Answer:
The second city is 54 miles behind the first city
Step-by-step explanation:
The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.
The speed of the second bus is then 54/0.6 = 90 mph
When 1 and a half hour has passed, the first bus has moved a distance of
[tex]X_1=54\times 1.5[/tex] = 81 miles
The second bus (behind the first bus) has moved
[tex]X_2=90\times 1.5[/tex] = 135 miles
The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city
So, the second city is 54 miles behind the first city
Alice wants to buy 3 pounds of veal at the grocery store, but the scales at the store only show weight in kilograms. If one kilogram is 2.20 pounds, how many kilograms of veal should Alice buy?
Alice should buy 1.36 kilograms of veal.
Step-by-step explanation:
Given,
According to store's scale;
2.20 pounds = 1 kilogram
1 pound = [tex]\frac{1}{2.20}\ kg[/tex]
As Alice wants to buy 3 pounds, therefore,
3 pounds = [tex]\frac{1}{2.20}*3\\[/tex]
[tex]3\ pounds = \frac{3}{2.20}\\3\ pounds = 1.36\ kg[/tex]
Alice should buy 1.36 kilograms of veal.
Keywords: unit rate, fractions
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Answer:
1.36
Step-by-step explanation:
she wants to buy 3 pounds of veal
we multiply 3 pounds by 1 kg/2.20 lbs
we get 1.36 pounds
How much water must be added to 1 liter of a 5% saline solution to get a 2% saline solution?
Answer:
- 1,5 liters
Step-by-step explanation:
If 1 liter has 5% of saline solution, we know that our solution has 2,5 times the salt we want it to have: [tex]\frac{5\%}{2\%} =2.5[/tex], which means that, in the liter of water, there is an amount of salt that is 1,5 greater than what is desired.Then, if we want to lower the concentration of salt, we just have to add water. How much water? 1.5 liters. Then, 5% of solution divided in 2.5 liters of water yields in a 2% solution.Answer:
The water must be added to 1 liter of a 5% saline solution to get a 2% saline solution is 1.5 litres
Explanation:
We assume that the quantity of water added to be x litres. The quantity of saline in the existing solution is 5% of 1litre = 0.05 litres, with the addition of water, the quantity of new solution becomes (1 + x) litres. As per the problem, the percentage of saline in new solution should be equal to 2%. Therefore,
[tex]\frac{0.05}{1+x} \times 100=2[/tex]
So, 5 = 2(1+x)
2x = 5 - 2
[tex]x=\frac{3}{2}=1.5[/tex]
So, 1.5 litres water should be added to make the 1litre 5% saline solution a 2% saline solution.
at 2:30 a.m. the temperature in joelle is – 3f. the temperature drops 3/4 of a degree in 30 minutes. what is the temperature in joelle at 3:00 a.m.?
The temperature in joelle at 3:00 a.m. will be -3.75F
Step-by-step explanation:
Given that the temperature was -3F at 2:30 am
Temperature drops by 3/4 of a degree in 30 minutes
3/4 of a degree = 0.75 F
Time difference between 2:30 am and 3:00 am is 30 minutes
Temperature at 3:00 will be;
-3F -0.75 F = -3.75 F
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What is the answer to 53
The solution is y=(7a+9b)÷8
Step-by-step explanation:
Given equation is;
[tex]\frac{2y-a}{3}=\frac{a+3b}{4}[/tex]
Multiplying both sides by 12;
[tex]12*\frac{2y-a}{3}=\frac{a+3b}{4}*12\\4(2y-a)=3(a+3b)\\8y-4a=3a+9b\\8y=3a+4a+9b\\8y=7a+9b[/tex]
Dividing both sides by 8;
[tex]\frac{8y}{8}=\frac{7a+9b}{8}\\y=\frac{7a+9b}{8}[/tex]
The solution is y=(7a+9b)÷8
Keywords: linear equations, variable
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Please answer this correctly
Answer: 30 minutes
Step-by-step explanation:
Start time: 25 minutes to noon means 25 minutes before* noon. End time: 5 minutes past noon means 5 minutes after* noon.
25mins
+5mins
______
30mins
A saleswoman earns 9% commission on all merchandise that she sells. Last month she sold $9000 worth of merchandise. How much commission (in dollars) did she earn last month
Answer:
$810
Step-by-step explanation:
you have to turn your commission into a decimal and then multiply it by the total amount and then you will get your answer
The saleswoman earned $810 in commission last month.
