Tom said that the difference in length between the longest trail and the shortest trail is 2 5/8 miles. Does Tom's answer make sense? What mistake did he make? Answer in at least two complete sentences. Use the sentences below to get started: "Tom's answer (makes sense/does not make sense). His mistake was ________."
Answers
Solution:
Given:
From the trail lengths given,
[tex]\begin{gathered} The\text{ longest trail is }1\frac{7}{8} \\ The\text{ shortest trail is }\frac{3}{4} \end{gathered}[/tex]The difference in length between the longest trail and the shortest trail:
[tex]\begin{gathered} 1\frac{7}{8}-\frac{3}{4}=\frac{15}{8}-\frac{3}{4} \\ =\frac{15-6}{8} \\ =\frac{9}{8} \\ =1\frac{1}{8} \end{gathered}[/tex]
The sum of the longest trail and the shortest trail.
[tex]\begin{gathered} 1\frac{7}{8}+\frac{3}{4}=\frac{15}{8}+\frac{3}{4} \\ =\frac{15+6}{8} \\ =\frac{21}{8} \\ =2\frac{5}{8} \end{gathered}[/tex]From the calculations above, the conclusion can be reached that:
Tom's answer does not make sense. His mistake was he did the sum of the longest trail and the shortest trail.
Related Questions
We have a deck of 10 cards numbered from 1-10. Some are grey and some are white. The cards numbered are 1,2,3,5,6,8 and 9 are grey. The cards numbered 4,7, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.
Answers
Given:
The cards numbered are, 1,2,3,5,6,8, and 9 are grey.
The cards numbered 4,7 and 10 are white.
The total number of cards =10.
Let X be the event that the drawn card is grey.
P(X) be the probability of X.
Required:
We need to find P(X) and P(not X).
Explanation:
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 1,2,3,5,6,8, and 9 for event X.
The favourable outcomes = 1,2,3,5,6,8, and 9
[tex]n(X)=7[/tex]Since X be the event that the drawn card is grey.
The probability of X is
[tex]P(X)=\frac{n(X)}{n(S)}=\frac{7}{10}[/tex]Let not X be the event that the drawn card is not grey,
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 4,7, and 10 for event not X.
The favourable outcomes = 4,7, and 10
[tex]n(not\text{ }X)=3[/tex]Since not X be the event that the drawn card is whic is not grey.
The probability of not X is
[tex]P(not\text{ }X)=\frac{n(not\text{ }X)}{n(S)}=\frac{3}{10}[/tex]Consider the equation.
[tex]1-P(not\text{ X\rparen}[/tex][tex]Substitute\text{ }P(not\text{ }X)=\frac{3}{10}\text{ in the equation.}[/tex][tex]1-P(not\text{ X\rparen=1-}\frac{3}{10}[/tex][tex]1-P(not\text{ X\rparen=1}\times\frac{10}{10}\text{-}\frac{3}{10}=\frac{10-3}{10}=\frac{7}{10}[/tex][tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]Final answer:
[tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]
A play court on the school playground is shaped like a square joined by a semicircle. The perimeteraround the entire play court is 182.8 ft., and 62.8 ft. of the total perimeter comes from the semicircle.aWhat is the radius of the semicircle? Use 3.14 for atb.The school wants to cover the play court with sports court flooring. Using 3.14 for, how manysquare feet of flooring does the school need to purchase to cover the play court?
Answers
The total perimeter of the court is 182.8 ft, of this, 62.8ft represents the perimeter of the semicircle.
a)
The perimeter of the semicircle is calculated as the circumference of half the circle:
[tex]P=r(\pi+2)[/tex]Now write it for r
[tex]\begin{gathered} \frac{P}{r}=\pi \\ r=\frac{P}{\pi} \end{gathered}[/tex]Knowing that P=62.8 and for pi we have to use 3.14
[tex]\begin{gathered} r=\frac{62.8}{3.14} \\ r=20ft \end{gathered}[/tex]The radius of the semicircle is r=20 ft
b.
