a. More than 3,000 people are killed yearly in crashes involving large trucks or buses.
The stopping distance of a large truck or bus is determined by calculating the kinetic energy (K) of the vehicle, the coefficient of friction (μ) between the road and the tires, and the weight (W) of the vehicle. The formula for calculating the stopping distance is K = (μ * W2) / 2g, where g is the acceleration due to gravity. This means that the heavier the vehicle and the lower the coefficient of friction, the longer the stopping distance. Since large trucks and buses are heavier than cars, they have a longer stopping distance and are more likely to be involved in fatal crashes.
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The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
The quadratic equation to find the width of the rectangle by formulating the area and length value is 2w² - w - 91 = 0.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The value for the area of the rectangle is given as = 91 in²
Let the width for the rectangle be = w
Then the length of the rectangle is 1 less than twice its width, l = (2w - 1)
The formula for the area of the rectangle is -
Area = length × width
Substitute the values to get the equation for width -
91 = (2w - 1) × w
Use the arithmetic operation of multiplication -
91 = w(2w - 1)
91 = 2w² - w
Rearrange in quadratic form -
2w² - w - 91 = 0
Therefore, the equation is obtained as 2w² - w - 91 = 0.
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factor the common factor of 9x + 36
9 is the common factor of 9x + 36.
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 9x+36
Factor is a number or algebraic expression that divides another number or expression evenly i.e., with no remainder.
The factors of 9 are 1,3,9
The factors of 36 are 1,2,3,4,6,9,12 and 18
The highest common factor is 9.
Take 9 as common from the expression.
9(x+4)
Hence, 9 is the common factor of 9x + 36.
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Brett has c more comic books in his collection than Erica does. Erica has 19 comic books in her collection. Write an expression that shows how many comic books Brett has in his collection.
The expression for the given conditions is Y=10+c
where Y=no. of books Brett has and c=no. of books Erica has.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given No. of books Erica has = 19
and Brett has c more comic books than Erica has
let Y=no. of books Brett has
Hence, the expression will be
Y=19+c
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Can someone help me with this asap?!
Inequality of 4x-6= 22 is x=7
Explain about the Inequality?In mathematics, inequalities describe the connection between two values that are not equal. Equal implies to be equal, not. The "not equal symbol is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine if they are less than or higher than.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
To the other side, move -6.
Changes from a -6 to a +6 sign.
4x-6+6= 22+6
4x= 22+6
4x= 28
Divide each side by 4
4x/4= 28/4
x= 7
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make x the subject for 8x+7=2y-1
Which of the following numbers is irrational? (1 point)
a fraction with numerator negative 15 and denominator 4, a fraction with numerator negative 7 and denominator 9, square root of 4, π
The only number that is irrational is π
How to identify the number that is irrational?
An irrational number is a number that can't be written as the quotient between two integers.
Also, square roots of non-square numbers are irrational.
In this case, the options are:
-15/4
-7/9
√4
π
The first 3 of these are rational, and the only irrational one is π, which is the quotient betwen the cicumference and the diameter of a circle.
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Printing company purchases an ad- vanced color copier/printer for $113,000 After 7 years, the equipment will be obsolete and have no value.
Write a linear equation giving the value of the equipment in terms of the time t
A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.
The value of the colour printer is 117000 $ and machine has no value after 7 years.
As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.
Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t
Thus, the required linear equation is v = 117000 - 16714.3t.
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necesito esto para hoy,porfavor x-3(x+5)=3x+10
No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.
¿Cómo resolver una ecuación algebraica?
En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:
3 · (x + 5) = 3 · x + 10
Segundo, halle la solución por propiedades algebraicas:
3 · x + 15 = 3 · x + 10
15 = 10 (CRASH!)
La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.
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The average high temperatures in degrees for a city are listed. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57 If a value of 42.5° is added to the data, how does the mean change and by how much? The means stays at 80.4°. The mean stays at 77.5°. The mean increases by 2.9°. The mean decreases by 2.9°.
The mean decreases by 2.9°. Therefore, option D is the correct answer.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, the average high temperatures in degrees for a city are 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57.
Here, average = Sum of all the observations/Number of observations
= (58+61+71+77+91+100+105+102+95+82+66+57)/12
= 965/12
= 80.41°
New average = 965+42.5/12+1
= 1007.5/13
= 77.5°
Difference in average =80.41-77.5
= 2.91°
Therefore, option D is the correct answer.
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What is the equation of the line that passes through the point (1, 8) and has a slope
of 1?