Explanation:To find the commission earned by the saleswoman, we need to calculate 9% of the total merchandise sold.
9% of $9000 = $9000 * 0.09 = $810.
Therefore, the saleswoman earned $810 in commission last month.
A 60-kilogram person stands on a compression spring. The spring constant is 2500 Newtons per meter What is the displacement of the spring?
A)0.00392M
B) 0.024m
C)0.1176m
D)0.2352M
The displacement [tex](\( \Delta x \))[/tex] of the compression spring when a 60-kilogram person stands on it, with a spring constant of 2500 N/m, is approximately -0.2352 meters. The negative sign indicates the direction of the displacement. Therefore, the correct answer is D.
To find the displacement [tex](\( \Delta x \))[/tex] of the spring, you can use Hooke's Law:
[tex]\[ F = -k \cdot \Delta x \][/tex]
Where:
- F is the force applied (weight in this case),
- k is the spring constant, and
- [tex]\( \Delta x \)[/tex] is the displacement of the spring.
Rearrange the formula to solve for [tex]\( \Delta x \)[/tex]:
[tex]\[ \Delta x = -\frac{F}{k} \][/tex]
Substitute the given values:
[tex]\[ \Delta x = -\frac{mg}{k} \]\[ \Delta x = -\frac{(60 \, \text{kg})(9.8 \, \text{m/s}^2)}{2500 \, \text{N/m}} \][/tex]
Calculate the result:
[tex]\[ \Delta x \approx -0.2352 \, \text{m} \][/tex]
The negative sign indicates that the displacement is in the opposite direction to the applied force. Therefore, the correct answer is:
D) [tex]\( -0.2352 \, \text{m} \)[/tex]
Terrance bikes 3.6 miles to school in 18 minutes. Jaqueline bikes 5.4 miles to school in 30 minuets assuming each student rode at a constant speed , who is traveling at a faster speed
Answer:
jaqueline, because 3.6/18 =0.2 and 5.4/30=1.8
Step-by-step explanation:
Final answer:
Terrance is traveling at a faster speed of 12 mph compared to Jaqueline's 10.8 mph, after converting their biking times to hours and calculating the speed for each.
Explanation:
To determine who is traveling at a faster speed, we calculate the speed (rate) at which each student is biking. Speed is computed using the formula: speed = distance / time. For Terrance, who bikes 3.6 miles in 18 minutes, we must first convert minutes to hours, so 18 minutes is 0.3 hours (since 1 hour = 60 minutes). Thus, Terrance's speed is 3.6 miles / 0.3 hours = 12 miles per hour (mph).
For Jaqueline, who bikes 5.4 miles in 30 minutes, we also convert the minutes to hours to get 0.5 hours. Jaqueline's speed is 5.4 miles / 0.5 hours = 10.8 mph.
Comparing the two speeds, Terrance has a faster speed at 12 mph compared to Jaqueline's 10.8 mph.
two numbers have these properties both numbers are greater than 6 the highest common factor is 6 the lowest common multiple is 60 find the two numbers
The two numbers that fulfill these properties are 12 and 30. They both have a highest common factor of 6 and a lowest common multiple of 60.
Explanation:The two numbers that fit the description provided both need to be greater than 6, have a highest common factor (HCF) of 6, and a lowest common multiple (LCM) of 60.
For two numbers to have an HCF of 6, they must be multiples of 6. Looking at multiples of 6 that are greater than 6, we have 12, 18, 24, 30 etc. Since the LCM must be 60, we aim to find two numbers that when multiplied would produce 60. This leads us to the pair 12 and 30.
12 and 30 have an HCF of 6 (because 12=2*2*3 and 30=2*3*5, so the HCF is 2*3=6), and 12 and 30 both have an LCM of 60. Therefore, the two numbers are 12 and 30.
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The two numbers that meet these criteria, are greater than 6 and the ones that have the highest common factor as 6 and lowest common multiple as 60, are 6 and 60.
Explanation:In this problem, we are asked to find two numbers that have the following properties: they are both greater than 6, their highest common factor(HCF) is 6 and their lowest common multiple(LCM) is 60. Since HCF is 6, it's logical to assume that the two numbers can be multiples of 6. As per hints given the highest common factor of two numbers is 6 and the lowest common multiple is 60, the numbers should be 6 and 60 as these are the only two numbers that satisfy all conditions.
