Jonas jogged up the hill at an average rate of of a 1/12 mile per minute and then walked down the hill at an average rate of of a 1/16 mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill?
Table
Rate Time Distance
Up the Hill 1/12 x 1/12(x)
Down the Hill 1/16 42-x ?
Answers
Answer - [tex] \frac{1}{16} (42-x)[/tex] (In miles)
EXPLANATION
We know that distance traveled is calculated by multiplying average speed by total time.
According to the table,
Uphill average speed = [tex] \frac{1}{12} [/tex] (in miles per minute)
Uphill travel time = x (in minutes)
Total distance uphill = [tex] \frac{1}{12} x[/tex] (In miles)
The same way,
Downhill average speed = [tex] \frac{1}{16} [/tex] (in miles per minute)
Downhill travel time = 42 - x
Total distance downhill = Speed * Time = [tex] \frac{1}{16} (42-x)[/tex] (In miles)
The formula for distance is d = rt; Where r = rate; t = time
d =? ; r = 1/16; t = 42-x
d = rt
= 1/16 * 42-x
= (42-x) / 16
Related Questions
What is the sum of each pair of binary integers?
a. 10101111 + 11011011
b. 10010111 + 11111111
c. 01110101 + 10101100?
Answers
Example: < means carry, decimal equivalent for checking
1011+1111
1 0 1 1 (8+2+1=11)
+ 1 1 1 1 (8+4+2+1=15)
---<---<----<----<----
1 1 0 1 0 (16+8+2=26)
Proceeding similarly,
a. 10101111+11011011 = 110001010 (394)
b. 10010111+11111111 = 110010110 (406)
c. 01110101+10101100 = 10010001 (289)
Final answer:
The sums for the given pairs of binary integers are: a. 10101111 + 11011011 equals 110001010, b. 10010111 + 11111111 equals 110010110, c. 01110101 + 10101100 equals 100100001.
Explanation:
The sum of each pair of binary integers is calculated using binary addition rules, which are similar to decimal addition, but instead, you only have two digits, 0 and 1, and carry over whenever you add two 1's. Let's perform the calculations for each given pair:
a. 10101111 + 11011011 = 110001010
b. 10010111 + 11111111 = 110010110
c. 01110101 + 10101100 = 100100001
Remember to start adding from the rightmost digit (least significant bit) and move left, carrying over as necessary when the sum of two bits is 2 (binary 10).
cody has $700 in a savings account that pays 4% simple interest how much will he have in one year
Answers
There are c players on the Cougars hockey team. The team scored a total of 36 goals this season. One of the players, Matthew, scored 2 more goals than the average per player.
Answers
[tex]36 \div 2 = 16 \\ 16 - 2 = 14[/tex]
so c=14
At the end of each year, how much money would you earn in interest if you invested $3,500 and earned 4.5% simple interest?
Answers
Ewan makes chess boards from wood. Each board has three different kinds of wood. He has five kinds of wood it is workshop maple, cherry walnut, Poplar and birch how many different types of chess board can he make?
Answers
This is a combination of 5 objects chosen 3 at a time:
[tex]_nC_r=\frac{n!}{r!(n-r)!} \\ \\_5C_3=\frac{5!}{3!2!}=\frac{120}{12}=10[/tex]
Answer:
D.10
Step-by-step explanation:
which least to greatest 125% 6/5 1.22
Answers
Hope I helped!
Let me know if you need anything else!
~ Zoe (Rank:'Genius')
Final answer:
To compare the numbers 125%, 6/5, and 1.22, they were all converted to decimal form which revealed the least to greatest order as 1.22, 6/5, and 125%.
Explanation:
To arrange the numbers 125%, 6/5, and 1.22 from least to greatest, we first need to express all of them in the same format for an accurate comparison. Let's convert each number to a decimal:
125% as a decimal is 1.25 (since 100% is equal to 1, hence 125% is 1.25).6/5 as a decimal is 1.2 (6 divided by 5 equals 1.2).1.22 is already in decimal form.Now, we can easily compare:
1.226/5 (1.2)125% (1.25)The arrangement from least to greatest is 1.22, 6/5, 125%.
find the area of each triangle 10inches 9inches
Answers
1/2 (9)(10)
1/2 (90)
45 in²
15)
1/2 (25)(7)
1/2(175)
87.5 m²
CAN I GET SOME HELP (RIGHT ANSWER)
Answers
1/2 |105 - 23|
1/2 |82|
41
82/2= 41
An easier way :)
A pitcher contains 3 1/2 pints of lemonade. Susan pours 5/8 of a pint into a glass, and Mateo pours 1/2 pint into a glass. How much lemonade is left in the pitcher?
