Car A leaves the Grand Canyon at noon. It travels at 80 mph, but stops at 3 pm for an hour. Car leaves the Grand Canyon at 2 pm and travels at 90 mph without stopping on the same route as car A When does Car B catch up with Car A? hours afternoon
Car B will catch up with Car A at 4:45pm, after travelling for 2 5/8 hours (3 hours minus 1 hour minus 3/8 of an hour).
Car A leaves the Grand Canyon at noon and travels at 80 mph. At 3 pm, it stops for an hour. Car B leaves the Grand Canyon at 2 pm and travels at 90 mph without stopping.To calculate when Car B will catch up with Car A, we need to find the time difference between their departure times and the difference in their speeds.Car A leaves one hour before Car B, so we can subtract 1 hour from the total travel time. The difference in their speeds is 10 mph, which is equivalent to 1/8 of an hour for every hour of travel. Therefore, we can subtract 1/8 of an hour from the total travel time for every hour of travel.We can use these two deductions to calculate the total travel time: 3 hours - 1 hour - 3/8 of an hour = 2 5/8 hours. Therefore, Car B will catch up with Car A at 4:45pm.
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How do you know if a midpoint Riemann sum is an overestimate or underestimate?
When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.
We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.
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f(x)=-(x+3)(4x-5)(x-1)
The x-intercepts of the function f(x) are (-3,0), (5/4,0), and (1,0).
What is a function?A relation is a function if it has only One y-value for each x-value.
To find the x-intercepts of the function f(x) = -(x+3)(4x-5)(x-1), we need to set f(x) equal to zero and solve for x:
f(x) = -(x+3)(4x-5)(x-1) = 0
Since the product of three factors is zero if and only if one or more of the factors is zero, we can set each factor equal to zero and solve for x:
x+3 = 0 => x = -3
4x-5 = 0 => x = 5/4
x-1 = 0 => x = 1
Therefore, the x-intercepts of the function f(x) are (-3,0), (5/4,0), and (1,0).
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EFG is a triangle. E is (5,2) and F is (1,-4) and x =1 is a line of symmetry. (a) Work out the coordinates of G. (b) Work out the name of the line through G and E.
a) The coordinates of G are (3, -4)
b) The name of the line through G and E is y = (-3/2)x + 13/2
(a) Since the line x=1 is a line of symmetry for triangle EFG, we know that G must lie on the same line of symmetry, and hence its x-coordinate should be reflected across the line x=1 from the x-coordinate of E.
The x-coordinate of E is 5, so the x-coordinate of G should be 5-2=3. That is, G has an x-coordinate of 3.
Similarly, since the line x=1 is a line of symmetry, the y-coordinate of G should be the same as the y-coordinate of F, which is -4. Therefore, G has a y-coordinate of -4.
Thus, the coordinates of G are (3, -4).
(b) To find the name of the line through G and E, we can first calculate the slope of the line:
slope = (y2 - y1)/(x2 - x1) = (-4 - 2)/(3 - 5) = -3/2
The line through G and E has a slope of -3/2.
Next, we can use the point-slope form of the equation of a line to find the equation of the line. We can use either point E or point G to write the equation, but it might be easier to use point G since we have already calculated its coordinates.
Using point-slope form with point G and the slope -3/2, we get:
y - (-4) = (-3/2)(x - 3)
Simplifying and rearranging, we get:
y = (-3/2)x + 13/2
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what is multiple of 2
The multiple of 2 means any number that is completely divisible by 2.
A multiple in mathematics is basically that number which is formed by multiplying a particular number and it is completely divisible by that number.
If we talk about the number 2, then the multiple of 2 will mean that any number that is formed by multiplying 2 into it.
For example, 6 is a number which can be written as 2 x 3.
Here, 3 is multiplying two times and it becomes 6, so, it is a multiple of 2. Also, if any number is appearing in the table of 2 then it is a multiple of 2.
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Mei Mei spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17 to the plane at point A. At some later time, she measures an angle of elevation of 36 to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
The distance between points A and B is 11785.2 ft.
What is algebraic expression?In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.