Answer:
y = x + 7
Step-by-step explanation:
Equation of line:[tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]
m = 1
(1 , 8) ; x₁ = 1 & y₁= 8;
y - 8 = 1*(x - 1)
y - 8 = x - 1
y = x - 1 + 8
y = x + 7
there are 14 desktops and 16 laptops what percent of the computers are laptops
Answer:
53.3%
Step-by-step explanation:
14 + 16 = 30
16/30 x 100 = 53.3% are laptops
2. Mai also got the expression 7x 1 and wrote her answer as 7x + (−1). Are the two
expressions equivalent? How do you know?
Answer:
Yes, the answers are equivalent.
Step-by-step explanation:
The answers are equivalent because when adding a positive to something it does not change the value of the number. So by adding the + in front of the -1 the value of -1 does not change in the equation.
Hope this helps!!
The volume of soda dispensed in a can during production is normally distributed with a mean of 358. 2 ml and a standard deviation of 1. 8 ml. The company does not want more than 2. 5% of all cans to be less than the volume on the label which is 355ml. Is the company meeting its goal? If not, what should the company do? (Show work)
To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
We can use the z-score formula to find the probability of cans having a volume less than 355 ml.
z-score = (355 - 358.2) / 1.8 = -1.78
Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372
The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.
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Determine the solution to the following system of linear equations by inspecting the graph below. Enter the solution set as an ordered pair in the form (x,y). If there are no solutions, enter None and enter ALL if there are infinitely many solutions.
The solution set to the system of linear equations as an ordered pair is (3, -3).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
Note: Each interval on this graph represents 1 unit.
By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).
In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.
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Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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What is ths measure of z. 3
6.4% as a fraction in simplest form
Answer:32/5
Step-by-step explanation:
32/5
Answer:
Solution: 6.4% as a fraction is 32/5.
Step-by-step explanation:
Harper has $0.70 worth of nickels and dimes. She has 5 more nickels than dimes. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Harper has.? Determine three ways to have 5 more nickels than dimes
The number of nickels, x, and the number of dimes y that Harper has are;
8 nickels and 3 dimes
How to solve algebra word problems?From conversion of coins we know that;
1 nickel = $0.05
1 dime = $0.10
Thus, if she has 5 more nickels than dimes, then;
Let x = the number of dimes Harper has
Let x + 5 = the number of nickels Harper has
Thus;
$0.05(x + 5) + $0.10(x) = $0.70
0.05x + 0.25 + 0.10x = 0.70
0.15x = 0.70 - 0.25
0.15x = 0.45
x = 0.45/0.15
x = 3 dimes
Nickels = 8 nickels
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can anyone help me with this?
$97.056 is the total interest accrued after the first month.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.
The cost of car = 19,725*(1.0475) = 20,661.9375
Down payment = 2,175
So balance amount, P= 20661.9375-2175 = 18,486.9375
So interest for the average rating of a new car = 6.30%
So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056
therefore, interest accrued after the first month is $97.056.
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Emilio has a bank account that pays 4% interest each year. He has $200 in his account. How much interest will he earn after 1 year?
if you answer this right you will get extra brainly points
Answer:
Step-by-step explanation:
That"ll be 37% hope this helps:))
anna leaves her house on her bike traveling at an averge speed of 6 mph. an hour later, her mother sets out after her on the same road, traveling by car. how fast must she drive to reach anna in twn minutes
The mother must drive at a speed of 6 mph to reach Anna in ten minutes.
To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.
Let x be the speed of the mother's car in mph.
In one hour, Anna will have covered 6 miles.
In ten minutes, the mother will have covered x * 10/60 miles.
The total distance between them is 6 + x * 10/60 miles.
The mother must cover this distance in ten minutes, so:
x * 10/60 = 6 / (10/60)
x = 6 * (10/60) / (10/60)
x = 6 mph
Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.
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using the multiple linear regression model you developed in part (a), what is the predicted freshman gpa of bobby engle, a student who has been admitted to ruggles college with a 660 sat score on critical reading and at a 630 sat score on mathematics?
y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.
A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.
Score on critical reading = 660
Score on mathematics = 630
Intercept = -2.6717
Reading(x1) = 0.0043
Mathematics(x2) = 0.0045
Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.
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mentum.com
Lxpre3310113, 1931
ial Expressions: Mastery Test
5
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
40+8+32+(15-7) × 2
Arrange the steps in the order in which they are performed.
3²
5+9
40+8
14+ 16
8x2
KNOW
15-7
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.
Given: 40/8 + 3² + (15 - 7) × 2
The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.
40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8
Then you evaluate exponential terms.
40/8 + 9 + 8 × 2 . . . . . 3² = 9
Next, multiply and divide from left to right. In this case, division comes before multiplication.