Answers
3 1/2- 1/2 (Mateo)=3
3- 5/8= 2 8/8- 5/8=2 3/8 lemonade left
A First City Bank accepted a $3,500, 5%, 120-day note dated August 8 from a Capstone Company in settlement of a past bill. On October 11, First City discounted the note at Park Bank at 6%.
a. What is the note’s maturity value? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
b. What is the discount period?
c. What is the bank discount? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
d.
What proceeds does First City receive? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
Answers
Notes Maturity Notes
Oct 22 ---> 284 daysAug 8 ---> 220
Grand Total --> 64 days passed
Discount Period
120-64 = 56 days
$3,500 x .05 x 120/360= $58.33$3,500 + $58.33= $3,558.33
Bank Discount
$3,558.33 x .06 x 56/360= $33.21
Proceeds
$3.558.33- $33.21 = $3,525.12
Last year Milwaukee had the total of snow amounting to 92 inches . The normal fall is 52 1/4 inches . How much above normal was the snowfall last year .
Answers
The snowfall in Milwaukee last year was 39.75 inches above the normal amount, calculated by subtracting the normal annual snowfall from last year's total.
Explanation:The student's question is related to subtraction of two amounts to find the difference between the actual snowfall and the normal snowfall in Milwaukee.
To determine how much above normal last year's snowfall was, we subtract the normal snowfall amount from last year's total snowfall.
Last year's snowfall in Milwaukee = 92 inches
Normal annual snowfall = 52 1/4 inches
To find how much above normal the snowfall was, we calculate:
92 inches - 52 1/4 inches = 92 inches - 52.25 inches
This equals 39.75 inches above normal snowfall.
a coin dealer buys
a coin for $850 and sells it for $1190. Find the percent of change.
Answers
.. = (1190/850 -1)*100%
.. = 40%
The coin was sold for a price 40% higher than its purchase price.
Jessica is making a repeating pattern following the rule “triangle square circle what will be the 50th shape in the pattern?
Answers
The 50th shape in the repeating sequence of shapes (triangle, square, circle) is a square. This conclusion is reached by dividing 50 by the 3 shapes in the sequence and noting that the remainder indicates the position in the sequence.
Explanation:The problem presented is one of patterns and sequences, a common topic explored in middle school mathematics. The repeating pattern here consists of three shapes: a triangle, a square, and a circle. This sequence of three shapes continues indefinitely.
To find the 50th shape in the sequence, divide 50 by 3. You'll get 16 remainder 2. This indicates that after 16 complete cycles of the pattern (each consisting of a triangle, square, or circle), the 50th shape is the 2nd shape in the next cycle - the square. Hence the 50th shape according to Jessica's rule is a square.
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The 50th shape in the repeating pattern of Triangle, Square, Circle is a Square.
To find the 50th shape, we need to understand the cyclical nature of this pattern, which repeats every 3 shapes.
Step-by-Step Solution:
The pattern repeats every 3 shapes: Triangle (1), Square (2), Circle (3).To find the position of the 50th shape within this cycle, we calculate the remainder of 50 divided by 3:50 ÷ 3 = 16 R2The remainder is 2, which means the 50th shape aligns with the 2nd shape in the pattern.
Therefore, the 50th shape is a Square.
99 POINTS I WILL MARK BRAINILIEST:
Given: ABCD rhombus, AC:BD = 4:3
Perimeter ABCD = 20 cm
Find: Area of ABCD
Answers
James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 315 64 379
Did not get math class requested 41 80 121
Total 356 144 500
Help James determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.
Answers
Jan is saving for a skateboard. She has saved $30 already, which is 20% of the total price. How much does the skateboard cost
Answers
Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?
Answers
calculate the length of a scarf with sections if each section is 1/2 foot long
Answers
A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 14 inches,and the bicycle wheel mkes 3 full rotations before stopping. How long is the trace of water on the floor?