Given is that the plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17° to the plane at point A. At some later time, she measures an angle of elevation of 36° to the plane at point B.
We can write -
tan (17°) = 6350/AC
tan (36°) = 6350/BC
Now, we can write -
AC = 6350/tan (17°) ... { 1 }
AC = 20483.9 ft
&
BC = 6350/tan (36°) ... { 2 }
BC = 8698.7 ft
We can write -
AB = AC - BC ... { 3 }
AB = 20483.9 - 8698.7
AB = 11785.2 ft
Therefore, the distance between points A and B is 11785.2 ft.
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a)T= √n, find the value of T when n=1HH.
b) Given that T:
Make 'n' the subject
Formula.
The value of T when n = 1 is 1 and the equation of n is n = T²
How to find the value of TFrom the question, we have the following parameters that can be used in our computation:
T= √n
When n = 1, we jave
T= √1
Evaluate
T = 1
Recall that
T= √n
Take the square of both sides
n = T²
Hence, the equation is n = T²
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x^5x^4⋅x. write your answer using only positive exponents.
Answer:
Below
Step-by-step explanation:
I will assume this question has messed up syntax and is supposed to be :
x^5 * x^4 * x =
x^5 * x^4 * x^1
x^(5 + 4+ 1) = x^10
Which of the contexts below could not be modeled by an exponential function?
• A car depreciates at a rate of 3.7% per year.
• A sunflower was growing at a rate of 2.75 inches per week.
• A certain population of 25 aggressive zombies quadruples every week.
Money invested in a savings account grows at an annual rate of 2.2%.
Answer:
The context that could not be modeled by an exponential function is "A car depreciates at a rate of 3.7% per year." Exponential functions are typically used to model situations involving growth or decay that occur at a constant rate over time. In this case, the rate of depreciation of the car is decreasing over time, so it cannot be modeled by an exponential function. A linear function or a more complex model may be more appropriate.
farmer ed has meters of fencing, and wants to enclose a rectangular plot that borders on a river. if farmer ed does not fence the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?
The length of 175 metres and width of 87.5 metres will maximise the area 15312.5 square metres.
We have been given that Farmer Ed has 350 metres of fencing and wants to enclose a rectangle mat plot that borders on a river. Farmer Ed does not fence the side along the river.
First of all we will make a relevant figure to represent the perimeter of fencing for 3 sides as shown in the attachment.
Since Ed will not fence the side along the river, fencing is needed for 3 sides and the perimeter of the fencing would be x + x + y = 2x + y.
Now we will equate perimeter with 350 as: 2x + y = 350
y=350-2x
We know that the area of the rectangle is width times length.
A = X•Y
Upon substituting the value of y in area equation, we will get:
A = x•(350-2x)
A(x) = 350x -2x²
Now we will find derivative of area function as:
A'(x) = d(350- 2)/dx
A'(x) = 350-4x
Now we will equate derivative with 0 and solve for x as:
0 = 350-4
4x = 350
x = 350/4 - 87.5
Upon substituting x = 87.5 in equation y = 350-2x, we will get:
y = 350 - 2x
= 350 - 2(87.5)
= 350-175
y = 175
Therefore, the length of 175 metres and width of 87.5 metres will maximise the area.
on substituting x = 87.5 in area function, we will get:
A(87.5) = 350(87.5)-2(87.5)²
A(87.5) = 30625-2(7656.25)
A(87.5) = 30625-15312.5
A(87.5)= 15312.5
Therefore, the largest possible area enclosed would be 15312.5 square metres.
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—--------- CORRECT QUESTION FORMAT IS GIVEN BELOW —----------
(Q).
Farmer Ed has 350 meters of fencing and wants to enclose a rectangle mat plot that borders on a river. If farmer Ed does not fence the side along the river find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed ?
5. Patsy is getting supplies for her daughter's birthday party. She's getting special large balloons (b) that are $3 each and unicorn headbands (h) that are $5 each. Patsy spends $61 for the balloons and headbands. a. Write an equation in standard form to represent the situation. b. There are going to be 8 girls (including her daughter) at the party. Each girl gets one unicorn headband. How many balloons did Patsy buy?
