sebastioan swam laps every day in the community swimming pool. he swam 45 minutes each day, 5 days each week, for 12 weeks. In that time, he swam 1,800 laps. What was his average rate in laps per hour?
The solution is : Sebastian swam 40laps in one hour in average.
Here, we have,
Sebastian swam 45minutes per day.
If she swam 5days a week, this is equivalent to Sebastian swimming 60days in 12weeks.
If Sebastian swam 45minutes in a day, she must have swam for (45×60)minutes in 60days which is equivalent to 2700minutes
Converting 2700minutes to hours;
60minutes = 1hour
2700minutes = x
x = 2700/60
x = 45hours
Since sebastian swam 1800laps in that 12weeks in 45hours, her average rate lap per hour can be calculated thus;
1800laps = 45hours
X laps = 1hour
30 × X = 1800
X = 1800/45
X = 40laps
This shows that Sebastian swam 40laps in one hour in average.
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A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
If 3 workers can paint a room in 2 hours, then approximately how long does it take 4 workers to paint the same room?
Assume the time needed to paint the room is inversely proportional to the number of workers.
O 1 hour
3 hours
1.5 hours
2 hours
Answer:
C// 1.5
Step-by-step explanation:
A survey in 2021 found that 68% of students prefer to take some of their courses fully online. If three students are selected at random, find the probability that all three prefer to take some of their courses fully online.
Will give brainly! Thank you!
Answer:
ΑΠSШЕЯ®
Step-by-step explanation:
The probability that all three students prefer to take some of their courses fully online can be found by multiplying the probabilities of each event together. Since each student has a 68% chance of preferring fully online courses, the probability that the first student prefers fully online courses is 0.68, the probability that the second student prefers fully online courses given that the first student does is also 0.68, and the probability that the third student prefers fully online courses given that the first two students do is also 0.68. Therefore, the probability that all three students prefer to take some of their courses fully online is 0.68 x 0.68 x 0.68 = 0.314. The probability is approximately 0.314 or 31.4%.
would like some help
Answer:
A
Step-by-step explanation:
-4x²+7x+8=0
4x²-7x-8=0
a = 4, b = -7, c = - 8
x= (−b ± √b²−4ac) ÷ 2a
x= [ −(−7) ± √(−7)²−4(4)(−8) ] ÷ 2(4)
x = 7±√177
Hence,
x = 7+√177 and x = 7-√177
It has two solutions
f(x) = x^2 what is g(x)?
A. g(x) = 1/3x^2
B. g(x) = (1/3x)^2
C. g(x) = (1/9x)^2
D. g(x) = 3x^2
Two people are planning their wedding. For the reception, they found the the cost C for 50 guests, g is $2150 whereas the cost for 75 guests is $3025. Calculate the slope to find the cost per guest?
The slope which shows the cost per guest is $35 per guest
The given cost for 50 guests is $2150.
The cost for 75 guests is $3025.
It can also be represented as:
(Guest, Cost) =(50, $2150) & (75, $3025)
The slope can now be calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (50, $2150) & (75, $3025)
Substituting the given values in the equation as follows:
Slope = (3025 - 2150)/(75 - 50)
Slope = 35
Hence, the slope is $35 per guest.
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three times a number increased by 12 is equal to five times the same number decreased by 18. Find the number.
the answer is 15. but i need the solution
Answer:
Step-by-step explanation:
Let us say that the number is x
Now , According to the question ,
let us start by considering the L.H.S first i.e. three times a number increased by 12 i.e. 3^x+12 -------(1)
Now , consider R.H.S i.e. Five times the same number decreased by 18 i.e.
5^x-18-------------(2)
Now we are given that both the numbers are equal so here we equate eqn (1) and eqn (2)
⇒ 3x + 12 = 5x - 18
⇒ 12 +18 = 5x - 3x
⇒ 30 = 2x
⇒ 2x = 30
⇒ x = 30/2
⇒ x = 15
∴ Hence 15 is the required number
Pls help me I don’t understand it
According to the given percentage,
The original price of the jacket was $64.
Jeremy surveyed 100 students for his math project.
