Answer:
0.5 891 7,800
Step-by-step explanation:
is because least always go first
To order from least to greatest, convert all measurements to grams: 7,800 mg becomes 7.8 g, and 0.5 kg becomes 500 g. The order is 7.8 g, 500 g, and 891 g.
To order the weights 891 g, 7,800 mg, and 0.5 kg from least to greatest, we first convert them all to the same unit. Given that there are 1,000 mg in a gram (g) and 1,000 g in a kilogram (kg), we can convert as follows:
7,800 mg is converted to grams by dividing by 1,000, which gives us 7.8 g.0.5 kg is converted to grams by multiplying by 1,000, which gives us 500 g.Now that we have all the weights in grams, we can easily compare them:
7.8 g891 g500 gOrdering these from least to greatest, we get: 7.8 g < 500 g < 891 g.
what are the vertices of triangle ABC, A(-2, 1), B(-3, -7) and C(4, -1) after translating ysing the rule (x, y)á(x+2,y-3).
The coordinates of triangle ABC after translation according to given rule are:
A'(0,-2), B'(-1,-10) and C'(6,-4)
Step-by-step explanation:
Given vertices are:
A(-2, 1), B(-3, -7) and C(4, -1)
The translation rule is: (x,y) => (x+2, y-3)
In order to translate the vertices, 2 will be added to x-coordinate and 3 will be subtracted from y-coordinate
So,
A(-2, 1) => A' (-2+2, 1-3) => A'(0,-2)
B(-3,-7) = > B'(-3+2, -7-3) => B'(-1, -10)
C(4,-1) => C'(4+2, -1-3) => C' (6, -4)
Hence
The coordinates of triangle ABC after translation according to given rule are:
A'(0,-2), B'(-1,-10) and C'(6,-4)
Keywords: Triangle, Translation
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Which of the following best defines 2 to the power of 2 over 3 ? (1 point) Cube root of 4 Square root of 4 Cube root of 2 Square root of 2
Answer:
C) [tex]\sqrt[3]{2}[/tex]
It is C because [tex]\sqrt[3]{2}=1.2599[/tex] which is the closest to [tex]1\frac{1}{3}[/tex]. Because [tex]\frac{2^{2} }{3}=1\frac{1}{3}[/tex].
Answer:
C) Cube root of 2
Step-by-step explanation:
use slope to determine whether the points A(3,5) B(-2,6) and C(-5,7) are on the same line
Answer:
The points are not on the same lineStep-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the given points:
for A(3, 5) and B(-2, 6):
[tex]m_{AB}=\dfrac{6-5}{-2-3}=\dfrac{1}{-5}=-\dfrac{1}{5}[/tex]
for B(-2, 6) and C(-5, 7):
[tex]m_{BC}=\dfrac{7-6}{-5-(-2)}=\dfrac{1}{-5+2}=\dfrac{1}{-3}=-\dfrac{1}{3}[/tex]
[tex]\large\boxed{m_{AB}\neq m_{BC}}[/tex]
I NEED HELP PLEASE. LOOK AT PICTURE
Answer:
Part 1) [tex]\frac{a^4}{4b^2}[/tex]
Part 2) [tex]-\frac{v^9}{w^6}[/tex]
Step-by-step explanation:
we know that
When divide exponents (or powers) with the same base, subtract the exponents
Part 1) we have
[tex]\frac{3a^{2}b^{-4}}{12a^{-2}b^{-2}}=(\frac{3}{12})(a^{2+2})(b^{-4+2} )=\frac{1}{4}a^{4}b^{-2}=\frac{a^4}{4b^2}[/tex]
Part 2) we have
[tex]\frac{v^3w^{-3}}{-v^{-6} w^3} =-v^{3+6}w^{-3-3}=-v^9w^{-6}=-\frac{v^9}{w^6}[/tex]
Please help with 11c!?
Answer:
"To the nearest year, it would be about 9 years"
Step-by-step explanation:
11c)
This is compound growth problem. It goes by the formula:
[tex]F=P(1+r)^t[/tex]
Where
F is the future amount
P is the present (initial) amount
r is the rate of growth, in decimal
t is the time in years
Given,
P = 20,000
r = 8% = 8/100 = 0.08
F = double of initial amount = 2 * 20,000 = 40,000
We need to find t:
[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]
To solve exponentials, we can take Natural Log (Ln) of both sides:
[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]
Using the rule shown below we can simplify and solve:
[tex]Ln(a^b)=bLn(a)[/tex]
We can write:
[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]
To the nearest year, that would be about 9 years
Which point could be removed in order to make the relation a function?
