Final answer:
Mridul will take 14.4 minutes to jog around a rectangular park for a total of 6 rounds, considering the total jogging distance of 2.16 kilometers at a pace of 9 kilometers per hour.
Explanation:
To calculate the time Mridul will take to jog around a rectangular park for 6 rounds, we need to compute the total distance he will cover and then use his speed to find the time. The perimeter of the rectangle is the sum of all its sides. Since the park is 100m by 80m, the perimeter will be (2 × 100m) + (2 × 80m), which equals 360 meters. For 6 rounds, the total distance will be 6 × 360 meters = 2160 meters or 2.16 kilometers.
Next, we use the formula for time:
Time = Distance / Speed
Given Mridul's jogging rate is 9 kilometers per hour, we can convert this speed into meters per second to match the distance units by multiplying by 1000 and dividing by 3600 (the number of seconds in an hour), which gives us 2.5 meters per second. Finally, to find the time taken:
Time = 2160 meters / (2.5 meters/second)
This calculation results in 864 seconds, which when converted to minutes is 14.4 minutes. Therefore, Mridul will take 14.4 minutes to jog 6 rounds around the park.
What is the value of y in terms of x in the equation 3x+y/2x=15/2 ?
Answer:
y=15x-6x^2
Step-by-step explanation:
3x+y/2x=15/2
y/2x=15/2-3x
y=2x(15/2-3x)
y=15x-6x^2
Kris runs a 5 K (kilometer) race for charity. It takes her 1 hour. What is Kris' average speed?
Answer: 5 Kilometers Per Hour
Answer:
1/12 km per minute
Step-by-step explanation:
1 hour=60 minutes
5/60=1/12
Greta and Marge are collecting money for a local charity by taking donations outside of busy
local businesses. Hoping to collect the most money today, Greta gets to her collection spot and
begins collections at 8am. Marge wanted to sleep in so she didn't start collections at her spot
until 11am, by which time Greta had already collected $45.00. If Greta continues to collect
money at a rate of $15 per hour, Marge collects money at a rate of $20 per hour and they each
take a 1 hour break at 2pm, at what time will Greta and Marge have collected the same amount
of money?
Answer:
At 9pm Greta and Marge have collected the same amount of money.
Step-by-step explanation:
Consider the provided information.
Let x represents the number of hours Greta and Marge are both collecting.
It is given that Greta had already collected $45.00 till 11 am.
Greta = 45 + 15x
Marge collects money at a rate of $20 per hour.
Marge = 20x
Greta and Marge have collected the same amount of money.
Thus,
45 + 15x = 20x
45 = 5x
9 = x
Hence, once Marge starts collecting, it would take 9 hours to collect same amount of money.
9 hours after 11am is 8pm. It is given that there is a break time of 1 hour
Hence, at 9pm Greta and Marge have collected the same amount of money.
Help. Explain good for brainliest
The measure of m∠J=90°, m∠G=55° and m∠H=35°
Step-by-step explanation:
Inscribed angles subtended by a diameter are right angles. Hence angle GJH =90°
The diameter GH and chord GJ intercepts an arc with a measure of 70°.The measure of an arc of a circle is equal to the measure of the central angle that intercepts the arc. Hence angle GOJ=70°. Radius of circle GO=OJ, which means triangle GOJ is an isosceles triangle thus ∠OJG=∠OGJ =(180° -70°) /2 = 55°. m∠G=55°
m∠H = (180°-(90°+55°) ) = 180° - 145° =35°
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Keywords : measures, angles, diameter, chord, intercepts, arc
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Which of the following are solutions to the following equation?
2x^2–98=0
Check all that apply.
Answer:
x=-7
x=7
Step-by-step explanation:
we have
[tex]2x^{2}-98=0[/tex]
Solve for x
Adds 98 both sides
[tex]2x^{2}-98+98=0+98[/tex]
[tex]2x^{2}=98[/tex]
Divide by 2 both sides
[tex]2x^{2}/2=98/2[/tex]
[tex]x^{2}=49[/tex]
take square root both sides
[tex]x=\pm7[/tex]
therefore
The solutions are
x=-7
x=7
Simplify the radicals.