Answers
one round of the tire = [tex]2 \pi r[/tex]
one round of the tire = [tex]2 \pi (14)[/tex]
one round of the tire = 87.96 inches
three rounds of the tire = 87.96 x 3 = 263.89 inches
Write each of the following expressions as a powers of 2: (4·25)÷(23· 1/16 )
Answers
= (2^2 · 2^5) ÷ (2^3 · 2^-4 )
= (2^7) ÷ (2^-1)
= 2^8
The value obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The given expression is,
(4×2⁵) ÷ (2³ × 1/16 )
Keep the base constant and add the exponents when multiplying similar bases. Maintaining the same base while multiplying the exponents will raise a base with power to another power. When dividing two bases with similar exponents, keep the exponents of the numerator and denominator constant.
= (2² × 2⁵) ÷ (2³ × 2⁻⁴ )
= (2⁷) ÷ (2⁻¹)
= 2⁸
Thus, the values obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.
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A student's cell phone plan has a monthly charge of $40 for 600 minutes of use and a $0.25/minute charge for each additional minute. Last month, the student talked on the phone for 790 minutes. Which of the following is the bill for the month?
Answers
The bill for the month is $87.50, including $40 for 600 minutes and $47.50 for 190 extra minutes.
To calculate the bill for the month, we need to consider the fixed monthly charge and the additional charge for the extra minutes used beyond the 600-minute limit.
Step 1: Calculate the additional minutes used beyond the 600-minute limit:
Total minutes used - Included minutes = Extra minutes
790 minutes - 600 minutes = 190 extra minutes
Step 2: Calculate the additional charge for the extra minutes:
Extra minutes × Additional charge per minute
190 minutes × $0.25/minute = $47.50
Step 3: Add the fixed monthly charge to the additional charge for the extra minutes:
Fixed monthly charge + Additional charge for extra minutes
$40 + $47.50 = $87.50
So, the bill for the month is $87.50.
What similarity statement can you write relating the three triangles in the diagram ?
Answers
triangle RST ~ triangle RUS ~ triangle SUT
The similarity statement that can be written is;
D(RST) ~ D(RUS) ~D(SUT)Discussion:
The triangles as represented are right-angled triangles.
In essence, they all have one of their angles to be 90°.The similarity statement therefore involves the right-angles and is thus; D(RST) ~ D(RUS) ~D(SUT)Read more on similar triangles:
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A rectangle has vertices A ( 1, 2) B (1, 7), C ( 4,7) and D (4, 2). What is the area of the rectangle
Answers
TOAD is a quadrilateral with vertices (9, 10), (18, 10), (14, 5), and (5, 5), respectively. The diagonals intersect at Point S.
Use the given information to:
a) classify the quadrilateral as a parallelogram, square, rectangle or rhombus
b) determine the intersection of the diagonals
c) use the distance formula to prove that the diagonals are bisectors of each other
Answers
B. I believe it'd be around (11.2,7.5)
C. √(10-5)^2+(9-4)^2 = 21, so yes they bisect
⇒Plotting the Quadrilateral on two Dimensional Plane
And finding the diagonal of Quadrilateral bisect each other.
If you will look at the Quadrilateral, none of the interior angle is of 90°, so it can't be Square or Rectangle.
Finding the length of two Adjacent Sides
[tex]TO=\sqrt{(18-9)^2+(10-10)^2}\\\\TO=9 \text{Unit}\\\\OA=\sqrt{(18-14)^2+(10-5)^2}\\\\OA=\sqrt{4^2+5^2}\\\\OA=\sqrt{41}[/tex]
As, the Length of Adjacent sides are not equal,so it can't be a Rhombus.
The Given Quadrilateral ,"TOAD" is a Parallelogram.
⇒The Point of Intersection of both Diagonal can be Obtained by
[tex]=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\\text{Point P}=(\frac{14+9}{2},\frac{5+10}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})\\\\\text{Point P}=(\frac{18+5}{2},\frac{10+5}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})[/tex]
Intersection of both diagonals is same, diagonals bisect each other.
