Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.
Considering their itineraries, the number of days it will take until all four buses return to the terminal on the same day is the lcm of 6, 8, 10 and 15.To find their least common factor, we factor each number by prime numbers, hence:
6 - 8 - 10 - 15|2
3 - 4 - 5 - 15|2
3 - 2 - 5 - 15|2
3 - 1 - 5 - 15|3
1 - 1 - 5 - 5|5
1 - 1 - 1 - 1
Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.
It will take 120 days until all four buses return to the terminal on the same day.
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A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 26 yd and is 5.1 feet deep. Find the cost for filling the pool if the city charges $1.50 per 1000 gallons. Use the conversion 1 gallon = 0.134 cubic ft.
Round your answer to two decimal places.
The cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
Given:
Length = 25 yd
width = 26 yd
Height = 5.1 ft
convert yard to feet
25 yd = 75 ft
26 ft = 78 ft
Volume of the pool = length × width× height
= 75 × 78 × 5.1
= 29,835 cubic ft
1 gallon = 0.134 cubic ft.
222,649.3 gallon = 29,835 ft
charges per 1000 gallon = $1.50
Total charges = 222,649.3 gallon / 1000 gallon × $1.50
= 222.6493 × 1.50
= 333.97395
Approximately,
$333.97
Therefore, the cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
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Solve |2x - 5| = 4.
a. {x | x = 0.5 or x = 4.5}
b. {x | 0.5 < x < 4.5}
c. {x | x = -4.5 or x = 4.5}
Help, please
Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.
−5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3:negative five times x over negative five = fifty-three over negative five
Step 4: x = negative fifty-three over five
Answer:
The first step.
Step-by-step explanation:
Sharon wants to buy a shirt that cost $60. The sales tax is 5%. How much is the sales tax. What is her total cost for the shirt?
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 7%.
Calculate the amount of sales tax Cassie will pay on the purchase. Round to the nearest cent if necessary.
sales tax: $
Listen to the complete question
Part B
Fill in the blank question.
How much will Cassie pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.
total cost: $
Answer:
$10.12
Step-by-step explanation:
Step one:
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
please help with this!!!!
Answer:
6311000
Step-by-step explanation:
The first thing we do is calculate the total amount of people in both states. 6.89 x10 raised to the 6th power is equal to 6890000. Then we multiply 5.79 by 10 to the fifth power, which equals to 579000. Then we subtract the numbers, and get 6311000. They want you to answer in standard notation, which is the regular way of writing numbers such as 10, instead of 10^1.
The difference in population
[tex] = (6.89 \times {10}^{6} ) - (5.79 \times {10}^{5} ) \\ = (6.89 \times 10 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 - 5.79) \times {10}^{5} \\ = 63.11 \times {10}^{5} [/tex]
Answer:
[tex]63.11 \times {10}^{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
0
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
(a) It looks like you're saying
[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
Help Meh I need it SOON
Step-by-step explanation:
the option you chose (<C~=<Y) is absolutely correct.
I don’t understand, please help
Answer:
cosA=root8/3 is the answer
Please help with this question please and thank you
Answer:
I need help with this too!!!
Step-by-step explanation:
Answer:
what does it mean?
Step-by-step explanation:
I do not understand.
The store is 7⁄8 of a mile away from your house. You walked 1⁄5 of a mile towards the store before getting on the bus. If the bus went directly to the store, how many miles long was the bus ride?
Image attached giving 25 points please help
Answer:
i think x = -5, y = -7 is a other solution set
One angle in a complementary pair of angles measures 3 times the other angle.
What is the measure, in degrees, of the
smaller angle?
Answer:
22.5 degrees
Step-by-step explanation:
Complementary angles add up to be 90 degrees. You can model the simple equation [tex]x+3x=90[/tex] where is x is the small angle and 3x is the large angle.
[tex]4x=90\\x=22.5[/tex]
the smaller angle is 22.5 degrees
What is the formula for calculating momentum?