Someone please help because my book doesnt explain how to do this.
Answer: [tex]6y^2i\sqrt{6}[/tex]
Step-by-step explanation:
For this exercise it is important to remember the following property:
[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]
Then, given the expression:
[tex]\sqrt{-216y^4}[/tex]
You can follow these steps in order to simplify it:
1. Descompose 216 into its prime factors:
[tex]216=2*2*2*3*3*3[/tex]
2. The Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then:
[tex]216=2^2*2*3^2*3[/tex]
3. Now you can substitute:
[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]
4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:
[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]
14 x 1 = 14 exemplifies which property
Answer:
multiplicative identity
Step-by-step explanation:
Anything that is divisible by 0 or 1 is called multiplicative identity.
3. Twenty-four students brought their permission slips to attend the class field
trip to the local art museum. If this represented eight tenths of the class, how
many students are in the class? Use a bar diagram to solve arithmetically. Then
use an equation to solve algebraically.
Answer:
x=30
Step-by-step explanation:
ratio: 8:10 as 24:x
8/10=24/x
10x * 8/10= 10x * 24/x
x * 8 = 10 * 24
8x = 240
8x/8 = 240/8
8x/8 = 30
x = 30
Monica brought some donuts for $0.50 Each and a box of coffee for $5.
Write and solve an inequality to find the possible number of donuts,d, she brought if she spent less than $15. Then graph the solution set
Answer:
[tex]d < 20\ donuts[/tex]
The graph of the solution set in the attached figure
Step-by-step explanation:
Let
d ----> the possible number of donuts Monica brought
we know that
The number of donuts d multiplied by $0.50 plus the cost of a box of coffee for $5 must be less than $15
so
The inequality that represent this situation is
[tex]0.50d+5 < 15[/tex]
Solve for d
subtract 5 both sides
[tex]0.50d < 15-5[/tex]
[tex]0.50d < 10[/tex]
Divide by 0.50 both sides
[tex]d < 10/0.50[/tex]
[tex]d < 20\ donuts[/tex]
The solution is all whole numbers greater than zero and less than 20 ( I say greater than zero because the problem states that Monica brought some donuts)
The solution set is the interval {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}
3.
of
The completely factored form
2d4 - 6d - 18d2 - 54d is
Answer:
2d(d³-9d-30)
Step-by-step explanation:
2d⁴ - 6d - 18d² - 54d
= 2d⁴- 18d²-60d
=2d(d³-9d-30)
Any help would be appreciated. Thank you!
Answer:
Area [tex]=62.5\sqrt{6}[/tex] square units
[tex]AB=5\sqrt{15}[/tex] units
[tex]BC=5\sqrt{10}[/tex] units
Step-by-step explanation:
In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.
So,
[tex]BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units[/tex]
a. The area of the triangle ABC is
[tex]A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.[/tex]
b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so
[tex]AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units[/tex]
help me again?- please.
Answer:
Step-by-step explanation:
y - 6 = b
y = b + 6
Answer:
6+b=y
Step-by-step explanation:
If you plug in real values (y=8 and b=2) you can see that at first, you had y-6=b. Basically, 8-6=2. In order to find eight, you would need to reverse the equation to 6+2. The answer is 6+b=y.
Which of the following tables represents a function?
Answer:
B seems right
Step-by-step explanation:
An engineering student answered 81 questons correctly on a 90 question test. What percent of the question did she answer correctly?
Answer:
90% of the questions she answered correctly
Step-by-step explanation:
%age = 81/90 * 100= 90 % correctness
PLEASE HELP number 5
Answer: Option 3, and 4
Is this true or false 4/3 = 8/9
Write the point-slope form of an equation of the line through the points at (-9,9) and (6,-6)
Answer:
y = -x
Step-by-step explanation:
Explained in picture:
SORRY IF INCORRECT!!!!!