To solve this exercise you have to calculate the area of the whole figure.
The figure can be decomposed in a rectangle and a semicircle, calculate the area of both figures and add them to have the total area of the ground.
Semicircle
The area of the semicircle (SC) can be calculated as
[tex]A_{SC}=\frac{\pi r^2}{2}[/tex]We already know that our semicircla has a radius of 10ft so its area is:
[tex]A_{SC}=\frac{3.14\cdot20^2}{2}=628ft^2[/tex]Rectangle
To calculate the area of the rectangle (R) you have to calculate its lenght first.
We know that the total perimeter of the court is 182.8ft, from this 62.8ft corresponds to the semicircle, and the rest corresponds to the rectangle, so that:
[tex]\begin{gathered} P_T=P_R+P_{SC} \\ P_R=P_T-P_{SC} \\ P_R=182.8-62.8=120ft \end{gathered}[/tex]The perimeter of the rectangle can be calculated as
[tex]P_R=2w+2l[/tex]The width of the rectangle has the same length as the diameter of the circle.
So it is
[tex]w=2r=2\cdot20=40ft[/tex]Now we can calculate the length of the rectangle
[tex]\begin{gathered} P_R=2w+2l \\ P_R-2w=2l \\ l=\frac{P_R-2w}{2} \end{gathered}[/tex]For P=120ft and w=40ft
[tex]\begin{gathered} l=\frac{120-2\cdot40}{2} \\ l=20ft \end{gathered}[/tex]Now calculate the area of the rectangle
[tex]\begin{gathered} A_R=w\cdot l \\ A_R=40\cdot20 \\ A_R=800ft^2 \end{gathered}[/tex]Finally add the areas to determine the total area of the court
[tex]\begin{gathered} A_T=A_{SC}+A_R=628ft^2+800ft^2 \\ A_T=1428ft^2 \end{gathered}[/tex]given the residual plot below, which of the following statements is correct?
Answers
Let me explain this question with the following picture:
We can recognize a linear structure when all the points have a pattern that seems like a straight line as you can see above for example.
In the graph of your question, we can see that the points don't have a definited pattern and that's clearly not seemed like a straight line.
Therefore, the answer is option B:
There is not a pattern, so the data is not linear.
The schedule for summer classes is available and Calculus and Introduction to Psychology are scheduled at the same time, so it is impossible for a student to schedule for both courses. The probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. What is the probability a student registers for Calculus or psychology?
Answers
Explanation
The given is that the probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. Since it impossible for a student to schedule for both courses, we will have
[tex]\begin{gathered} Pr(Psychology\text{ or calculus\rparen=Pr\lparen P\rparen+Pr\lparen C\rparen-Pr\lparen P}\cap C) \\ =0.05+0.62-0 \\ =0.67 \end{gathered}[/tex]Answer: 0.67
Line segments, AB,BC,CD,DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 BC: y = -3x + 11
Answers
The equations of the line segments are,
[tex]\begin{gathered} AB\colon y=\frac{1}{3}x+1 \\ BC\colon y=-3x+11 \end{gathered}[/tex]Calculate the equations of CD and AD.
The equation of line Cd is,
[tex]\begin{gathered} (y-(-3))=\frac{-1+3}{4+2}(x+2) \\ y+3=\frac{1}{3}(x+2) \\ 3y=x-7 \end{gathered}[/tex]The equation of the line AD is,
[tex]\begin{gathered} y-0=\frac{-3-0}{-2+3}(x+3) \\ y=-3x-9 \end{gathered}[/tex]1)If two lines are parallel slope will be equal and perpendicular product of slope will be -1.
From the equation, the slope of AB is 1/3
From the equation, the slope of Cd is 1/3.
So, they are parallel.
2)The slope of AB is 1/3.
The slope of BC is -3.
The product of two slopes is -1. Therefore, AB is perpendicular to BC.
3) The slope of AB is 1/3 and slope of AD is -3. Since, the product is -1, they are perpendicular.
Another pair of line segments that are perpendicular to each other is AB and AD.
Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10
Answers
Given:
[tex]\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}[/tex]Now, let's find (-1/2)A.
Each term of the matrix A is multiplied by -1/2.
[tex]\begin{gathered} \frac{-1}{2}A=\frac{-1}{2}\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-12}{2}} & {\frac{-4}{2}} & {} \\ {\frac{4}{2}} & {\frac{10}{2}} & {} \\ {\frac{6}{2}} & {-\frac{12}{2}} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}[/tex]Now let's find (-1/2)A+B.
To find (-1/2)A+B, the corresponding terms of the matrices are added together.
[tex]\begin{gathered} \frac{-1}{2}A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}[/tex]Therefore,
[tex]undefined[/tex]Find functions f and g such that (f o g)(x) = [tex] \sqrt{2x} + 19[/tex]
Answers
We have the expression:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]So:
[tex]g(x)=2x[/tex][tex]f(x)=\sqrt[]{x}+19[/tex]***
Since we want to get the function g composed in the function f, and the result of this is:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]When we replace g in f, we have to get as answer the previous expression. And by looking at it the only place where we will be able to replace values is where the variable x is located. The function f will have the "skeleton" or shape of the overall function and g will be injected in it.
From this, we can have that f might be x + 19 and g might be sqrt(2x), but the only options that are given such that when we replace g in x of f, are f = sqrt(x) + 19 and g = 2x.
Solye for x.7(x - 3) + 3(4 - x) = -8
Answers
Explanation
Step 1
apply the distributive property to eliminate the parenthesis
[tex]\begin{gathered} 7(x-3)+3(4-x)=-8 \\ 7x-21+12-3x=-8 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 7x-21+12-3x=-8 \\ 4x-9=-8 \end{gathered}[/tex]Step 3
add 9 in both sides
[tex]\begin{gathered} 4x-9=-8 \\ 4x-9+9=-8+9 \\ 4x=1 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=1 \\ \frac{4x}{4}=\frac{1}{4} \\ x=\frac{1}{4} \end{gathered}[/tex]Simplify the expression (6^2)^46^?
Answers
The given expression is
[tex](6^2)^4[/tex]We would apply the rule of indices or exponent which is expressed as
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]What does "equidistant” mean in relation to parallel lines?O The two lines lie in the same plane.The two lines have the same distance between them.The two lines go infinitely.The two lines have an infinite number of points.
Answers
we have that
parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
therefore
the answer is
The two lines have the same distance between them.Simplify the expression leave expression in exact form with coefficient a and b so we have a✔️b.
Answers
coefficient of a = 2x
Explanation:[tex]\text{The expression: 2}\sqrt[]{x^2y}[/tex]Simplifying:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = x} \\ 2\sqrt[]{x^2\times y}\text{ = 2x}\sqrt[]{y} \end{gathered}[/tex]Since we are told the coefficient of a can be the product of a number and variable:
[tex]\begin{gathered} 2x\sqrt[]{y}\text{ is in the form a}\sqrt[]{b} \\ a\text{ = 2x},\text{ b = y} \\ 2\text{ = number, x = variable} \\ 2x\text{ = product of number and variable} \\ \text{coefficient of }a\text{ = 2x} \end{gathered}[/tex]Necesito saber si los ejercicios están correctos o no y la explicación
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None of the operations with radicals are correct, as two radical terms can only be added or subtracted if they have the same radical and the same exponent.
Addition and subtraction with radicalsTerms with radicals can only be added or subtracted if they have the same radical and same exponent, for example:
[tex]3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}[/tex]
In the above example, they have the same radical, of 2, and same exponent, also of 2.
The first example is given by:
[tex]7\sqrt{3} + 4\sqrt{2} = 11\sqrt{5}[/tex]
The mistake is that the two terms cannot be added, as they have different radicals, of 3 and 2.
The second example is given as follows:
[tex]3\sqrt[3]{k} - 6\sqrt{k} = -3\sqrt{k}[/tex]
The terms have the same radical, of k, but they have different exponents, of 3 and 2, hence they cannot be subtracted.
