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.
When Dustin goes to work, he drives at an average speed of 55
miles per hour. It takes about 2 hour and 15 minutes for Dustin to
arrive at work. His car travels about 25 miles per gallon of gas. If
gas costs $2.75 per gallon, how much money does Justin spend to
travel each mile to work?
Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile
Step-by-step explanation:
we have to caalculate the distance between Dustin's home and work
So
Given
Speed =s = 55 miles per hour
Time = t = 2 hours and 15 minutes
Converting time into fraction
Time = 2.25 hours
We know that
[tex]s = \frac{d}{t}\\d = s * t\\d = 55 * 2.25\\d = 123.75\ miles[/tex]
So the distance is 123.75 miles
The car travels 25 miles per gallon
We have to calculate the total number of gallon first
So,
[tex]No.\ of\ gallons = \frac{Miles}{Miles\ per\ gallon}\\=\frac{123.75}{25}\\=4.95\ gallons[/tex]
So the total amount is:
[tex]2.75*4.95\\= 13.6125\ dollars[/tex]
Total amount is $13.6125. Dividing it by total distance will give us the cost of each mile
So,[tex]Cost\ of\ mile = \frac{Total\ amount}{Distance}\\= \frac{13.6125}{123.75}\\=0.11\ dollars[/tex]
Hence,
Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile
Keywords: Speed, Distance
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Climate change in Canada
According to the 2019 report Canada's Changing Climate Report (CCCR) which was commissioned by Environment and Climate Change Canada, Canada's annual average temperature over land has warmed by 1.7 C since 1948. The rate of warming is even higher in Canada's North, in the Prairies and northern British Columbia
Please help meeee (1/2) to the 4th power
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{1}{2} *\frac{1}{2} *\frac{1}{2} =[/tex][tex]\frac{1}{16}[/tex]
[tex]\frac{1}{2}*\frac{1}{2} =\frac{1}{4}[/tex]
[tex]\frac{1}{4} *\frac{1}{2} =\frac{1}{8}[/tex]
[tex]\frac{1}{8}*\frac{1}{2}=\frac{1}{16}[/tex]
Simplify. 5√⋅12−−√⋅50−−√
Answer:
Here's the answer. I got it right on my quiz. Hope I could help:)
Answer:
10 square root over 30
Step-by-step explanation:
took the test
help me answer this question please.
The right answer is Option B.
Step-by-step explanation:
Given expression is;
5x√2 - 3√2 + x√2
We can add or subtract square roots only when the values inside the square root are same and the variables are also same.
In the given expression, variable x is same with √2, therefore, adding both the roots
[tex]6x\sqrt{2} -3\sqrt{2}[/tex]
6x√2 - 3√2 is equivalent to 5x√2 - 3√2 + x√2.
The right answer is Option B.
Keywords: square roots, subtraction
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The fraction 7/9 is in the lowest terms. True or false ??
Answer:
True
Step-by-step explanation:
This is true because there is no common factor for 7 annd 9
One positive number is five times another number is the difference between the two numbers is 1676 find the numbers
Answer:
The two numbers are -419 and -2095.
Step-by-step explanation:
5x=y
x-y=1676
----------------
x-5x=1676
-4x=1676
x=1676/-4
x=-419
5(-419)=y
y=-2095
Given: E-midpoint of DA
F - midpoint of DB
E, F, C collinear, FC ≅ EF
Prove: EABC is a parallelogram.
By proving that triangles DEA and EFB are congruent due to the Side-Angle-Side postulate and demonstrating that AE is parallel to FB as well as AD parallel to BC, we can conclude that EABC is a parallelogram.
To prove that quadrilateral EABC is a parallelogram, we can use the properties of triangles and the definition of a parallelogram. According to the given information, E is the midpoint of DA and F is the midpoint of DB. Additionally, we know that E, F, and C are collinear and that FC is congruent to EF.
Leveraging these pieces of information, we observe that triangle DEA is congruent to triangle EFB because they have a side (EF or DE), an angle (at point E, since DE is an extension of EF), and another side (EA or FB, which are halves of DA and DB, respectively) in common (Side-Angle-Side postulate).
Since the two triangles are congruent, angle DEA is congruent to angle EFB, and angle DAE is congruent to angle FEB. These congruent angles imply that line AE is parallel to line BF. Since E and F are midpoints, AE is half of DA and BF is half of DB. If we continue the line AE to meet CD at point A and the line BF to meet CD at point B, EA will be parallel to FB, and AD will be parallel to BC, meeting the definition of a parallelogram.
EABC is a parallelogram because opposite sides are parallel and equal due to the Midpoint Theorem.
Given:
E - midpoint of DA
F - midpoint of DB
E, F, C collinear, FC ≅ EF
To Prove: EABC is a parallelogram.
