The vehicle going at 60 mph travelled 88 feet in one second
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Speed is the ratio of distance to time taken. It is given by:
Speed = distance / time
If a vehicle is going 60 mph.
1 second = 1/3600 hr
Therefore in one second:
Speed = distance / time
60 mph = distance / (1/3600)
distance= 60 * 1/3600 = 1/60 miles
1 mile = 5280 feet
1/60 miles = 1/60 miles * 5280 feet per mile = 88 feet
The vehicle travelled 88 feet
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Laura and Sean find the product of 3x4 using different methods.
Laura: It's 2 thirds of 4.
²×4 = 3 +
Use words, pictures, or numbers to compare their methods in the space below.
Sean: It's 4 groups of 2 thirds.
2|3
+
= 4x
8
83 this is also worth 100 points
Both Laura and Sean arrive at the same answer of 8/3 by using different methods.
Laura starts by multiplying 2/3 by 4 to find the total amount of 2/3 in 4 units.
Sean starts by finding the total amount of 2/3 in one group and then multiplying that amount by the number of groups, 4.
Both methods lead to the same answer, so it doesn't matter which method is used. The important thing is that the answer is correct.
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
The antifreeze used by each brand will be V₁ = 72 gal. and V₂ = 108 gal.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that
ω₁ = 70% ÷ 100% = 0.7; 70% pure antifreeze.
ω₂ = 95% ÷ 100% = 0.95.
ω₃ = 85% ÷ 100% = 0.85.
V₁ = ?; volume of 70% antifreeze.
V₂ = ?; volume of 95% antifreeze.
V₃ = V₁ + V₂.
V₃ = 180 gal.
The quantity will be calculated as:-
V₁ = 180 gal - V₂.
ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.
0.70 · (180 gal - V₂) + 0.95 · V₂ = 0.85 · 180 gal.
126gal - 0.7V₂ + 0.95V₂ = 153 gal.
0.25V₂ = 27 gal.
V₂ = 27 gal ÷ 0.25.
V₂ = 108 gal.
V₁ = 180 gal - 108 gal.
V₁ = 72 gal.
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if a set of standardized test scores is normally distributed, having a mean of 85 and a standard deviation of 8, approximately 95 percent of the scores are somewhere between
In this case, with a standard deviation of 8 and a Z-score of 1.96 (which represents the 95th percentile), the interval would be from 85 - (8 * 1.96) to 85 + (8 * 1.96), or approximately 69 to 101.
A normal distribution of standardized test scores with a mean of 85 and a standard deviation of 8 has an approximately 95 percent of scores that fall between two points on the distribution. These points are commonly referred to as the "margin of error" and are used to create a confidence interval around the mean. To find the interval, we use the standard deviation and the Z-score to determine the number of standard deviations away from the mean the interval bounds lie. In this case, with a standard deviation of 8 and a Z-score of 1.96 (which represents the 95th percentile), the interval would be from 85 - (8 * 1.96) to 85 + (8 * 1.96), or approximately 69 to 101. This means that if the test scores are normally distributed, approximately 95 percent of the scores will fall between 69 and 101.
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CAN SOMEONE HELP WITH THESE QUESTIONS?
The population after seven years is 12301
The velocity is 194 m/s
The acceleration is 126 m/s^2
What is the population?We know that we need to use the equation that can be written by the value that says that;
P = Poe^rt
P = population at time t
Po = Initial population
t = time
r = population growth rate
We now have that;
3Po =Poe^11r
3 = e^11r
r = ln3/11
r = 0.0998
In the next seven years;
P = 6117e^0.0998* 7
P = 12301
Then we have the equation;
s(t) = 7t^3 + 5t + 9
v(t) = 21t^2 + 5
at t = 3
We have 194 m/s
Then also;
a(t) = 42t
At t = 3
We have 126 m/s^2
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17% of the group wanted to go out on Friday instead of doing homework. The group had 19 members. How many wanted to go out?
Answer:
Step-by-step explanation:
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A golden retriever weighing 85lb was prescribed a medication. If the dosage is 1mg for every 5lb, how much medicine was the dog given?
The dog should be given 17 mg of dosage.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: A golden retriever weighing 85 lb was given a dosage of 1 mg per 5 lb
For every 5 lb 1 mg of the product is given
Thus for 85 lb the number of doasages would be
N= 85/5
= 17 mg
Hence, The dog should be given 17 mg of dosage.
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Dani wants to spend less than 1 hour at the gym. She will spend 20 minutes lifting weights and then will walk around the indoor track. It takes her 4.5 minutes to walk around the track. How many times can Dani walk around the track?
Dani can walk around the track 8 times.
What is an inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Dani wants to spend less than 1 hour at the gym.
She will spend 20 minutes lifting weights and then will walk around the indoor track.
It takes her 4.5 minutes to walk around the track.
The number of times that Dani can walk around the track,
< (60 - 40)/4.5
< 40/4.5
< 8.9
Therefore, she can walk around 8 times around the track.
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xa rectangular box is to have a square base and a volume of 40 ft3. rectangular box with a square base the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x
The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x[/tex].