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Find the solution of the system by graphing.-x - 4y=4y=1/4x-3Part B: The solution to the system,as an ordered pair,is
Answers
Solution
-x -4y = 4
y= 1/4 x -3
Replacing the second equation in the first one we got:
-x -4(1/4x -3) =4
-x -x +12= 4
-2x = 4-12
-2x = -8
x= 4
And the value of y would be:
y= 1/4* 4 -3= 1 -3= - 2
And the solution would be ( 4,-2)
-Jun 18 of
Find the domain and the range of the given relation.
{(6,8), (-3,4), (-1,-6), (-6, -1)}
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Range: [-6, -1, 4, 8]
Which expression is equivalent to a + 0.2c?O 1.23O 0.22O 0.2x01.023
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If we have the expression:
This is the same to write:
So the answer is 1.2x.
Nikolas bought a Falcon's ticket for $80. The sales tax on the ticket is 7%. How much was the tax?
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ok
100% ---------------------------- $80
7% ---------------------------- x
x = (80 x 7)/100
x = 560/100
x = 5.6
The tax was of $5.6
Solve for x:
A
+79
X
Answers
Answer: -11
Step-by-step explanation: 66+46=112
180-112=68
79+?=68
79+-11=68
The circumference of a circle is 18pi meters. What is the radius?Give the exact answer in simplest form. ____ meters. (pi, fraction)
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Given:
The circumference of a circle, C=18π m.
The expression for the circumference of a circle is given by,
[tex]C=2\pi r[/tex]Put the value of C in the above equation to find the radius.
[tex]\begin{gathered} 18\pi=2\pi r \\ r=\frac{18\pi}{2\pi} \\ r=9\text{ m} \end{gathered}[/tex]Therefore, the radius of the circle is 9 m.
Find the length of the rectangle pictured above, if the perimeter is 82 units.
Answers
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the information given,
width = 16
Perimeter = 82
Thus, we have
82 = 2(length + 16)
By dividing both sides of the equation by 2, we have
82/2 = 2(length + 16)/2
2 cancels out on the right side of the equation. We have
41 = length + 16
length = 41 - 16
length = 25
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?
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Given that initial time for jogging is,
[tex]a_{_1}=14[/tex]After each week the time is increased by
[tex]d=7[/tex]This gives an arithmetic sequence.
To find n such that,
[tex]a_n=70[/tex]Therefore,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]So,
[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]Therefore, 9 weeks before you are up to jogging 70 minutes.
a) Consider an arithmetic series 4+2+0+(-2)+.....i) What is the first term? And find the common difference d.ii) Find the sum of the first 10 terms S(10).b) Solve [tex] {2}^{x - 3} = 7[/tex]
Answers
Answer:
Explanation:
Here, we want to work with an arithmetic series
a) First term
The first term (a) of the arithmetic is the first number on the left
From the question, we can see that this is 4
Hence, 4 is the first term
To find the common difference, we have this as the difference between twwo subsequent terms, going from left to right
We have this as:
[tex]2-4\text{ = 0-2 = -2-0 = -2}[/tex]The common difference d is -2
ii) We want to calculate the sum of the first 10 terms
The formula for this is:
[tex]S(n)\text{ = }\frac{n}{2}(2a\text{ + (n-1)d)}[/tex]Where S(n) is the sum of n terms
n is the number of terms which is 10
a is the first term of the series which is 4
d is the common difference which is -2
Substituting these values, we have it that:
[tex]\begin{gathered} S(10)\text{ = }\frac{10}{2}(2(4)\text{ + (10-1)-2)} \\ \\ S(10)\text{ = 5(8+ (9)(-2))} \\ S(10)\text{ = 5(8-18)} \\ S(10)\text{ = 5(-10)} \\ S(10)\text{ = -50} \end{gathered}[/tex]Austin walks 3.5km every day. How far does he walk in 7 days?Write your answer in meters.