{(0, 2), (3, 8), (-4,-2), (3, 6), (-1, 8), (8, 3)}
O (8,3)
O (3,6)
0 (-1,8)
0(-4,-2)
Answer:
(3,6)
Step-by-step explanation:
the x input cannot repeat in order for it to be a function
1+9i and 5-3i midpoint
Answer:
[tex]3+3i[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two complex numbers (a+bi) and (c+di) points is equal to
[tex](\frac{a+c}{2})+(\frac{b+d}{2})i[/tex]
we have
(1+9i) and (5-3i)
substitute the given values
[tex](\frac{1+5}{2})+(\frac{9-3}{2})i[/tex]
[tex]3+3i[/tex]
Final answer:
The midpoint of the complex numbers 1+9i and 5-3i is calculated using the average of their real and imaginary parts, resulting in the midpoint of 3 + 3i.
Explanation:
To find the midpoint of two complex numbers, 1+9i and 5-3i, we use the midpoint formula for complex numbers which is the average of the real parts and the average of the imaginary parts separately. The formula for the midpoint M is given by:
M = ½(x1 + x2) + ½(y1 + y2)i
For our complex numbers, the real parts are 1 and 5, and the imaginary parts are 9 and -3. Applying the midpoint formula, we get:
M = ½(1 + 5) + ½(9 - 3)i = ½(6) + ½(6)i = 3 + 3i
Therefore, the midpoint of the complex numbers 1+9i and 5-3i is 3 + 3i.
The two figures shown are congruent. Which statement is true?
Help me :(
Answer:
i think it is the second answer
Step-by-step explanation:
i think this because the upside down ? is reflecting the ?
Answer:
One figure is a reflection of the other.
Step-by-step explanation:
Each point of the shape of one figure is equidistant to the equivalent point of the other, observing a symmetry line which perpendicular to the distance between each corresponding pair of points.
Select all statements that are true about the linear equation.
y= 1/3x + 2
The graph of the equation is a single point representing one solution to the equation.
The point (9,5) is on the graph of the equation.
The graph of the equation is the set of all points that are solutions to the equation.
The point (-3,-1) is on the graph of the equation.
Answer:
The point (9,5) is on the graph of the equation
The graph of the equation is the set of all points that are solutions to the equation
Step-by-step explanation:
we have the linear equation
[tex]y=\frac{1}{3}x+2[/tex]
This is the equation of the line in point slope form
where
the slope is [tex]m=\frac{1}{3}[/tex]
the y-intercept is [tex]b=2[/tex]
Remember that
If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation
The graph of the equation is the set of all points that are solutions to the equation
Verify each statement
case 1) The graph of the equation is a single point representing one solution to the equation
The statement is false
Because the graph of the equation is the set of all points that are solutions to the equation
case 2) The point (9,5) is on the graph of the equation
The statement is true
Because
For x=9, y=5
substitute the value of x and the value of y in the linear equation
[tex]5=\frac{1}{3}(9)+2[/tex]
[tex]5=3+2[/tex]
[tex]5=5[/tex] ----> is true
so
the ordered pair satisfy the linear equation
therefore
The point is on the graph of the equation
case 3) The graph of the equation is the set of all points that are solutions to the equation
The statement is true
case 4) The point (-3,-1) is on the graph of the equation
The statement is false
Because
For x=-3, y=-1
substitute the value of x and the value of y in the linear equation
[tex]-1=\frac{1}{3}(-3)+2[/tex]
[tex]-1=-1+2[/tex]
[tex]-1=1[/tex] ----> is not true
so
the ordered pair not satisfy the linear equation
therefore
The point is not on the graph of the equation
A bacteria culture has an initial population of 25. This bacteria reproduces at a daily rate of 1.28 percent. How long will it take for the population to grow to 375 bacteria?
Answer:
212.9 days
Step-by-step explanation:
The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P(t).
Using growth formula:
P(t) = Po ( 1 + r)^t where r is rate in percent and t is time in days
r = 1.28%, P(t) = 375, and Po = 25
substituting this values into the equation above yields
375 = 25 (1 + 1.28/100)^t
375÷25 = ( 1 + 0.0128)^t
15 = (1.0128)^t
take logarithm of both sides
log 15 = log (1.0128)^t remember the law log a^b = b log a
applying the same law gives
log 15 = t log 1.0128
divide both side by log 1.0128
log 15 ÷ log 1.0128 = t log 1.0128 ÷ log 1.0128
t = 212.9 days
Answer:
211 days
Step-by-step explanation:
the Parks and recreation department in your town offers a season pass for $150.