If the jacket was on sale for 25% off, that means the price Linda paid was equal to 75% of the original price. We can set up an equation to represent this:
0.75x = 48
where x is the original price of the jacket. To solve for x, we divide both sides by 0.75:
x = 48 / 0.75
x = 64
If 18% of the students surveyed selected hamburgers, that means the remaining 82% did not select hamburgers. We can represent this with an equation:
0.18x + 0.82x = x
where x is the total number of students surveyed. The left-hand side of the equation represents the number of students who selected hamburgers (0.18x) plus the number who did not (0.82x), which must equal the total number surveyed (x).
Simplifying the equation, we get:
x = 100x / 100
Dividing both sides by 100, we get:
x = 1 / 0.01
x = 100
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m the measure of A. 26° B. 31° C. 44° D. 59° E. 61°
Option - B is correct that is the measure of angles A is 31° when ∠A and ∠B are complementary angles.
Given that,
The part of your question is missing that is ∠A and ∠B are complementary angles with ∠A = (2x - 3)° and ∠B = (3x + 8)°.
We have to measure the angle A.
We know that,
Complementary angles means sum of the angles is equal to 90°
That means,
∠A + ∠B = 90°
2x -3 + 3x + 8 = 90°
5x + 5 = 90°
5x = 90 - 5
5x = 85
x = [tex]\frac{85}{5}[/tex]
x = 17°
Now by substituting
∠A = 2x -3
∠A = 2(17) -3
∠A = 34 - 3
∠A = 31
Therefore, The measure of angles A is 31°.
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Find the volume of a right circular cone that has a height of 15.4 m and a base with a
radius of 6.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
600.1 m³
Step-by-step explanation:
V = (1/3)πr²h
V = (1/3)(3.14159)(6.1 m)²(15.4 m)
V = 600.1 m³
The mortgage on your new condominium cost you $1,040 per month. You are trying to budget for the year and want to know what your monthly property tax bill will be. Residential property is assessed at 29% of its market value. You originally purchased your condo for $135,000. The mill rate in your county is 81.85%o.
Determine how much you will pay in property tax for the year. $
The monthly property tax bill will be $2,670.42.
To determine the property tax, we need to first find the assessed value of the condominium:
Assessed value = 29% of market valueMarket value = $135,000Assessed value = 0.29 x $135,000 = $39,150Next, we need to find the property tax rate:
Mill rate = 81.85%o = 0.8185
To find the annual property tax, we multiply the assessed value by the mill rate:
Annual property tax = Assessed value x Mill rateAnnual property tax = $39,150 x 0.8185Annual property tax = $32,045.03Finally, to find the monthly property tax, we divide the annual property tax by 12:
Monthly property tax = Annual property tax / 12Monthly property tax = $32,045.03 / 12Monthly property tax = $2,670.42 (rounded to the nearest cent)Therefore, the monthly property tax bill will be $2,670.42.
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PLS HELP 20 POINTS HELP!! I BEG
I am a little confused by the wording on the question. It says "within the circle" but the image is of 2 squares.
I am just going to answer it as if the question said "probability that a randomly selected point within the square falls in the red shaded square."
So red square area = 3 x 3 = 9.
The area of the bigger square = 4x4 = 16.
The prob of landing in that red square = 9/16 = 0.5625 or approx 56%.
The two triangles each have a height of 5.5m and a base of 2 m. The smaller base of the trapezoid has a length of 8.5 m. What is the area of the trapezoid?
The area of the trapezoid is 57.75m²
The area of the trapezoid is given by the equation below:
A = (a+b)*h/2
where, a = length of smaller parallel line, b = length of larger parallel line & h = height of the trapezium.
The given values are a= 8.5m, b = 8.5+2+2=12.5m & h = 5.5m
Substituting the given values in the equation above to get the area.
Area = (8.5+12.5)*5.5/2
Area = 57.75m²
Hence, the area of the given trapezoid is 57.75m².
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Use the information to answer the question. The table shows the amount of lemon juice and water that 4 students mix. Student Luca Kal Jenna Micah Lemon Juice Water (fluid ounces) (fluid ounces) 2 6 4 6 10 8 9 B Which two students mix the same ratio of lemon juice to water? Choose two students to show the answer.
The two students that mix the same ratio of juice to water is given as follows:
A. Luca.
D. Micah.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
Hence the ratio of juice to water for each person is given as follows:
Luca: 2/6 = 1/3.Kal: 6/10 = 3/5.Jenna: 4/8 = 1/2.Micah: 3/9 = 1/3.Hence Luca and Micah used the same ratio, meaning that options A and D are correct.