Which dimensions cannot create a triangle?
three angles measuring 109, 25º, and 1450
three sides measuring 9 m, 15 m, and 9 m
• three angles measuring 40°, 70°, and 650
o three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
three angles measuring 109º, 25º, and 145º cannot create a triangle
three angles measuring 40º, 70º, and 65º cannot create a triangle
Step-by-step explanation:
Verify each dimensions
Part 1) three angles measuring 109º, 25º, and 145º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]109^o+25^o+145^o=279^o[/tex]
[tex]279^o> 180^o[/tex]
therefore
three angles measuring 109º, 25º, and 145º cannot create a triangle
Part 2) three sides measuring 9 m, 15 m, and 9 m
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 9+15 > 9 ---> is ok
2) 9+9 > 15 ---> is ok
therefore
three sides measuring 9 m, 15 m, and 9 m can create a triangle
Part 3) three angles measuring 40º, 70º, and 65º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]40^o+70^o+65^o=175^o[/tex]
[tex]175^o< 180^o[/tex]
therefore
three angles measuring 40º, 70º, and 65º cannot create a triangle
Part 4) three sides measuring 6 cm, 8 cm, and 10 cm
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is ok
2) 8+10 > 6 ---> is ok
3) 6+10 > 8 ---> is ok
therefore
three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle
Answer:
its c i promise
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 22 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
10 small boxes and 11 large boxes were shipped.
Step-by-step explanation:
Given,
Total boxes shipped = 21
Total volume of shipped boxes = 342 cubic feet
Volume of each small box = 10 cubic feet
Volume of each large box = 22 cubic feet
Let,
Number of small boxes = x
Number of large boxes = y
According to given statement;
x+y=21 Eqn 1
10x+22y=342 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132[/tex]
Dividing both sides by 12
[tex]\frac{12y}{12}=\frac{132}{12}\\y=11[/tex]
Putting y=11 in Eqn 1
[tex]x+11=21\\x=21-11\\x=10[/tex]
10 small boxes and 11 large boxes were shipped.
Keywords: linear equation, subtraction
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Find the slope of 3,6 and 6,9
Hey there!
To find the slope of the two points that you were given, use the slope formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
y2 is the y value of the second point pair, y1 is the y value of the first point pair, x2 is the x value of the second point pair, and x1 is the x value of the first point pair.
Now, plug in your values:
y2= 9
y1= 6
x2= 6
x1= 3
[tex]\frac{9-6}{6-3}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Therefore, the slope of the two points is 1.
There are (53)2 ⋅ 50 hens in a bird enclosure. What is the total number of hens in the enclosure? (1 point)
0
55
56
530
Answer:
The correct answer is C. 5⁶
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Number of hens in a bird enclosure = (5³)² * 5⁰
2. What is the total number of hens in the enclosure?
Let's recall a couple of properties of the exponents:
1. When you raise any number to a zero power you'll always get 1, with the exception of zero itself.
x⁰ = 1, x ≠ 0
2. The power of a power property says that to calculate a power of a power you just have to multiply the exponents, this way:
(x⁴)⁵ = x ⁴°⁵ = x²⁰
Now, applying those two properties, we have:
(5³)² * 5⁰ = 5³°² * 1 = 5⁶
The correct answer is C. 5⁶
Answer:
c
Step-by-step explanation:
AN EASY PERCENTAGE PROBLEM. In a semiconductor companies quality control test machine found that 22 out of a sample of us 600 computer chips were defective how many of the three 36,000 computer chips the company makes each year would you expect to be defective???
Final answer:
To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion: 22 defective chips / 600 chips = x defective chips / 36,000 chips. Dividing both sides by 600, we find that x = 1,320. Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.
Explanation:
To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion:
22 defective chips / 600 chips = x defective chips / 36,000 chips
Cross-multiplying, we get 600x = 22 * 36,000
Dividing both sides by 600, we find that x = 22 * 36,000 / 600 = 1,320
Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.