Answer:
(c) p = vm
Step-by-step explanation:
Momentum, represented by 'p', is the product of mass and velocity. It is a vector quantity, just as velocity is a vector quantity.
p = vm
Simplify fully
x2 - 9
3x2 + 8x - 3
+
X-3
x+2
(-3x³+2x²+4x+24) (x-2)
---------------------------------
8x
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See explanation
Step-by-step explanation:
Dilation of 4
G (0, 1) G' (0, 4)
F (1, 1) F' (4, 4)
Gx'/Gx = 0 / 0 = 0
Gy' / Gy = 4 / 1 = 4
Fx' / Fx = 4 / 1 = 4
Fy' / Fy = 4 / 1 = 4
need help with solving this please
Answer:
3/2
Step-by-step explanation:
Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio
s : 2s : sroot3
The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3
In this diagram the short leg is (root3)/2 .
(root3)/2 × root3 = 3/2
See image.
A bakery asks 75 customers to vote for a new bagel flavor. Onion flavor receives 33 votes. Cheddar flavor receives 42 votes. Use this information to answer the questions below. What fraction shows the proportion of customers who voted for cheddar flavor? What percent of customers voted for cheddar flavor?
Using proportions, it is found that:
The fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]56% of customers voted for cheddar flavor.A proportion is the number of desired outcomes divided by the number of total outcomes.A percentage is the proportion multiplied by 100%.In this question, 42 out of 75 customers voted for the cheddar flavor, hence:
[tex]p = \frac{42}{75}[/tex]
That is, the fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]
The percentage is:
[tex]\frac{42}{75} \times 100\% = 56\%[/tex]
56% of customers voted for cheddar flavor.
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Use the GCF and the Distributive property to find the sum of 66+78
Here is ur answer of your question
The base of a triangle is 4 ft more than the height. If the area is 30ft2, find the base and the height.
Answer:
Base = 10 ft. and the height = 6.
Step-by-step explanation:
Area of triangle = 1/2bh
base is 4 + h ⇔ base = 4 + h
height = h
Using the formula for the area of triangle substitute into the formula the given facts.
A = 1/2bh
30 = 1/2(4 + h) (h)
30 = 1/2(4h + h²) Multiply both sides by 2
60 = 4h + h²
-60 = -60 Add -60 to both sides
0 = h²+ 4h -60
(h + 10)(h - 6) = 0 Factor
h + 10 = 0 h - 6 =0
h = -10 h = 6
reject any negative number and use the positive answer for h.
So h = 6 and the base = 4 + 6 ; base = 10
expand and simplify 3(5x+1)+5(5x-4)
Answer:
40x-17
Step-by-step explanation:
Which function results in f(x)=13?
Answer:
The answer is B
Step-by-step explanation:
plug 2 into x to see
A.
x^2 + 8
2^2 + 8
4 + 8 = 12
B.
3x^2 + 1
3(2)^2 + 1
3(4) + 1
12 + 1 = 13
C.
2x^3 + 5
2(2)^3 + 5
2(8) + 5
16 + 5 = 21
D.
x^2 + x
2^2 + 2
4 + 2 = 6
Customers at Musicland can buy 4 DVDs for $15. How many DVDs can April buy at Musicland with $75?
Answer:
20 I believe because 15 divided by 4 is 3.75 so I then divided 75 by 3.75 giving me 20:)
Luigi's Fine Dining charges $32.09 for its prix fixe meal plus $39.26 for every drink, d, you purchase. The equation that models the total cost (T) is T(d )= 39.26d + 32.09 Which value in the equation represents the rate of change?
A .. The number of drinks purchased
B .. $32.09
C .. $39.26
D .. $71.35
Answer:
C. $32.09, since it's not the fixed cost, it changes based on how much drinks are purchased.
what is linear independent vector
Melissa has 120 kilograms of rice. Her mother sold 105 kilograms. What percent of the rice was sold? with solution :D please
Answer:
225
Step-by-step explanation:
po ang answer ko
please comment if I'm wrong
SOMEBODY PLZ CHECK IF MY ANSWER ARE CORRECT NO LINKS PLZ AND THANK YOU
Answer:
the first one's right i think
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Therefore, the solved inequality is z > -4.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Helppp it’s due today
Answer:
128
Step-by-step explanation:
Which statement is generally true about retirement?
A. Your income will increase, while your expense will stay the same.
B. Your income will decrease, while your expenses will increase.
C. Your income will increase, while your expenses will decrease.
D. Your income will decrease, while your expenses will stay the same.
The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.
During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.
Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Learn more about retirement on:
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Answer:
It's B
Step-by-step explanation:
Just took it