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Eva and jin are new volunteers at the animal shelter . If they both volunteer the first of the month,in how many days will they volunteer on the same day again? Eva volunteers every 3 days and jin volunteers every 5 days
Answer:
In 15 days
Step-by-step explanation:
Eva Volunteers Every 3 Days:
So, Eva volunteers on:
3rd, 6th, 9th, 12th, 15th, 18th, 21st...and so on DAYS
Jin Volunteers Every 5 Days:
So, Jin volunteers on:
5th, 10th, 15th, 20th, 25th...and so on DAYS
So, we see NEXT which day they vounteer together. Looking at the list, we see that it is on 15th day. This is also the LCM (Least Common Multiple) of 3 and 5.
So, in 15 days, they volunteer on the same day again.
With a convenience sample, a population is broken up into different subgroups and then simple random samples are conducted within each of these subgroups.
A. True
B. False
Answer:
i would like to say the answer is FALSE
Step-by-step explanation:
Max constructed a scale model of the Eiffel tower. The base area of the model is 0.25 square meters, while the base area of the actual Eiffel tower is 15,625 square meters
What is the scale factor of the model?
A) 1:625
B) 1:250
C)250:1
D)625:1
Answer:
1:250
Step-by-step explanation:
[tex]\sqrt{15625/0.25}[/tex]
=[tex]\sqrt{62500}[/tex]
=250
A community hall is in the shape of a cuboid.
tile:
The hall is 40 m long, 15m wide and
3 m high.
3 m
total
The community hall needs re-decorating
with new paint for the walls and ceiling,
and new tiles on the floor.
15 m
40 m
A 10 litre tin of paint covers
1 m2 floor tiles cost £3 each.
Work out the total cost of
to re-decorate the community hall.
Answer:
The total cost of to re-decorate the community hall is £2172.
Step-by-step explanation:
We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m wide and 3m high.
The paint will be required for 4 walls and ceiling.
Let us find area of walls and ceiling.
Are of Walls and Ceiling = [tex]2(l+b)h+lb=2(40+15)3+(40\times15)= 6\times55+600= 330+600 =930m^2[/tex]
Therefore, the area of walls and ceiling is 930 square meters.
Given: Cost for 10 litre of paint is £10 and 10 litre paint covers 25 square meter. Therefore,
Total Painting cost = [tex]10 \times \frac{930}{25} = \£372[/tex]
Therefore, the total painting cost of wall is £372.
Tiles will be required for floor. Let us find the area of floor.
Area of floor = [tex]l \times b = 40\times15 =600m^2[/tex]
Given: 1m squared floor tiles costs £3. So,
Total Cost for tiles = [tex]3\times600= \£1800[/tex]
Therefore, the total cost for tiles is £1800.
Now let us find total cost of to re-decorate the community hall;
Total Cost = the total painting cost of wall + the total cost for tiles = [tex]\£1800+\£372= \£2172[/tex]
Hence, the total cost of to re-decorate the community hall £2172.
To redecorate the community hall, the cost for tiling the floor will be £4500, and the cost for painting will depend on the price per tin, with a total of 93 tins needed to cover 930m².
Explanation:To calculate the total cost of re-decorating the community hall, we need to find the areas that need painting and tiling. Since the hall is a cuboid, the paintable area includes the four walls and the ceiling. The floor requires tiling.
The combined area of the four walls can be found by calculating the perimeter of the base, which is the sum of all sides ((2 × length) + (2 × width)), and then multiplying by the height. The ceiling is simply the length multiplied by the width.
Here is how to calculate the areas and costs:
Therefore, the cost for tiling the floor will be £4500, and the cost for painting will be 93 tins (if each tin is assumed to cost a certain amount, which is not specified in the question).
Sarah is 12 years old. Her sister, Emily, is 8 years less than 3 times Sarah's age. Write an expression for Emily's age in terms of Sarah's age, s.
Answer:
x= 3s -8
3 times Sarah's age is 3s hence the expression is as shown
Emily's age in terms of Sarah's age can be expressed by the algebraic expression '3s - 8', where 's' is Sarah's age.