Santa’s elves are selling are selling cookies for a sale. on the first day they sold 120 peppermint cookies and 30 cinnamon sugar cookies for total of $81. the next day they made $60 by selling 70 peppermint cookies and 60 cinnamon sugar cookies. find total cost of each cookie
The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30
Step-by-step explanation:
Let,
Cost of 1 peppermint cookie = x
Cost of 1 cinnamon cookie = y
According to given statement;
120x+30y=81 Eqn 1
70x+60y=60 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(120x+30y=81)\\240x+60y=162\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](240x+60y)-(70x+60y)=162-60\\240x+60y-70x-60y=102\\170x=102\\[/tex]
Dividing both sides by 170
[tex]\frac{170x}{170}=\frac{102}{170}\\x=0.60[/tex]
Putting x=0.60 in Eqn 2
[tex]70(0.60)+60y=60\\42+60y=60\\60y=60-42\\60y=18[/tex]
Dividing both sides by 60
[tex]\frac{60y}{60}=\frac{18}{60}\\y=0.30[/tex]
The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30
Keywords: linear equation, elimination method
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d/dx(sin x/2+cos x) = (a + b cos x)/(2+cos x)^2 find a and b.
Answer:
a = 1 and b = 2
Step-by-step explanation:
Using the Quotient Rule>
d/dx[(sin x)/(2+cos x) ]
= [(2 + cos x) * cosx - sin x * - sin x)] / (2 + cos x)^2
= 2cos x + cos^2x + sin ^2 x) / (2 + cos x)^2
But cos^2x + sin^2x = 1 so we have:
(1 + 2 cos x) / (2 + cos x)^2
- so a = 1 and b = 2.
destiny sells pencil cases for $5 each and mechanical pencils for $2 each at the school supply store. she sells p pencil cases and (p+4) mechanical pencils. which expression represents destiny's total sales
Answer:
Step-by-step explanation:
5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.
-7/8 is less than or greater than -3/4?
Answer:
-3/4
Step-by-step explanation:
The least common denominator is 8.
So you make -3/4 into -6/8 by multiplying 2 in the numerator and denominator.
Now just compare them -6/8 compared to -7/8
-6/8 is bigger since it is closer to 0 (since we are dealing with negative numbers.)
Have a great day!
You are gathering data in the cafeteria, recording which condiments are most popular on students' hamburgers. The data you gather is
A. quantitative.
B. categorical.
C. discrete.
D. bivariate.
what solution is
y=9x+35
y=-8/9x+4/5
Answer:
x=-1539/445, y=1724/445. (-1539/445, 1724/445).
Step-by-step explanation:
y=9x+35
y=-8/9x+4/5
-------------------
9x+35=-8/9x+4/5
9x-(-8/9x)=4/5-35
9x+8/9x=4/5-175/5
81/9x+8/9x=-171/5
89/9x=-171/5
x=(-171/5)/(89/9)
x=(-171/5)(9/89)
x=-1539/445
y=9(-1539/445)+35
y=1724/445
Find the following angle measures.
MZEAD =
mZCAB =
Answer:
m∠EAD = 29°
m∠CAB = 119°
Step-by-step explanation:
m∠EAD = 180 - 61 - 90 = 29°
m∠CAB = 180 - 61 = 119°
Which system of linear inequalities is represented by the
graph?
Answer:
y<x+1 y>x-2
Step-by-step explanation:
upper line: (0,1) (-1,0)
y=x+1
Lower line: (0,-2) (2,0)
y=x-2
I did not see any solid boundry on the line
Shaded: y<x+1 y>x-2
Answer:
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]
Step-by-step explanation:
According to the graph, the system is formed by two inequalities. Let's find out the equation to each line in first place.
Notice that the upper line passes through points (-1,0) and (0,1). First, we find its slope
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-0}{0-(-1)}=\frac{1}{1}=1[/tex]
Then, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-(-1)\\y=x+1[/tex]
Now, the dashed line indiactes that the inequalities must have sings < or >.
Notice that point (0,0) is part of its solution, that means the inequality is
[tex]y <x+1[/tex]
We do the same process to find the other inequality.
The line passes through points (0,-2) and (2,0).
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-(-2)}{2-0}=\frac{2}{2}=1[/tex]
Then,
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
Notice that point (0,0) is part of its solution, so the inequality is
[tex]y>x-2[/tex]
Therefore, the system of inequalities is
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]