Proof:
1. By the Midpoint Theorem, EF || AB and EF = 1/2 * AB. (Midpoint Theorem)
2. Since E, F, C are collinear and FC ≅ EF, EC bisects EF at C. Therefore, AB || EC. (Definition of a parallelogram)
3. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = AB, EC = 1/2 * AB. Similarly, EF = 1/2 * AB. Hence, EC = EF. Therefore, EA || BC. (Midpoint Theorem)
4. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = BC, EC = 1/2 * BC. Similarly, EF = 1/2 * BC. Hence, EC = EF. Therefore, EB ≅ AC. (Midpoint Theorem)
Therefore, EABC is a parallelogram.
Solution to system of equations
Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system
Leo has 9 times as many red marbles as blue marbles.
If he has 2288 more red marbles than blue marbles, how many red marbles does he have?
Answer:20592
Step-by-step explanation:
Because you multiply 5 times 2288
Leo has 2574 red marbles.
Explanation:Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.
It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.
Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.
Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.
an inflatable swimming pool holds 1,000 gallons of water. It sprang a leak. and 5% of the water leaked out of the pool. How many gallons of water leaked out
50 gallons of water leaked out of swimming pool.
Step-by-step explanation:
Total no. of gallons in swimming pool = 1000
Percentage of leaked water = 5%
Gallons of water leaked = 5% of total no. of gallons
[tex]Gallons\ of\ water\ leaked=\frac{5}{100}*1000\\\\Gallons\ of\ water\ leaked=\frac{5000}{100}\\\\Gallons\ of\ water\ leaked= 50\ gallons[/tex]
50 gallons of water leaked out of swimming pool.
Keywords: percentage, division
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if Sin A = 0.5736, what is the Cos A =
The value of CosA is 0.8191
Step-by-step explanation:
Given SinA= 0.5736
We know that [tex]SinA^{2} + CosA^{2} = 1[/tex]
Replacing value of SinA,
[tex](0.5736)^{2} + CosA^{2} = 1[/tex]
[tex](0.3290) + CosA^{2} = 1[/tex]
[tex] CosA^{2} = 1-0.3290[/tex]
[tex] CosA^{2} = 0.6709 [/tex]
[tex] CosA = 0.8191 [/tex]
The value of CosA is 0.8191
Please help! And if u do label the answers so Ik which is which if u answer n say idk I’ll report u
Answer:
5. y-intercept is 8
6. slope is -1/2
7. y=-1/2x+8
What is the value of the red dot on the number line below?
Answer:
B, 9.625
Step-by-step explanation:
I know there's a more surefire method of doing this problem but since this is multiple choice, you can use process of elimination to solve it.
What is log39 = x in exponential form?
3x = 9
o 9x = 3
o x3 = 9
o 39 = x
оооо
DONE
Answer:
9 = [tex]3^{x}[/tex]
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{3}[/tex] 9 = x ⇔ 9 = [tex]3^{x}[/tex] ← in exponential form
Answer:
its A on edge
Step-by-step explanation:
(x-1)(2x^2+2x+2)
Please show all the work!
Thank You
Answer:
2x³ - 2
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
= x(2x² + 2x + 2) - 1(2x² + 2x + 2) ← distribute both parenthesis
= 2x³ + 2x² + 2x - 2x² - 2x - 2 ← collect like terms
= 2x³ - 2
Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more than
the other, find the price of the less expensive piece of equipment. Assume all data are accurate
to two significant digits unless greater accuracy is given.
The price of less expensive equipment is $1575.
Step-by-step explanation:
Let,
Price of one equipment = x
Price of other equipment = y
According to given statement;
x+y=4000 Eqn 1
x = y+850 Eqn 2
Putting Eqn 2 in Eqn 1
[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]
Putting y=1575 in Eqn 2;
[tex]x=1575+850\\x=2425[/tex]
The price of less expensive equipment is $1575.
Keywords: linear equation, substitution method
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Final answer:
The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.
Explanation:
To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:
x + (x + $850) = $4000
To solve for x, we combine like terms and get:
2x + $850 = $4000
Subtracting $850 from both sides gives us:
2x = $3150
Dividing both sides by 2, we find the value of x:
x = $1575
Therefore, the price of the less expensive piece of equipment is $1575.
The perimeter of a rectangle is 10. The length of the rectangle is five less than four times the width. Find the width of the rectangle
L=4*W-5
10=W*2+(4*W-5)*2
10=W*2+8*W-10
20=10*W
2=W
L=4*2-5
L=3
Which of the following pairs are alternate exterior angles?
A.6 and 7
B.2 and 7
C.5 and 4
D.5 and 2
How many 2/3 cup servings are in a 4 cup container of food
Answer:
6
Step-by-step explanation:
4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.
Alicia conducted an experiment in which a spinner landed on green seven times if the experimental probability of the spinner landing on green is 1/5 how many trials did Alicia perform
Answer:
35 trials
Step-by-step explanation:
Probability = Favorable Outcome / Total Outcome
P = 1/5
Favorable Outcome = 7
Substitute the values,
1/5 = 7 / Total Outcomes
1/5 =7/x
Cross multiplication:
1x=5*7
x=35
Total Trials = 35
PLEASE ANSWER THIS QUICKLY BUT ALSO PLEASE GIVE ME THE RIGHT ANSWER. WHOEVER ANSWERS THE FASTEST GETS A BRAINLIEST!!!!!!!!
