decimal solutions to the following equation, and then graph the solution set.
5x+4y=20
Answer:
To find three integer or decimal solutions to the equation 5x + 4y = 20, we can first divide both sides of the equation by the GCF of the coefficients, which is 1. This gives us the equation 5x + 4y = 20/1, which can be rewritten as 5x + 4y = 20. We can then use the substitution method to solve for x in terms of y, by setting 4y = 20 - 5x and solving for x. This gives us x = (20 - 4y) / 5. Substituting this expression for x into the original equation, we get 5((20 - 4y) / 5) + 4y = 20, which simplifies to 20 - 4y + 4y = 20, or 20 = 20. This means that any value of y that satisfies the equation will also satisfy the original equation.
For example, if we choose y = 3, then x = (20 - 4 * 3) / 5 = 2, and the solution (x, y) = (2, 3) satisfies the equation 5x + 4y = 20. Similarly, if we choose y = 0, then x = (20 - 4 * 0) / 5 = 4, and the solution (x, y) = (4, 0) satisfies the equation. Finally, if we choose y = -1, then x = (20 - 4 * -1) / 5 = 5, and the solution (x, y) = (5, -1) satisfies the equation.
The solution set for the equation 5x + 4y = 20 is the set of all ordered pairs (x, y) that satisfy the equation. The three solutions we found are (2, 3), (4, 0), and (5, -1), and these solutions can be plotted on a coordinate grid to show the solution set. The graph of the solution set is a line that passes through the points (2, 3), (4, 0), and (5, -1).
Step-by-step explanation:
A 6-sided polygon is classified as a heptagon.
True
False
Answer:
true 6=hepti
Step-by-step explanation:
A merchant mixed 20 pounds of a cinnamon tea with 10 pounds of a spice tea. The 30-pound mixture sells for $80. A second
mixture included 12 pounds of the cinnamon tea and 8 pounds of the spice tea. The 20-pound mixture sells for $54. What is the
price per pound of the cinnamon tea?
A.$3.50
B.$2.50
C.$5.50
D.$0.50
Answer:10x+2y=38, where x is the dollar cost of cinnamon and y the dollar cost of the spice.1
6x+8y=80multiply the top by -4-40x-8y=-15216x+8y=80.
Add them and y is eliminated.-24x=-72
Step-by-step explanation:
Find the radius of the circle containing 36° arc of a circle whose length is 13 m.
Answer:
20.69 m
Step-by-step explanation:
36/360 * 2πr = 13
r = 130/2π = 20.69 m
MATHEMATICAL CONNECTIONS Solve a system of linear equations to find the values of x and y.
The values of x and are 28° and 58° respectively
How to determine the valuesIt is important to note the properties of a trapezium;
Bases are parallel to each otherAdjacent interior angles sum up to 180°Sum of all the interior angles is 360°Length of both diagonals are equalDiagonals intersect each otherWe then have that;
2y + (y + 6) = 180
4x + 2x + 12 = 180
From equation (1), we have;
3y + 6 = 180
collect like terms
3y = 180 -6
3y = 174
y = 58°
From equation (2), we have;
6x = 180 -12
6x = 168
x = 28°
Hence, the values are 28° and 58°
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One number is two less than a second number. Twice the second number is nine less than three times the first find the two numbers.
Answer:
13 and 15
Step-by-step explanation:
We set up equations.
X=Y-2
2Y=3X-9
We change X=Y-2 into Y=X+2.
Substituting for Y, we get 2Y=2X+4=3X-9
We now solve for x.
2X+4=3X-9 |-2X
4=X-9 |+9
13=X.
X=13
Substituting for Y, we get that Y =15 from the equation Y=X+2.
So, X=13 and Y=15
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need help on these math questions
The evaluation of the table, equations, and graphs in the question are as follows;
First question;
Part A; The table does not represent a function
Part B; The value of f(300) is $123 represents the total cost for driving 300 miles
Second question;
Part A; The equation is; y = -2·x + 8
Part B; The graph can be obtained by finding the ordered pair of values for the first five hours and plotting the result on a graph, to form a straight line graph.
Third question;
Part A; The solution is; (2, -1)
Part B; Two solutions for f(x) are; (1.5, 0) and (0, 3)
Part C; The solution for the equation, g(x) = f(x) is the point (0, 3)
What is a function?A function is rule, law or expression that maps the elements of one set A unto the elements of another set B such that each element of the set A maps unto exactly one element of the set B.