With the season pass you pay $5 per session to use the town's tennis courts. Without the season pass you pay $15 per session to use the tennis courts.
Write a system of equations to represent the situation
The system of equations are p = 150 + 5n and p = 15n
Solution:
Given that, The Parks and recreation department in your town offers a season pass for $150.
With the season pass you pay $5 per session to use the town's tennis courts.
Without the season pass you pay $15 per session to use the tennis courts.
We have to write a system of equations to represent the situation
Now, let the number of sessions be "n" and total paying amount be "p"
Then in case of taking season pass
total amount = season pass cost + $5 per session
p = 150 + 5 x n
p = 150 + 5n
And in case of no season pass
total amount = 15 per session
p = 15 x n
p = 15n
Hence, the system of equations are p = 150 + 5n and p = 15n
Final answer:
To represent the cost of using the town's tennis courts with and without a season pass, we use two equations: C = 150 + 5x for with a pass, and C = 15x for without a pass, where C is the total cost and x is the number of sessions.
Explanation:
The Parks and Recreation Department offers two options for using the town's tennis courts: with a season pass and without a season pass. We need to write a system of equations to represent the cost for each option depending on the number of sessions a person attends.
Equations
With Season Pass: C = 150 + 5x
Without Season Pass: C = 15x
In these equations, C represents the total cost of using the tennis courts for a given number of x sessions. For the pass option, there is an upfront cost of $150 plus $5 per session. Without the pass, each session costs $15.
These equations can help determine the point at which purchasing a season pass becomes more cost-effective than paying per session.
Somebody please help me with this
Answer:
see the explanation
Step-by-step explanation:
Part 1) Record the coordinates of the given triangle
Looking at the graph
Let
A(-4,2)
B(-2,5)
C(3,2)
Part 2) Translate the given triangle down 2 units and right 5 units. Graph the translation
we know that
A translation of 5 units at right means (x+5)
A translation of 2 units down means (y-2)
so
The rule of the translation is equal to
(x,y) -----> (x+5,y-2)
Apply the rule of the translation at each vertices
A(-4,2) ----->A'(-4+5,2-2)
A(-4,2) ----->A'(1,0)
B(-2,5) -----> B'(-2+5,5-2)
B(-2,5) -----> B'(3,3)
C(3,2) -----> C'(3+5,2-2)
C(3,2) -----> C'(8,0)
using a graphing tool
The graph in the attached figure
the length of a rectangle is 4 meters less than twice the width the perimeter is 34 Meters find the length and width in meters
The width and length of the rectangle are 7 meters and 10 meters, respectively, as determined by using algebraic expressions to relate the given perimeter with the width and length formulas.
Explanation:To solve for the length and width of a rectangle given the perimeter, we can use algebra. Since we know the length (L) is 4 meters less than twice the width (W), we can write this relationship as L = 2W - 4. The formula for the perimeter (P) of a rectangular shape is P = 2L + 2W. We are given that the perimeter is 34 meters.
Substituting the expression for L into the perimeter formula gives us:
P = 2(2W - 4) + 2WP = 4W - 8 + 2WP = 6W - 8Since the perimeter is 34 meters, we set 6W - 8 = 34.
Add 8 to both sides: 6W = 42Divide by 6: W = 7 metersNow, we find the length using the expression L = 2W - 4:
L = 2(7) - 4L = 14 - 4L = 10 metersTherefore, the width is 7 meters and the length is 10 meters.
the perimeter of a rectangle is 46m. the length is 3 m more than 3 times the width find the length and the width of the rectangle
Answer:
width =5m
length=18m
Step-by-step explanation:
w=x
l=3x+3
perimeter =2(l+w)
46=2(x+3x+3)
46=2(4x+3)
46=8x+6
46-6=8x
40=8x
x=40/8
x=5
l=3x+3=3*5+3=15+3=18
Final answer:
To find the length and width of a rectangle with a given perimeter, use algebra to solve for the width first, then use that value to find the length. The width is 5 meters and the length is 18 meters based on the given perimeter and the relationship between length and width.