Let x represent the length of the side of the square base, then the area of the base is given by [tex]x2[/tex]. If the volume of the box is given to be 40ft3, then the height of the box is given by [tex]40/x2[/tex]. The total cost of material used in constructing the box is given by the cost of the base, the cost of the top, and the cost of the sides. The total cost of material in cents is given by the expression:
Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2)[/tex]
The cost of the base is given by [tex]29x2[/tex], since the material for the base costs 29 cents/ft2. The cost of the top is given by [tex]24(40/x2)[/tex], since the material for the top costs 24 cents/ft2. The cost of the sides is given by [tex]10(4x)(40/x2)[/tex], since the material for the sides costs 10 cents/ft2.
Therefore, the total cost of materials used in constructing the box in cents is given by the expression:
Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2) = 1176/x2 + 960x[/tex]
The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x.[/tex]
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translated 1 unit right and five units down
Answer:
y'=|x-5|-1
Step-by-step explanation:
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Fill in the blanks to follow the steps in solving the equation:
5x − 12 − 6x = −10x + 7 − 1
Answer:
see explanation
Step-by-step explanation:
5x - 12 - 6x = - 10x + 7 - 1
step 1 : combine like terms
- x - 12 = - 10x + 6
step 2 : collect x- terms on the left side of the equation
add 10x to both sides
9x - 12 = 6
step 3 : collect constants on the right side of the equation
add 12 to both sides
9x = 18
step 4 : isolate x by dividing both sides by 9
x = 2
To solve the equation 5x - 12 - 6x = -10x + 7 - 1, combine like terms and isolate the x term and we get x=2
Explanation:To solve the equation 5x - 12 - 6x = -10x + 7 - 1, we need to combine like terms on both sides of the equation. Let's start by combining the x terms on the left side:
(5x - 6x) - 12 = -10x + 7 - 1
Simplifying further:
-x - 12 = -10x + 6
Next, we want to get all the x terms on one side of the equation. We can do this by adding 10x to both sides:
-x - 12 + 10x = -10x + 6 + 10x
Simplifying further:
9x - 12 = 6
Now, we want to isolate the x term. Let's add 12 to both sides:
9x - 12 + 12 = 6 + 12
Simplifying further:
9x = 18
Finally, divide both sides of the equation by 9 to solve for x:
x = 2
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Evaluate and simplify the following complex fraction. -2/-7|4/-9
The solution of the complex function is ( 71- 8i ) / (16 +8i).
What is a complex function?The area of mathematical analysis that studies functions of complex numbers are known as complex analysis, often known as the theory of functions of a complex variable.
Given that the function is ( 2 -7i) / ( 4 - 9i). The complex function will be solved as below:-
E = ( 2 -7i) / ( 4 - 9i)
E = ( 2 -7i) x ( 4 + 9i ) / ( 4 - 9i) x ( 4 + 9i )
E = ( 8 - 8i + 63 ) / ( 4 - 9i )²
E = ( 71 - 8i ) / ( 16 - 8i )
Therefore, the solution of the complex function is ( 71- 8i ) / (16 +8i).
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Consider the sequence defined recursively by a1=?2, a2=2, an+1=8an?1?2an. We can use matrix diagonalization to find an explicit formula for an.
a. Find a matrix that satisfiesn [an an+1] = M [an-1 an]
The matrix M is:
M = [8 -2]
[1 0]
This satisfies the relation [an] = [an-1] * M.
Matrix Diagonalization Sequence AnThe matrix M is determined by the recurrence relation. The first row of the matrix represents the coefficients of an and an-1 in the expression for an+1, and the second row represents the coefficients of an-2 and an-3.
Here, in the recurrence relation an+1 = 8an - 2an-1, the coefficient of an is 8 and the coefficient of an-1 is -2, so the first row of the matrix M is [8 -2].
Similarly, the second row of the matrix represents the coefficients of an-2 and an-3 in the expression for an-1. However, in the recurrence relation, there is no explicit expression for an-2 and an-3, so we set them to zero in the second row of the matrix, giving [1 0].
Thus, the matrix M is:
M = [8 -2]
[1 0]
This satisfies the relation [an] = [an-1] * M.
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consider the following correct implementation of the selection sort algorithm: public static arraylist selectionsort(arraylist arr) { int currentminindex; //line 3 int counter
The call to selection causes the statement of algorithms of the elements[minded] = temp; in line 19 of the method to be executed three times.
The declared array is 30 40 10 50 20; int [] err; The selection Sort method would be used to sort the array shown above. Flip the numbers 10 and 30 around. Move the numbers 20 and 40 around. exchange the new position of 40 for the number 50. Consequently, line 19 of the selection Sort algorithm would be run three times. Anyone static can access the method because it has the access specifier public. Accessing static members in this situation is independent of the object. This means that the method returns a void or nothing at all. A grouping of homogeneous (same type) components is known as an array. Option "B" is the appropriate way to provide a two-dimensional array into a function in the computer language; the following options are incorrect:
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