Answer:
Step-by-step explanation:
16
based only on the information given in the diagram which congruence theorems or postulates could be given as reasons why JKL=QRS
The congruence theorems and postulates that could be given as reasons why JKL=QRS are
HL, LL, SSS, SASWhat is the HL Theorem?HL is the hypotenuse-leg theorem. It states that if the hypotenuse and leg of one triangle are congruent to the hypotenuse and corresponding leg of another triangle, the triangles are congruent. We have that both legs of the triangles are congruent as well as the hypotenuse, so the HL theorem applies.
LL is the leg-leg theorem. It states that if both legs of one right triangle are congruent to both legs of the second triangle, the triangles are congruent. We have that both legs are congruent; this is the LL theorem.
SSS is the side-side-side theorem. It states that if all three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. All three sides of both triangles are congruent, so this is the SSS theorem.
SAS is the side-angle-side theorem. It states that if two sides and an included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. We have JL≅QS, ∠L≅∠S and LK≅SR. This is the SAS theorem.
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Determine the correlation for the situation. Choose positive/negative/ or no correlation for each.
The outside temperature in the sumer and the cost of the electric bill ( for air conditioning)
Based on the shipment, what is the probability that a motor is defective?
Write the probability as a percent.
__%
Answer:
3%
Step-by-step explanation:
We know
In a shipment of 700 motors, 21 are defective.
Based on the shipment, what is the probability that a motor is defective?
We take
21 divided by 700, times 100 = 3%
So, the probability is 3%.
Jon put a pie in the oven at 5:15 p.m. He took the pie out of the oven 35 minutes later. At what time did Jon take the pie out of the oven?
Answer: 5:50 PM
Step-by-step explanation:
5:15 PM + 0:35 minutes = 5:50 PM
Which equation, written in the form of y=x+b, represents the table of values?
X y
2 7
3 8
4 9
5 10
A.y=x+2
B.y=x+5
C.y=x+7
D.y=x+9
Answer:
Option B. y=x+5
Step-by-step explanation:
If x=2 and y=7
Inserting the values into y=x+5
7=5+2
7=7
If x=3 and y=8
y=x+5
8=3+5
8=8
If x=4 and y=9
y=x+5
9=4+5
9=9
If x=5 and y=10
y=x+5
10=5+5
10=10
how many acres is a lot that totals 19,602 square feet...?
The area covered by 19, 602 square feet in acres is around 0.45, according to the relation between the two.
As per the known relation between acre and square foot, the two quantities are related through the formula -
1 acre is equal to 43, 560 square feet
Therefore, formula to convert square feet to acre will be -
Amount of area in acres = area covered in square feet/unit equivalent area in square feet
So, rewriting the above mentioned relation.
43, 560 square feet is equal to 1 acre
Thus, 19, 602 square feet will be equal to acres = 19, 602/43, 560
Performing division on Right Hand Side of the equation
The amount of area in acres = 0.45 acres
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Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.
Vertical plane x intersects horizontal plane y. Line R S is horizontal on plane y. Lines A B and C G are vertical and beside each other on plane x. A right angle is indicated between the lines on the y plane and x plane. Lines A B and D G are parallel.
Which statements are true? Select three options.
Based on the given information, the following statements are true:
1. Line R S is perpendicular to lines A B and C G on the y plane.
2. Line R S is parallel to line D F on the x plane.
3. Lines A B and C G are perpendicular to each other on the x plane.
What is Right angle ?
A right angle is an angle that measures exactly 90 degrees, or a quarter of a complete turn. It is often represented by a small square drawn at the vertex of the angle, as shown in the symbol "∟".
Explanation:
Statement 1 is true because line R S lies in plane Y and is perpendicular to the intersection of planes X and Y, which is represented by the right angle between lines A B and C G in the x plane.
Statement 2 is true because line R S is horizontal on plane Y, and line D G is parallel to line A B on the x plane, so line R S is also parallel to line D F on the x plane.
Statement 3 is true because lines A B and C G are beside each other and do not intersect on plane X, so they must be parallel to each other and perpendicular to line R S in the y plane.