Explanation:
The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. According to the problem, the perimeter is 46 meters, and the length is 3 meters more than 3 times the width. Therefore, we can express the length as l = 3w + 3. Let's set up the equation using the perimeter formula:
P = 2l + 2w46 = 2(3w + 3) + 2w46 = 6w + 6 + 2w46 = 8w + 640 = 8ww = 5Now that we've found the width to be 5 meters, we can find the length:
l = 3w + 3l = 3(5) + 3l = 15 + 3l = 18 metersThe width of the rectangle is 5 meters and the length is 18 meters.
The price of a car was decreased by 10% to £729. What was the price before the decrease?
Answer:
810
Step-by-step explanation:
90/100=729/x
100×729= 90x
72900=90x
810 = x
Answer:
£810
Step-by-step explanation:
100% - 10% = 90%
£729 is 90 % after the price was decreased by 10%. Therefore, Divide £729 by 90% to get the original price.
£729/90% = £810
6. Leo earns $16/h as a gardener in a city
park. For time worked above 35 h in a
week, he earns time-and-a-half. How much
does he earn for each of the following
numbers of hours worked in a week?
a) 36 h b) 39 h c) 42 h
h
a) He will earn $584 for working 36 hours.
b) He will earn $656 for working 39 hours.
c) He will earn $728 for working 42 hours.
Step-by-step explanation:
Amount per hour = $16
Time and a half means 1.5 times more than the original payment.
Therefore, above 35 hours, the earning for one hour,
Extra time per hour = 16*1.5 = $24
A) 36 h
For the first 35 hours, he will get $16 per hour, therefore,
Amount of 35 hours = [tex]35*16= \$560[/tex]
Amount of one hour = $24 (as calculated above)
Total = 560+24 = $584
He will earn $584 for working 36 hours.
B) 39 h
39 h = 35h + 4h
Amount of 35 hours = $560
Amount of extra 4 hours = $24*4 = $96
Total = 560+72 = $656
He will earn $656 for working 39 hours.
C) 42 h
42 h = 35h + 7h
Amount of 35 hours = $560
Amount of extra 7 hours = 24*7 = $168
Total = 560+168 = $728
He will earn $728 for working 42 hours.
Keywords: addition, multiplication
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At the movie theater, childs admission is $6.10. Adult admission is $9.40. On Tuesday four times as many adult tickets as child tickets were sold. For a total of $1179.90. How many child tickets were sold that day?
Answer:
The number of children's tickets sold was 27
Step-by-step explanation:
Let
x ----> the number of children's tickets sold
y ----> the number of adult's tickets sold
we know that
[tex]6.10x+9.40y=1,179.90[/tex] ----> equation A
[tex]y=4x[/tex] ----> equation B
Solve the system by substitution
Substitute equation B in equation A
[tex]6.10x+9.40(4x)=1,179.90[/tex]
solve for x
[tex]6.10x+37.6x=1,179.90[/tex]
[tex]43.7x=1,179.90[/tex]
[tex]x=27[/tex]
therefore
The number of children's tickets sold was 27
Could someone help me with this?
Answer:
1. 18.74%
2. 33.34%
3. 45.5%
4. 20%
5. 33.11%
6. 16.38%
Step-by-step explanation:
1. For Shoes, the actual price is $79.99 and the selling price is $65.00.
The discount is [tex]\frac{79.99 - 65}{79.99} \times 100 = 18.74[/tex]%.
2. For 12 pack og golf balls, the actual price is $29.99 and the selling price is $19.99.
The discount is [tex]\frac{29.99 - 19.99}{29.99} \times 100 = 33.34[/tex]%.
3. For Exercise bike, the actual price is $1099 and the selling price is $599.
The discount is [tex]\frac{1099 - 599}{1099} \times 100 = 45.5[/tex]%.
4. For Basketball, the actual price is $49.99 and the selling price is $39.99.
The discount is [tex]\frac{49.99 - 39.99}{49.99} \times 100 = 20[/tex]%.
5. For Sports socks, the actual price is $14.95 and the selling price is $10.00.
The discount is [tex]\frac{14.95 - 10}{14.95} \times 100 = 33.11[/tex]%.
6. For Hockey sticks, the actual price is $299 and the selling price is $250.
The discount is [tex]\frac{299 - 250}{299} \times 100 = 16.38[/tex]%.
Anna is a teacher at an elementary school. She purchased 73 tickets to take the first-grade children and some parents on a field trip to the zoo. She purchased
children's tickets for $9 each and adult tickets for $15 each. She spent a total of $771. How many of each ticket did she buy?