5 + 9 + 8 × 2 . . . . . divide 40/8 = 5
5 + 9 +16 . . . . . . multiply 8 × 2 = 16
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
The complete question is:
Using the order of operations, what are the steps for solving this expression?
40/8+3^2+(15-7)*2
Arrange the steps in the order in which they are performed.
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Please help ASAP!!!!!!!!!
The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."
Option A is correct.
What is slope of line?In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.
We are given equation as 4x-7y=62
First, let's write it in the slope-intercept form .In general, slope-intercept form is y=mx + b
where m is the slope
So, writing the equation in the form, we get
⇒-7y = 62-4x
⇒7y = 4x-62
⇒y = 4x/7-62/7
Now, matching the equation with the general form,
m = 4/7
Hence, the slope of the line represented by 4x-7y=62 is 4/7.
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Exercise 2. 5. 2: Proof by contrapositive of statements about integer division. About Prove each statement by contrapositive (a) If x and y are integers such that 3xy then 3x. Solution (b) For any integers x, y, and z, if x|y and xz, then x(y z). (c) If x and y are integers such that x > 1, and x divides y, then x(y 1)
The statements
(a) If x and y are integers such that 3xy then 3x.
(b) For any integers x, y, and z, if x y and xz, then x(y - z).
(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)
are proved.
The term integers in math is defined as are the collection of whole numbers and negative numbers.
Here we know that x and y are the integers,
Then it takes both positive and negative numbers.
Then we take y=1, then we apply it on the expression then we get,
=> 3x(1) = 3x.
Similarly here we have take that xy|z means xy is a factor of z,
Here we can say xym = z for some integer m.
=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.
Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.
Where in the third one, we can take x|y means there exists a constant is written as y = kx
Where as y|x means there exists a constant written as x = cy
When we compare these, then we get,
=> y = kx = kcy
Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1
Therefore y = kx becomes y = 1*x or y = x
Similarly x = cy becomes x = 1*y or x = y
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Need some help with this paper
well, it comes down to, if f(x) is indeed an inverse of g(x) and the other way around, then f( g(x) ) = x, and likewise g( f(x) ) = x, so let's check if f( g(x) =x
[tex]f(x)=3x+11\hspace{5em}g(x)=-\cfrac{1}{3}x-\cfrac{11}{3} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=3\left( -\cfrac{1}{3}x-\cfrac{11}{3} \right)+11 \\\\\\ f(~~g(x)~~)=-x-11+11\implies f(~~g(x)~~)=-x ~~ \bigotimes[/tex]
now, we could do a test by doing g( f(x) ), however we don't need to, since f( g(x) ) ≠ x, they're not inverse of each other.
Answer questions 8 and 9.
Find the measure of an arc from the central angle.
By using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
What is the measure of an arc from the central angle?
The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.
In the given figure
by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 360° - 225° = 135°
In the second figure,
If m(arc KJH) = 312°
m∠1 = 360° - 312° = 48°
Hence, by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
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A man walks due west for 4km. he then changes direction and walks on a bearing of 197 degrees until he is southwest of his starting point. how far is he to the then from his starting point
Step-by-step explanation:
To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,
c² = a² + b² - 2abcos(C)
In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.
Therefore, we can use the law of cosines to find the distance he traveled in the second leg:
c² = a² + b² - 2abcos(90)
c² = 4² + b²
c = √(4² + b²)
c = √(16 + b²)
We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.
So we can use the law of cosines to find the distance he traveled in the second leg:
b = √(c² + a² - 2ac cos (-163))
We can now plug in the values we know:
b = √(c² + 4² - 24c*cos(-163))
We can now solve for c:
c = √(b² + 16 - 8bc)
The man is then southwest of his starting point, so the distance from his starting point to the final point is c.
Quadrilaterals Q and P are similar. What is the scale factor of the dilation that takes P to Q?
A. 3/5
B. 4/5
C. 5/4
D. 5/3
Answer:
C. 5/4
Step-by-step explanation:
Let s = the scale factor
4s = 5 divide both sides by 4
s = 5/4
Two numbers are in the ratio 8cm:1m,if the smaller number is250,what is the greater number
Two numbers are in the ratio 8cm:1m, he greater number is 3,125.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all examples of ratios.
Given that, Two numbers are in the ratio 8cm:1m and smaller number is 250.
let the greater number is x.
ratio = 8cm/1m
= 8cm/100cm
= 1/12.5 or 1:12.5
1/12.5 = 250/x
⇒ x = 250 * 12.5
⇒ x = 3,125
So, the greater number is 3,125.
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