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a numerical description of the outcome of an experiment is called ______
Answer: A random variable.
Step-by-step explanation:
a numerical description of the outcome of an experiment is called a random variable.
describe the transformation of f(x)=cos x to g(x)=cos (x+pi/4)
The Correct answer will be B. f(x) is shifted π/4 units to the left.
What is the cosine transformation equation?The general equation for a sine and cosine curve is y = A sin ( x − h ) + k and y = A cos ( x − h ) + k , respectively. Similar to other function transformations, is the horizontal shift (also called a phase shift), and is the vertical shift.Changes to the amplitude, period, and midline are called transformations of the basic sine and cosine graphs. Changing the midline shifts the graph vertically. The graph is stretched or compressed vertically depending on the amplitude. The graph is stretched or compressed horizontally depending on the era.
To determine the transformation;
Dim x=t+π/4
so, f(t+π/4)=cos(t+π/4)=g(t)
t+π/4→t:units to the left.
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What is the conversion of 3 1/3 as a decimal ?
Answer: 3.33 repeating
Step-by-step explanation: .
Sue is n years old. Her sister is 7 years old and her brother is twice Sue's age. All three siblings have a total age of 31.
Write an equation to represent this.
n = 10
Her sister is 7 years old subtract that from 31 gets you 24, then double 7 is 14 so subtract 14 from 24, and that gets you the value of 10 which equals 10
Which expression shows 50+ 30 written as a product of two factors
Hence, 10(5 + 3) is the equation that represents 50 + 30 written as the product of two elements.
what is expression ?It is able to multiply, divide, add, or deduct in mathematics. The follows is how an utterance is put together: Number, expression, and mathematical operator The components of a linear equation include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast terms and phrases. An expression, usually known as an algebraic expression, is there any mathematical statement that contains variables, quantities, and an arithmetic function between them. For instance, the word m in the given equation is distinguished from the words 4m and 5 by the arithmetic symbol +, just like the variable m in the statement 4m + 5.
given
Check each choice.
(A) 5(10 + 7)
= 5(10) + 5(7) (7)
= 50 + 35
(B)5(10+ 3)
= 5(10) + 5(3) (3)
= 50 + 15
(C)10(5+ 2)
= 10(5) + 10(2) (2)
= 50 + 20
(D) 10(5 + 3)
= 10(5) + 10(3) (3)
= 50 + 30
Hence, 10(5 + 3) is the equation that represents 50 + 30 written as the product of two elements.
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yuson thinks the design she made is symmetric across the dashed line she drew. How can she use coordinates to show that her design is symmetric?
She can compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.
How to show if her design is symmetricTo show that a design is symmetric across a line using coordinates, you can use the following steps:
Choose the equation of the line that the design is supposed to be symmetric across. Let's assume that the line is the x-axis and it is represented by the equation y = 0.Identify the coordinates of each point in the design. For example, if a point is located at (2, 4), its x-coordinate is 2 and its y-coordinate is 4.Reflect each point in the design across the line of symmetry by changing the sign of its y-coordinate. For example, if a point is located at (2, 4), its reflection across the x-axis is located at (2, -4).Compare the original design with its reflection across the line of symmetry. If the reflected design is identical to the original design, then the design is symmetric across the line.Here's an example of how to use coordinates to show that a design is symmetric across the x-axis:
Suppose Yuson has a design with three points: A(2, 4), B(4, 6), and C(6, 4), and she drew a dashed line along the x-axis to represent the line of symmetry.
To check if the design is symmetric across the x-axis, she can reflect each point across the x-axis to obtain the following new coordinates: A'(2, -4), B'(4, -6), and C'(6, -4).
She can then compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.
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Solve five-ninths times four equals blank.
thirty-six fifths or seven and one-fifth
twenty-ninths or two and two-ninths
nine-tenths
five thirty-sixths
five-ninths times four equals two and two-ninths.
What is an Algebraic Expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.
For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.
In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.
Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations
To solve five-ninths times four, we multiply 5/9 by 4, which gives:
5/9 x 4 = 20/9
So, the expression "five-ninths times four" is equal to 20/9.
Out of the options given, the answer closest to 20/9 is "two and two-ninths," which can be written as 20/9. Therefore, the answer is:
Therefore, five-ninths times four equals two and two-ninths.
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Is the exact time it takes to evaluate 27 + 72 a discrete random variable, a continuous random variable, or not a random variable?
The time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any uncertainty or probability.
According to given condition:The exact time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any element of chance or uncertainty. The result of the addition is always the same and can be calculated precisely in a finite amount of time.
Random variables, on the other hand, are variables that can take on different values with certain probabilities, and are used to model phenomena that involve uncertainty or randomness. Discrete random variables take on a countable set of values, while continuous random variables take on an uncountably infinite range of values.
In summary, the time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any uncertainty or probability.
In mathematics, a variable is a symbol or letter that represents a value or quantity that can change or vary. Variables are used to express relationships between different quantities and to solve equations.
For example, in the equation y = 2x + 3, x and y are variables. The value of y depends on the value of x, which can vary. We can solve for the value of y for different values of x, and the solution will be a set of ordered pairs (x, y) that form a straight line when plotted on a graph.
Variables can be used to represent a wide range of quantities, including numbers, vectors, functions, and more. They are an essential tool in many branches of mathematics, including algebra, calculus, and statistics.
In addition to mathematics, variables are also used in many other fields, including science, engineering, and computer programming, to represent quantities that can change or be controlled. In these fields, variables are often used to model complex systems or to simulate experiments, and are a fundamental concept in data analysis and computational thinking.
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What is the conversion of 164 cm to feet ?
Answer:5 feet 4.567 in hes
Step-by-step explanation:
The conversion of one unit i.e., 164 centimetres to other feet is equals to the 5.37 feet.
Unit conversion, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units.
How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. So, 164 meters = 164 × 3.28 feet
= 537.92 feet --(1)
But we need to convert 164 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 164 meters = 16400 centimeters --(2). Now from equations (1) and (2),
16400 centimeters = 537.92 feet,
Divide both parts by 100,
=> 164 centimetres = (537.92/100 ) feet
= 5.37 feet
Hence required value is 5.37 feet.
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you can compare two marginal distributions to see if the corresponding two variables are related.truefalse
False. Comparing marginal distributions of two variables only gives information about each variable separately and not their relationship.
Comparing the marginal distributions of two variables only shows the distribution of each variable individually and not their relationship. For example, suppose we have two variables X and Y. If we compare the marginal distributions of X and Y separately, we may see that one variable has a higher frequency of a certain value than the other variable, but this does not necessarily imply that there is a relationship between the two variables. To determine whether there is a relationship, we need to look at the joint distribution of X and Y, which can be displayed in a scatterplot or analyzed using a correlation coefficient.
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At a NASCAR race, the lead car has 7 1/2 laps to go. Suddenly there is a caution flag, so all the racers must hold position while continuing at a reduced speed for 5/6 of a lap. When racing resumes, how many laps does the lead car have to go?
After reduced speed when race resumes the number of laps left are 6 2/3 laps.
What is the definition of speed?
The following is the definition of speed:
The rate with which the position of an item changes .
The ratio of distance travelled to time taken in travelling is known as speed. Speed is a scalar number because it has only one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s= speed in metres per second, d = distance travelled in metres, and t = time in seconds.
Now,
Total laps left for the lead car= 7 1/2
After race is paused or reduced speed for race until 5/6 of a lap
so only 1/6 of a lap had normal racing
so total lap left is 15/2-1+1/6
=45-6+1/6
=40/6
=20/3
=6 2/3
Hence,
when race resumes the number of laps left are 6 2/3 laps.
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Ian walks 4 1/2 miles every day. How many miles does Ian walk in 4 1/2 days.
The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
Ian walks 4 1/2 miles every day
i.e. in 1 day walks = 9/2 mile
so, Ian walk in 4 1/2 days is.
in 9/2 days walks = 9/2* 9/2 miles
=81/4 miles
Hence, The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.
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