Explanation:The student's question asks to express Emily's age in terms of Sarah's age, s. In the problem, it is stated that Emily is 8 years less than 3 times Sarah's age. This relationship can be expressed as an algebraic expression, where Emily's age, e, is equal to '3s - 8'. In this expression, 's' represents Sarah's age(12 years old in this case), '3s' means '3 times Sarah's age', and '- 8' represents '8 less than' the amount.
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Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of y. Do not include parentheses in your answer.
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
Answer:
this is the answer. hope it helps you
Here this is the answer, i hope this helps u have a great day ik this is late sorry...
NEVERMIND sorry this was the answer for another question, this is incorrect for this one.
(4x squared) to the third power
Answer:
64x⁶
Step-by-step explanation:
(4x²)³
= 4³(x²)³ <=the third power applies to both of the terms in the bracket
= 64x⁶ <=simplify
(x²)³ = x⁶ because when powers are raised to a power, they multiply.
(x²)³ = x²⁽³⁾ = x⁶
Write the quadratic equation whose roots are 2 and 3, and whose leading coefficient is 1.
Answer:
[tex]x^{2}[/tex]-5x+6
Step-by-step explanation:
(x-2)(x-3)
= [tex]x^{2}[/tex] -5x + 6
The price of packs of bubble gum are listed in the table below.
Bubble Gum Prices
Size of Pack Price
5 pieces $0.35
10 pieces $0.75
12 pieces $1.00
15 pieces $1.35
Which size pack of bubble gum has the lowest unit rate?
Answer:
The first one
Step-by-step explanation:
0.35÷5=0.07
0.75÷10=0.075
1.00÷12=0.08
1.35÷15=0.09
Two times a number, plus five, equals the number, minus five.
Find the number and type it in the box.
Answer:
Answer:
x= -5
Step-by-step explanation:
let the number be x.
2x+5= -5 ====> equation
2x= -5-5. (shifted the +5 to the other side)
2x= -10
x= -10/2 ( shifted 2 on the other side as it was multiplying with x)
x= -5
Final answer:
To solve the equation 'two times a number, plus five, equals the number, minus five,' we set up and simplify the algebraic equation 2x + 5 = x - 5, which ultimately gives us the number x = -10.
Explanation:
The problem states that two times a number, plus five, equals the number, minus five. To find the number, we can set up the equation 2x + 5 = x - 5, where x represents the number we're trying to find.
Step 1: Start by subtracting x from both sides of the equation to get all the x terms on one side and the constant terms on the other side. The equation then becomes: 2x - x + 5 = x - x - 5, simplifying to x + 5 = -5.Step 2: Next, we subtract 5 from both sides of the equation to solve for x: x + 5 - 5 = -5 - 5, which simplifies to x = -10.Therefore, the number we were trying to find is -10.
The center of a circle is located at (3.8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle?
Answer:
The general equation of a circle is x² + y² - 6x - 16y + 48 = 0
What is the difference between calculations and patterns
Answer:
"Calculation" is a mathematical determination of finding the size or number of something while "pattern" is a sequence of elements that is being repeated in a predictable manner.
Step-by-step explanation:
Calculation- This process allows you to put elements together or transform them into a new result. It produces an obvious change.
For example: 7 x 6 = 42
The numbers 7 and 6 when multiplied produces 42.
Pattern- This process allows you to put the elements in an intelligible way. The elements are organized or repeated regularly.
For example: A, B, C, A, B, C, A, B, C
It is noticeable that the letters A, B and C are being repeated in the same way.
A spinner has 12 equal sections:5 red 4 green and the rest are black. In 921 spins how many times can you expect to spin black?
Answer:
230
Step-by-step explanation:
12 sections total
5 red, 4 green, the rest black
12-5-4 = 3 sections are black
3/12 = 1/4 of the sections are black
1/4 represents the probability of landing on black for one spin
(1/4)*921 = 230.25 which rounds to 230
We expect to land on a black section about 230 times out of 921 times total.
If Johnny has 22 biscuits and Lucy has 5 how many biscuits does Ruby have?
Answer:
Ummmmm none I guess
Step-by-step explanation:
rawr
Answer: 27
Step-by-step explanation: bc thats what some random persons teacher said.
✓ Express 9 inches of rain in 72 hours as a unit rate. *
The unit rate of 9 inches of rain in 72 hours is calculated by dividing the depth of the rainfall by the duration, resulting in a unit rate of 0.125 inches of rain per hour.