Adults
Children
Total
She bought 54 child tickets and 19 adult tickets.
Step-by-step explanation:
No. of tickets purchased = 73
Cost of tickets = $771
Cost of one child ticket = $9
Cost of one adult ticket = $15
Let,
Child ticket = x
Adult ticket = y
According to given statement;
x+y=73 Eqn 1
9x+15y=771 Eqn 2
Multiplying Eqn 1 by 9;
[tex]9(x+y=73)\\9x+9y=657\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 3 from Eqn 2;
[tex](9x+15y)-(9x+9y)=771-657\\9x+15y-9x-9y=114\\6y=114\\[/tex]
Dividing both sides by 6;
[tex]\frac{6y}{6}=\frac{114}{6}\\y=19[/tex]
Putting y=19 in Eqn 1
[tex]x+19=73\\x=73-19\\x=54\\[/tex]
She bought 54 child tickets and 19 adult tickets.
Keywords: linear equations, subtraction
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Final answer:
Anna bought 54 children's tickets at $9 each and 19 adult tickets at $15 each to spend a total of $771 for a field trip to the zoo.
Explanation:
The question is asking us to solve a system of linear equations to find out how many children's and adult's tickets were purchased for a zoo field trip. The total cost of the tickets was $771, with children's tickets costing $9 each and adult's tickets costing $15 each. Anna purchased a total of 73 tickets.
Let's define two variables, C for the number of children's tickets, and A for the number of adult tickets. We have two equations based on the information given:
9C + 15A = 771 (Total cost equation)
C + A = 73 (Total number of tickets equation)
To solve this system, we can use substitution or elimination. Here's how you might solve it using substitution:
From the second equation, we express one variable in terms of the other: A = 73 - C.
Substitute A in the first equation: 9C + 15(73 - C) = 771.
Simplify and solve for C: 9C + 1095 - 15C = 771, which simplifies to -6C = -324, so C = 54.
Use the value of C to find A: A = 73 - 54, so A = 19.
Anna bought 54 children's tickets and 19 adult tickets.
find the area of the shaded region
Answer:
21 centimeters is the answer
Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?
what is the answer and would it be positive or negative?
Michael is left with $181 and it is positive.
Step-by-step explanation:
Balance in Michael's account = $550
Per month withdrawal = $30.75
One year = 12 months
Total amount of withdrawal = Per month withdrawal * months
Total amount of withdrawal =[tex]30.75*12[/tex]
Total amount of withdrawal=[tex]\$369[/tex]
Net change = Balance in account - Amount of withdrawal
[tex]Net\ change= 550-369\\Net\ change=\$181[/tex]
Michael is left with $181 and it is positive.
Keywords: multiplication, subtraction
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The net change in Michael's account balance following the withdrawals is $181.
none of the option.
To find the net change in Michael's account balance following the withdrawals, we need to calculate the total amount withdrawn over one year and then subtract it from the initial balance.
Amount withdrawn per month: $30.75
Number of months: 12 (one year)
Total amount withdrawn over one year: [tex]\(30.75 \times 12 = $369\)[/tex]
Now, to find the net change in Michael's account balance, we subtract the total amount withdrawn from the initial balance:
Initial balance: $550
Total amount withdrawn: $369
Net change = Initial balance - Total amount withdrawn
Net change = $550 - $369
Net change = $181
The net change in Michael's account balance following the withdrawals is $181.
complete question given below:
Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?
A.-$519.25
B.-$369
C.$369
D.$519.25
O
The distance between the library and the station is 15 km, while
the station and the school are 33 km apart. How many kilometers
do you have to walk from the library to get to the school if you go
via the station?
18 km apart
You subtract 33 and 15
Solve the equation using the zero-product property.
(x - 3)(5x - 6) = 0
Answer:
x = 3 or x = 6/5
Step-by-step explanation:
The zero product property (or rule) tells you the product will only be zero if one (or more) of the factors is zero. Here, that means the solutions are values of x such that ...
x -3 = 0 ⇒ x = 3
5x -6 = 0 ⇒ x = 6/5
Can someone help me find the value of x?
Thanks!
Answer:
x = 7
Step-by-step explanation:
The segment joining the midpoints of the 2 sides of the triangle is one half the length of the third side, that is
2x - 6 = 8 ( add 6 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
Simon Wu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5
ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.
The total deposit made by Simon Wu is $634.22 which includes the amount from two checks, various dollar bills and coins.