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You deposit $5000 in an account earning 3% interest compounded monthly. How much will you have in the
account in 10 years?
Compound interest, also known as interest on principal and interest, is the practice of adding interest towards the principal amount of a loan or deposit.
How does compound interest work?The yearly interest rate is raised to the amount of compounded periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.
P = $5,000 for the principle (initial investment)
Annual interest rate equals 0.03 (as a decimal)
t = the number of years (10).
Euler's number is e = 2.718281.
A = the sum at time t, or A = P·(e(rt))
[tex]\sf A = 5000(2.718281^{(0.03\times10)})[/tex]
[tex]\sf A = \$6,749.29[/tex]
After 10 years, you'll have $6,749.29 in your account.
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2x+=-x² +8 x+22²2² 2 Consider the expression: 1.1.1 How many terms are in the expression? 1.1.2 Write down the coefficient of x³. 1.1.3 What is the degree of the expression? 1.1.4 Give the value of the constant term. 1.1.5 What type of polynomial is the expression?
The value of coefficient of x³ is,
⇒ 2
The value of degree of the expression is,
⇒ 3
The value of constant term is,
⇒ 22
The polynomial is the expression of third degree.
Given that;
Expression is,
⇒ 2x³ - x² + 8x + 22
Now, We get;
There are 4 terms in the expression,
And, The value of coefficient of x³ is,
⇒ 2
The value of degree of the expression is,
⇒ 3
The value of constant term is,
⇒ 22
And, The polynomial is the expression of third degree.
Thus, The value of coefficient of x³ is,
⇒ 2
The value of degree of the expression is,
⇒ 3
The value of constant term is,
⇒ 22
The polynomial is the expression of third degree.
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Please graph “you are emptying a full 500 ML pop bottle at the rate of 25ML/S”
The linear equation will be y = - 25x + 500. And the graph is given below.
Given that:
Slope, m = -25 mL/s
Y-intercept, c = 500 mL
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of seconds and 'y' be the remaining amount. Then the equation is given as,
y = - 25x + 500
The diagram is given below.
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would like some help asap
Answer:
A. one solution
Step-by-step explanation:
The only solution was negative one half
Help me please If you were proving the theorem about the equality of the corresponding angles in this diagram, what would you need to prove first?
A)That the angles are interior.
B)That the angles are vertical.
C)That the angles are all acute.
D)That the angles are congruent.
If you were proving the theorem about the equality of the corresponding angles in this diagram, first you will prove d)That the angles are congruent.
Corresponding angles are generated when a line intersects two parallel lines, resulting in angles that are in the same location with regard to the lines. In this circumstance, all of the angles have measurements that are connected. These are the facts regarding the formed lines and angles.
The parallel lines do not cross. The transversal is the line that connects the parallel lines. Each parallel line has a straight angle, which means that the line measures 180 degrees.
The angles generated by the lines are either equal or supplementary, which indicates that the sum of two angles is 180 degrees. It is necessary that the corresponding angles are congruent angles hence we will check for them first.
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Simplify [tex]\sqrt[/tex]105
Step-by-step explanation:
you are sure ?
sqrt(105)
[tex] \sqrt{105} [/tex]
105 = 3×35 = 3×5×7
there is no factor that is a square number.
therefore, this cannot be further simplified.
it can be split into parts like
sqrt(3)×sqrt(5)×sqrt(7)
but I would not call that simplified.
we could use exponents :
sqrt(105) = 105^(1/2)
but that's about it.
Please help me guys, this is hurting my brain
Answer:
60
Step-by-step explanation:
To find the volume of this object, find The volume of the cuboid as a whole (ignore the hole as if it's not there) and then remove the volume of the hole (cuboid) from it.
Volume of whole solid = 9 × 6 × 5/4 = 67.5 ft³
For the invisible solid (hole part), you already have width and height, you can find the length too. Length = 9 - (2+3) = 9 - 5 = 4 ft
Volume of invisible solid = 5/4 × 4 × 5/2 = 12.5 ft³
Required volume = 67.5 - 12.5 = 55 ft³
What is the range of the function f(x) = 3x + 2 over the interval -3 < x < 5?