To express 9 inches of rain in 72 hours as a unit rate, you divide the total amount of rain by the total number of hours to find the rainfall intensity per hour. The calculation would go as follows:
Write down the total rainfall depth: 9 inches.
Write down the duration over which the rain occurred: 72 hours.
Divide the total rainfall depth by the duration to calculate the unit rate: 9 inches / 72 hours = 0.125 inches per hour.
So, the unit rate is 0.125 inches of rain per hour.
deigo pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how much water was in the full bottle?
Answer:
20% x 5 = 100%
6.8 x = 34
so there was 34 oz of water in the full bottle
Step-by-step explanation:
Y=2x+5 rotate 90 degrees
Answer:
Don't know
Step-by-step explanation:
Which way? Clockwise or Counterclockwise?
2 divided by 1 6/7 in simplest form
Answer:
1 1/13
Step-by-step explanation:
2/1 6/7
2/ 13/7
2/1*7/13
14/13
1 1/13
The division of '2' by '1 6/7' involves the conversion of the mixed number to an improper fraction, after which it becomes '2 * 7/13'. This simplifies down to '14/13' or '1 1/13'.
Explanation:To calculate the division of '2' by '1 6/7', we first have to convert '1 6/7' to an improper fraction. '1 6/7' equals '13/7' when simplified. So, now the task is to divide '2' by '13/7'. In the division of fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, this becomes '2 * 7/13' (i.e. '2' over '1' times '7' over '13'). Multiplying the numerators together gives us '14', and multiplying the denominators together gives us '13'. Therefore, '2 divided by 1 6/7', in simplest form, is '14/13' or '1 1/13' when converted to a mixed number.
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How much can 7 go to 57
Answer:
8 times
Step-by-step explanation:
57/7=8.1428571428... round down to the nearest whole number.
Write a word problem using 7 groups. Solve your problem?
A real-world problem using 7 groups can be illustrated like a builder constructing 7 buildings each requiring 15 bricks per day. Multiplying these, 7 times 15 gives us 105, which is the total number of bricks needed each day.
Explanation:Consider a scenario where a builder is constructing 7 buildings. Each building needs 15 bricks per day for construction. We can therefore write a multiplication problem to find out how many total bricks are needed each day.
So, 7 (groups of buildings) multiplied by 15 (bricks per building) equals a total daily brick requirement. To solve this, you simply multiply 7 by 15 which equals 105 bricks needed each day.
This is a simple real-world problem to help understand the concept of multiplication as repeated addition. Here, you're adding 15 bricks 7 times since there are 7 buildings.
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Find the measure of DF
Answer:
DF = 50Step-by-step explanation:
[tex]\bold{METHOD\ 1:}[/tex]
[tex]\triangle ABC\sim\triangle DE F\qquad(\text{similar tringles)}\\\\\text{Therefore corresponding sides are in proportion:}\\\\\dfrac{BA}{AC}=\dfrac{ED}{DF}\\\\\text{Substitute}\ BA=360,\ AC=600,\ ED=30\\\\\dfrac{360}{600}=\dfrac{30}{DF}\qquad\text{cross multiply}\\\\360DF=(600)(30)\\\\360DF=18000\qquad\text{divide both sides by 360}\\\\DF=50[/tex]
[tex]\bold{METHOD\ 2:}[/tex]
[tex]\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=40,\ leg=30,\ hypotenuse=DF.\\\\\text{Substitute:}\\\\40^2+30^2=DF^2\\\\1600+900=DF^2\\\\2500=DF^2\to DF=\sqrt{2500}\\\\DF=50[/tex]
The measure of DF cannot be determined without additional context or a specific function. DF could imply distance in a physics scenario or represent an infinitesimal change in a function in calculus.
Explanation:The measurement of DF seems to be a question related to calculus and physics, specifically pertaining to infinitesimal changes and dynamics. In calculus, df represents an infinitesimally small change in a function, often a result of changing variables x and y. In a physics context, DF can be interpreted as the distance fallen in a typical free fall scenario under gravity, with an initial velocity. Unfortunately, without additional context or a specific function provided, the measure of DF cannot be accurately determined.
For example, in the context of electromagnetism, dF could represent the infinitesimal force on a wire carrying current in a magnetic field, according to the formula dF = i (dl) x B, where i represents current, dl represents an infinitesimal length of wire, and B represents the magnetic field.