Explanation:Let's break down Simon Wu's total deposit into components and add them up. First, we have two checks: one for $123.45 and another for $432.90. Then, we have cash which can be further broken down into: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. You need to add all these amounts together to find the total deposit.
Here is a step-by-step calculation:
Checks: $123.45 + $432.90 = $556.35Dollar bills: 3*1 + 9*5 + 5*10 = $74Coins: 15*0.25 (quarters) + 10*0.1 (dimes) + 18*0.05 (nickels) + 32*0.01 (pennies) = $3.87Final step is to add the value of the checks, the value of the dollar bills and the value of the coins together:
$556.35 + $74 + $3.87 = $634.22
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Find the Percent Change.
TV was reduced from $300 to $200.
it's either 2/3 or 66.6 (neverending 6s)
Answer:it changed from $100
Step-by-step explanation:
A sheriff patrols several neighborhoods in her patrol car it requires 3/15 of an hour to patrol an entire neighborhood how many neighborhoods can the sheriff patrol in 5/8 of an hour
Answer:
Neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.
Step-by-step explanation:
The Time taken to patrol an entire neighborhood = 3/ 15 hour
Total amount of time, the Sheriff has to do patrolling = 5/ 8 of an hour.
Now, let us assume the total neighborhoods paroled in the given time = m
So, [tex]\textrm{ Number of neighborhoods patrolled} = \frac{\textrm{Total available time}}{\textrm{Time used in 1 paroling 1 neighborhood}}[/tex]
[tex]m = \frac{\frac{5}{8} }{\frac{3}{15} } = {\frac{5}{8} \times {\frac{15}{3} =3.125[/tex]
or, the number of neighborhoods covered = 3.125
Hence, neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.
To find out how many neighborhoods the sheriff can patrol in 5/8 of an hour, divide 5/8 by 3/15, which simplifies to 1/5. The calculation gives us 3.125, meaning the sheriff can complete 3 full neighborhood patrols.
Explanation:The question involves determining how many neighborhoods a sheriff can patrol in 5/8 of an hour if it takes 3/15 of an hour to patrol one neighborhood. To solve this, we divide the total time available by the time it takes to patrol one neighborhood.
First, simplify the fraction that represents the time to patrol one neighborhood, which is 3/15. This reduces to 1/5 when divided by 3.Next, divide the total time available, 5/8 of an hour, by the time per neighborhood, 1/5 of an hour. This is equivalent to multiplying 5/8 by the reciprocal of 1/5, which is 5.The calculation is: (5/8) * (5/1) = 25/8 = 3.125.Thus, the sheriff can patrol 3 full neighborhoods in 5/8 of an hour, with some additional time remaining that is not enough to complete a fourth patrol.
What is the relationship between the place-value position of
the 7 and the 5 in the number 462,903.75?
of the place
The place value of the 7 represents
value of the 5
The place value of the 5 represents 10 times the place
Value of the 7
The place value of the 7 represents 100 times the place
value of the 5
of the place value
D The place walue of the 5 represents
of the 7
Answer:7
Step-by-step explanation:
Because it’s the place value of 5
Least common denominator of 7/9 and 2/3
Answer: 9
Step-by-step explanation: The common denominator will be the least common multiple for the two denominators.
To find the least common multiple or lcm of 3 and 9, begin by listing the first few multiples for each number.
Multiples of 6
1 × 9 = 9
2 × 9 = 18
3 × 9 = 27
Notice that we skipped 0 × 9 in our list of multiples. That's because 0 × 6 is 0 according to the zero property of multiplication and our least common multiple can't be 0.
When listing the multiples of 3, it's a good idea to keep an eye on the list of multiples for 9 so that we will notice when we find a least common multiple.
Multiples of 3
1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
Notice that in both lists, we have the least common multiple which is 9.
Therefore, the least common denominator of 9 and 3 is 9.
given that the area of the smaller square is 10cm2 .find the area of the larger square.
The calculated area of the bigger square is 22.5 square cm
How to determie the area of the larger square
From the question, we have the following parameters that can be used in our computation:
The square
Where, we have
Area of smaller square = 10 cm²
Using the above as a guide, we have the following:
Area of bigger square = Area of smaller square * Scale factor²
In this case, we have
Scale factor = 1.5
Substitute the known values into the equation
Area of bigger square = 10 * 1.5²
Evaluate
Area of bigger square = 22.5
Hence, the area of the bigger square is 22.5 square cm