Answer:
-7 < f(x) < 17
Step-by-step explanation:
f(x) = 3x + 2
The given domain is -3 < x < 5
If x = -3, f(x) = f(-3) = 3(-3) + 2 = -9 + 2 = -7
If x = 5, f(x) = f(5) = 3(5) + 2 = 15 + 2 = 17
The range of f(x) is the set of permissible values for f(x) for the given domain -3 < x < 5
Therefore range of f(x): -7 < f(x) < 17
Restaurants often slip takeout menus under Britney's apartment door. Britney counted how many menus there were from each type of restaurant. What is the experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant?
After considering the given data we conclude that the experimental probability of next menu slipping under Britney's apartment door will be from a Chinese restaurant is 0.1 or 10%.
The experimental probability refers to a specified event that is classified on the basis of count that projects the event which has taken place during the experiment and the total number of times the experiment was conducted.
For the given case, the total of 20 menus from different restaurants were slipped under Britney's apartment door.
In which , 2 were from Chinese restaurants. Then, the experimental probability of the next menu being slipped under Britney's door would come from a Chinese restaurant is
2/20
= 0.1 or 10%.
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The complete question is
Restaurants often slip takeout menus under Britney's apartment door. Britney counted how many menus there were from each type of restaurant.
A) Chinese 2
B) Japanese 9
C) Mediterranean 1
D) Thai 2
E) Italian 6
1) What is the experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant?
180 miles in 3 hours write in simplest form
Answer:
Step-by-step explanation:
60 miles per hour.
a person is 21 years old and plans on retiring at age 55. This person is going to invest $75 each month into an ira
For the person to reach a retirement savings goal (future value) of $100,000 at age 55, they need to invest an additional $81 monthly.
Determining the additional monthly investment:
The additional monthly investment is computed as the difference between the expected monthly deposits and the intended monthly deposits.
The expected monthly deposits (periodic payments) are determined using an online finance calculator.
Current age = 21 years old
Retirement age = 55 years old
Investment period = 34 years (55 - 21)
N (of periods) = 408 months (34 years x 12)
I/Y (Interest per year) = 2.5%
Present Value = $0
FV (Future Value) = $100,000
Periodic Payments (PMT) = $155.75
Sum of all periodic payments = $63,546
Total Interest = $36,454
Intended monthly deposits = $75
Additional monthly deposits required = $80.75 ($155.75 - $75) = $81
Thus, the investor needs to invest an additional $81 to the $75 monthly deposits to reach a future value of $100,000 in 34 years, compounded at 2.5% monthly.
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The complete question =
A person is 21 years old and plans on retiring at age 55. This person is going to invest $75 each month into an IRA that is expected to earn 2.5% interest, compounded monthly. How much more money, rounded to the nearest dollar, is needed per month to reach a retirement savings goal of $100,000?
Now It's Time to Practice on Your Own
What is the exact area of a regular hexagon with a side length of 50 ft?
Enter your answer in the box.
ft²
URGENT
The exact area of a regular hexagon with a side length of 50ft is 6495.15ft²
The given length of the side of the hexagon is 50ft. Since a regular hexagon consists of 6 equilateral triangles therefore the area of the hexagon is equal to [tex]A=6*A_{triangle}[/tex].
Area of an equilateral triangle = √3/4{a}²
=1082.53ft²
Therefore, the area of the hexagon=6*1082.53ft²=6495.15ft²
Hence, the area of the hexagon is 6495.15ft².
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What is the value of x in the quadrilateral shown below
A.35°
B.45°
C.55°
Answer:
A
Step-by-step explanation:
All quadrilaterals have a total of 360° for the interior angles
X = 360 - (125+95+105) = 360 - 325 = 35°
Change the word phrase to an algebraic expression. The difference between three times a number and three
Answer: 3x-3
Step-by-step explanation: Let's express "a number" by the variable x.
The symbol for "three times a number" is 3x.
"The difference between a number of times three and three" can be expressed mathematically as:
"3x - 3".
need help will give brainlist
Answer: C
Step-by-step explanation: Okay it is very simple. Slope Formula= Y2-Y1/X2-X1
So -4-6/-7-3= -10/-10= 1
Option C
Given (3,6) (-7,-4)
X1=3
Y1=6
X2=-7
Y2=-4