A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no scrap wood left over.
What is the longest length of boards he can cut?
A. 2 inches
B.6 inches
Answer:
B.6 inches
Step-by-step explanation:
Given: Three boards with measurement 24, 36, and 42 inches.
For the longest length of board we have to find out the H.C.F.
And for H.C.F. we will find out the factors,
[tex]24=2\times2\times2\times3\\36=2\times2\times3\times3\\42=2\times3\times7[/tex]
Here 2 and 3 is the common factor of given length of boards.
So the H.C.F. is 6.
Hence the longest length of board that carpenter can cut is 6 inches.
there were 50 rabbits on an island. After three months the number of rabbits had increased to 70. If the number of rabbits increased exponentially, answer the questions that follow:
A. in the equation above (where t is in months:, find the value of the growth rate k. (round k to 4 decimal places)
Answer:
0.1187
Step-by-step explanation:
A = P (1 + k)^t
where A is the final amount,
P is the initial amount,
k is the monthly growth rate,
and t is the number of months.
70 = 50 (1 + k)^3
1.4 = (1 + k)^3
∛1.4 = 1 + k
k = -1 + ∛1.4
k = 0.1187
2. Find 16.36 - 2.954
14.918
O 13.954
O 14.314
13.406
Answer:
13.406
The drawing will help
Answer:
13.406
Step-by-step explanation:
Included side between < S and < W.
A) side SA
B) side WA
C) side SW
Answer:
C) Side SW
Step-by-step explanation:
Hello! The included side between <S and <W is side SW. According to the included side rule, this would be the correct answer. I know this is not much of an explanation, but there is not much to it! Hope this helps.
What set of integers fall in the solution set of the following inequality:
1/3x<3x+8<-5x
Answer:
-2Step-by-step explanation:
[tex]\dfrac{1}{3}x<3x+8<-5x\qquad\text{multiply all sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x<3\cdot3x+3\cdot8<3\cdot(-5x)\\\\x<9x+24<-15x\\\\\text{Let split it into two inequalities}\\\\(1)\qquad x<9x+24\ \text{and}\qquad (2)\qquad 9x+24<-15x[/tex]
[tex](1)\\x<9x+24\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\-8x<24\qquad\text{change the signs}\\\\8x>-24\qquad\text{divide both sides by 8}\\\\\boxed{x>-3}\\\\(2)\\9x+24<-15x\qquad\text{add}\ 15x\ \text{to both sides}\\\\24x+24<0\qquad\text{subtract 24 from both sides}\\\\24x<-24\qquad\text{divide both sides by 24}\\\\\boxed{x<-1}\\\\\text{From (1) and (2) we have}\\\\-3<x<-1\to\text{There is only one integer in this solution: -2}[/tex]
10+x=5(1/5x+2) Equations with infinite and no solution
Answer:
Infinitely many solutions.
Step-by-step explanation:
10+x=5(1/5x+2)
10+x=x+10
infinitely many solutions
The equation 10+x=5(1/5x+2) has an infinite number of solutions.
Explanation:To solve the equation 10+x=5(1/5x+2), we need to simplify both sides and then isolate the variable x. Let's start by distributing the 5 to the terms inside the parentheses.
10+x = 5(1/5x+2) becomes:
10+x = 1x+10
Next, we can combine like terms on each side of the equation. Subtracting x from both sides:
10 = x+10-x
The x terms cancel out, leaving us with:
10 = 10
This equation is always true, which means that there are an infinite number of solutions.
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The complete Question is given below
10+x=5(1/5x+2)
Determine whether it has one solution, an infinite number of solution, or no solutions
Mr. Lee drove 8 miles from his house to pakside.parkside i 4 miles south of springfield.from parkside, he drove 3 miles to springdale .then he drove 20 miles from springdale to brookville. How far did mr. Lee drive in all , from his house to brookville ? Identify the extra or missing information .solve i possible.
Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
Solution:Given that
Mr. Lee drove 8 miles from his house to park side .
Parkside is 4 miles south of springfield.
From Parkside he drove 3 miles to springdale
Then he drove 20 miles from springdale to brookville.
Need to determine how far Mr Lee drive in all, from his house to Brookville.
Also need to identify Extra or missing information.
Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.
=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles
Information that is parkside is 4 miles south of springfield is extra information which is not required to determine mr. Lee drive , from his house to Brookville .
Hence Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
To begin a bacteria study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 15%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
Answer:
The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
Step-by-step explanation:
Given
[tex]t[/tex] be the number of hours.
[tex]y[/tex] number of bacteria cells.
And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent
The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]
In the equation as [tex]C[/tex] is function of time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.
To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]
So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]
Check:
[tex]15\% of 1800 =0.15\times 1800=270[/tex]
So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.
The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]
That can also be from the formula.
[tex]C(t)=1800(1.15)^1=2070[/tex]
So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.
Final answer:
The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.
Explanation:
To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.
Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.
solve the equation for all real values of x.