Point of Intersection of Diagonal is Point P
[tex]=(\frac{23}{2},\frac{15}{2})[/tex]
Part C
Distance formula
[tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2)}\\\\TP=\sqrt{(\frac{23}{2}-9)^2+(\frac{15}{2}-10)^2}\\\\TP=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PA=\sqrt{(\frac{23}{2}-14)^2+(\frac{15}{2}-5)^2}\\\\PA=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PD=\sqrt{(\frac{23}{2}-5)^2+(\frac{15}{2}-5)^2}\\\\PD=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PD=\frac{\sqrt{169+25}}{2}\\\\PD=\frac{\sqrt{194}}{2}\\\\PO=\sqrt{(\frac{23}{2}-18)^2+(\frac{15}{2}-10)^2}\\\\PO=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PO=\frac{\sqrt{169+25}}{2}\\\\PO=\frac{\sqrt{194}}{2}[/tex]
→DP=PO
→PT=PA
Length of Segments from point of intersection of two diagonal is same.So, Diagonal are bisector of each other.
For the data in the table, does y vary directly with x? If it does write an equation for the direct variation. x 2 6 10 y 5 15 25
Answers
2 + 4 = 6 5 + 10 = 5
6 + 4 = 10 15 + 10 = 25
The proof is that everytime we increase x by a number (in this case 4), y also increases by some number (in this case 10);
So increasing x by 4, we increase y by 10;
The equation of data that shows direct proportionality is that of a line;
The gradient (represented by m) of the line is going to be how much y changes when we change x;
Using the information above, we can deduce the gradient (m) like so:
m = +10/+4
= 5/2
Now, we use the formula for the equation of the line:
y - y₁ = m(x - x₁)
y - 5 = 5/2(x - 2)
2(y - 5) = 5(x - 2)
2y - 10 = 5x - 10
2y = 5x
y = 5x/2
the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z each represent a different digit from 0 to 9 what is the value of (x)(y)(z)?
Answers
[tex]z+7+5=4 \\ z+12=4[/tex]
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
[tex]z+12=14 \\ z=2[/tex]
For the tens positions of all numbers we have:
[tex]4+2+x+1=1 \\ 7+x=1[/tex]
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
[tex]7+x=11 \\ x=4[/tex]
Now we insert x and z to find out y:
[tex]42+27+45=y14 \\ 114=y14 \\ y=1[/tex]
Now we need to find out the product of these three numbers:
[tex]x*y*z=4*1*2=8[/tex]
-1 + 5 * 6 is less than 29
Answers
Which represents the solution set of 5(x+5)<85?
A.) x<12
B.) x>12
C.) x<16
D.) x>16
Answers
YOUR answer is x<12
__________________________________________________
Given:
__________________________________________________
" 5(x + 5) < 85 " ; Simplify/ solve for "x" ;
__________________________________________________
Method 1)
__________________________________________________
Note the "distributive property of multiplication" :
__________________________________________________
a(b + c) = ab + ac ;
a(b – c) = ab – ac .
__________________________________________________
So, take the "left-hand side" of the inequality; and expand:
__________________________________________________
→ 5(x + 5) = (5*x) + (5*5) = 5x + 25 ;
Now, rewrite the inequality:
→ 5x + 25 < 85 ;
Subtract "25" from each side of the inequality ;
→ 5x + 25 – 25 < 85 – 25 ;
to get:
_______________________________________
→ 5x < 60 ;
Divide each side of the inequality by "5" ;
→ 5x / 5 < 60 / 5 ;
→ x < 12 ; which is: Answer choice: [A]: " x < 12 " .
_______________________________________
Method 2)
_______________________________________
Given:
_______________________________________
" 5(x + 5) < 85 " ; Simplify/ solve for "x" ;
_______________________________________
Divide EACH SIDE of the equation by "5" ;
[5(x + 5) ] / 5 < 85 / 5 ;
to get:
→ x + 5 < 17 ;
Subtract "5" from EACH SIDE of the inequality:
→ x + 5 – 5 < 17 – 5 ;
to get:
→ x < 12 ; which is: Answer choice: [A]: " x < 12 " .
_________________________________________________
Three cards are drawn from a deck without replacement. what is the probability that all three cards are clubs?
Answers
What is the value of m in the equation 1/2m-3/4m=16, when n = 8
Answers
If this is (1/2)m -(3/4)n = 16:
Then (1/2)m - (3/4)(8) = 16
(1/2)m = 22
m = 44
But if this is (1/2)n -(3/4)m = 16:
Then (1/2)(8) - (3/4)m = 16
4 - (3/4)m = 16
(3/4)m = -12
m = -16