Answers
Answer:
24,500 meters
Step-by-step explanation:
20) Determine if the number is rational (R) or irrational (I)
Answers
EXPLANATION:
Given;
Consider the number below;
[tex]97.33997[/tex]Required;
We are required to determine if the number is rational or irrational.
Solution;
A number can be split into the whole and the decimal. The decimal part of it can be a recurring decimal or terminating decimal. A recurring decimal has its decimal digits continuing into infinity, whereas a terminating decimal has a specified number of decimal digits.
The decimal digits for this number can be expressed in fraction as;
[tex]Fraction=\frac{33997}{100000}[/tex]In other words, the number can also be expressed as;
[tex]97\frac{33997}{100000}[/tex]Therefore,
ANSWER: This is a RATIONAL number
a store donated 2 and 1/4 cases of cranes to a daycare center each case holds 24 boxes of crayons each box holds 8 crayons how many crayons did the center receive
Answers
Answer:
The center recieved 432 crayons
Explanation:
Given the following information:
There are 2 and 1/4 cases
Each case holds 24 boxes of crayons
Each box holds 8 crayons.
The number of crayons the center receive is:
8 * 24 * (2 + 1/4)
= 8 * 24 * (8/4 + 1/4)
= 192 * (9/4)
= 1728/4
= 432
f(x)=1-x when f(x)=2
Answers
By solving the equation, we know that f(x) = 1 - x is - 1 when f(x) = 2.
What are equations?In mathematical equations, the equals sign is used to show that two expressions are equal.An equation is a mathematical statement that uses the word "equal to" in between two expressions of the same value.As an illustration, 3x + 5 equals 15.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary types of linear equations are slope-intercept, standard, and point-slope equations.So, f(x) = 1 - x when f(x)= 2:
Solve for f(x) as follows:
f(x) = 1 - xf(x) = 1 - 2f(x) = - 1Therefore, by solving the equation, we know that f(x) = 1 - x is - 1 when f(x) = 2.
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The perimeter of a rectangular room is 80 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Write the equation that could model this situation.
Answers
Answer:
2x+2y=80
Step-by-step explanation:
a rectangles perimeter has the formula of width+width+length+length
we can combine like terms so we get 2x+2y and according to the problem this rectangle has the perimeter of 80
Interpreting the whale population on the graph. I think (A).
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The y-intercept is the value in the vertical axis (y-value) when the value on the horizontal axis is zero (x = 0).
Looking at the horizontal axis, the value of x indicates the generation since 2007.
That means x = 0 indicates the generation in year 2007.
The value of y for x = 0 is 240, so the population in year 2007 is 240.
Correct option: A
The endpoints CD are given. Find the coordinates of the midpoint m. 24. C (-4, 7) and D(0,-3)
Answers
To find the coordinates of the midpoint
We will use the formula;
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2})[/tex]x₁ = -4 y₁=7 x₂ = 0 y₂=-3
substituting into the formula
Xm = x₁+x₂ /2
=-4+0 /2
=-2
Ym= y₁+ y₂ /2
=7-3 /2
=4/2
=2
The coordinates of the midpoint m are (-2, 2)
Identify the coffecient of x in the expression below.-5x-4y^2
Answers
A coeffecient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression,
So in the given expression, the value "-5" is placed before x and hence is the coffecient of x .
Answer:
Step-by-step explanation:
3
Let be two sets E and F such that:E = {x € R: -4 ≤ x ≤ 4}F = {x € R: | x | = x}What is the Cartesian product of the complement of E × F =?
Answers
Given:
[tex]\begin{gathered} E=\mleft\lbrace x\in\mathfrak{\Re }\colon-4\leq x\leq4\mright\rbrace \\ F=\mleft\lbrace x\in\mathfrak{\Re }\colon\lvert x\rvert=x\mright\rbrace \end{gathered}[/tex]If |x|=x that mean here x is grater then zero.
E is move -4 to 4 and F is grater then zero that mean multiplication of the function is obtaine all real value:
[tex]E\times F=\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace[/tex]