First question;
Part A: The value of x = 4 has two values of y = 2, and -2
The value of x = 9 has to values of output, y = 3 and -3
The function therefore is; y = f(x) = ±√x
The above function indicates that a value of x returns two values of y, which indicates that a vertical line drawn through the graph of the function f(x) = ±√x intersects the graph twice for values of x > 0, therefore, the equation, f(x) = ±√x, represented by the values in the table is not a function
Part B: The function for the total cost of driving a car is f(x) = 90 + 0.11·x
Where; f(x) = The total cost in dollars
x = The distance the car is driven in miles
Therefore, f(300) is obtained by plugging in x = 300 as follows;
f(300) = 90 + 0.11 × 300 = 123
The value of f(300) = $123
f(300) represents the total cost of driving the car for 300 miles
Second question set;
The velocity of the runner after one hour = 6 km/h
The velocity of the runner after three hours = 2 km/h
Part A: The ordered pair of points of the function are; (1, 6) and (3, 2)
Making use of a linear model, we get;
Slope of the equation of the model, m = (2 - 6)/(3 - 1) = -2
The equation of the model is therefore; y - 6 = (-2) × (x - 1) = -2·x + 2
y = -2·x + 2 + 6
y = -2·x + 8
Where: y = The speed of the runner
x = The number of hours the runner has been running
Part B:
The graph of the equation can be plotted from the values of y obtained from the corresponding values of x for the first 5 hours as follows;
[tex]\begin{array}{|c|c|}x & y \\1 & 6 \\2 & 4\\3 & 2 \\4 & 0 \\5 & -2\\\end{bmatrix}[/tex]
Please find attached the graph of the velocity of the runner with time created using the above table of values found with MS Excel
Third Question;
Part A; The solution to pair of equation can be found from the point of intersection of their graphs
Therefore, the solution of the pair of equations represented by p(x) and f(x) is the point of intersection of the graph of f(x) and p(x), which is the point (2, -1)
Part B; Two solutions for the function f(x) can be obtained by the point of intersection of the x- and y-axis as follows;
The x-intercept of f(x) = (1.5, 0)
The y-intercept of f(x) = (0, 3)
Part C; The solution for g(x) = f(x), is the point of intersection of g(x) and f(x), which is the point (0, 3)
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I want to know what is 2/5 x -3
Answer:
I think your answer is [tex]\frac{2}{5} x-3[/tex]
Step-by-step explanation:
Jordan had a bake sale. Muffins cost $3 each and cookies cost $2 each. Jordan earned $24.
(Select all)
- 0 muffins and 8 cookies
- 9 muffins and 2 cookies
- 2 muffins and 9 cookies
- 6 muffins and 4 cookies
- 4 muffins and 6 cookies
Answer:
0 muffins and 8 cookies
6 muffins and 4 cookies
Explain:
These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.
Vue wonders how long the ball was in the air when it was 54 feet in the air so he writes the equation 54=-16s2+96s. Solve the equation for time(s) to determine how long the ball was in the air when it was 54 feet above the ground . Round your answer to the nearest hundredth of a second . On a piece of paper , Identify which of the following methods you used to solve this question : factoring , completing the square, the Quadratic Formula, using a graph. Then explain how your solution helps Vue answer his question
Answer:
0.63 or 5.37 seconds
Step-by-step explanation:
You want to know how long a ball was in the air when its height is 54 feet, and its height is described by -16s^2 +96s, for time (s) in seconds.
SolutionA graph shows the value of the height function is 54 when s = 0.63 or 5.37.
These solutions mean the ball was in the air 0.63 seconds when it passed 54 feet going up, and it was in the air 5.37 seconds when it was 54 feet in the air on the way down.
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.
The inequality that describes the base length of the triangle is b ≤ 28/h
How to determine the inequality that describes the base length of the triangle?From the question, we have the following parameters that can be used in our computation:
Base = bHeight = hArea = At most 14 square feetThe area of a triangle can be calculated using the following formula
Area = 1/2 * Base * Height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * b * h
Evaluate the products
Area = 1/2bh
Recall that
Area = At most 14 square feet
This means that
Area ≤ 14
So, we have
1/2bh ≤ 14
Multiply through by 2
bh ≤ 28
Divide both sides by h
b ≤ 28/h
Hence, the inequality is b ≤ 28/h
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