1a) HCF of 224 and 336 = 112, LCM of 224 and 336 = 672.
1b) HCF of 18 and 42 = 6, LCM of 18 and 42 = 126.
1c) HCF of 45 and 150 = 15, LCM of 45 and 150 = 450.
2. The LCM of 28, 44, and 68 is 2,744 seconds, which is equivalent to 45 minutes and 44 seconds.
3. The LCM of 15 minutes and 18 minutes is 90 minutes, which is equivalent to 1 hour and 30 minutes.
Therefore, the bell will be rung and the whistle blown at the same time again after 1 hour and 30 minutes.
4. To find the time it takes for Anthony and Joseph to be at the same point again, we need to find the LCM of 65 seconds and 75 seconds. The LCM is 975 seconds, which is equivalent to 16 minutes and 15 seconds.
For finding the HCF (Highest Common Factor) and LCM (Least Common Multiple), we can use the following formulas:
a) For 224 and 336:
To find the HCF, we can use the Euclidean algorithm:
336 = 1 [tex]\times[/tex] 224 + 112
224 = 2 [tex]\times[/tex] 112 + 0
Therefore, the HCF of 224 and 336 is 112.
To find the LCM, we can use the formula:
LCM = (a [tex]\times[/tex] b) / HCF
LCM = (224 [tex]\times[/tex] 336) / 112
LCM = 2 [tex]\times[/tex] 336
LCM = 672
b) For 18 and 42:
HCF of 18 and 42 is 6.
LCM = (18 [tex]\times[/tex] 42) / 6
LCM = 6 [tex]\times[/tex] 42
LCM = 252
c) For 45 and 150:
HCF of 45 and 150 is 15.
LCM = (45 [tex]\times[/tex] 150) / 15
LCM = 3 [tex]\times[/tex] 150
LCM = 450
Therefore, the HCF and LCM for the given pairs are:
a) HCF: 112, LCM: 672
b) HCF: 6, LCM: 252
c) HCF: 15, LCM: 450
To find the date when three patients next go to the doctor on the same day, we need to find the LCM of the given intervals: 8, 15, and 24 days.
LCM of 8, 15, and 24 is 120 days.
Since they all went to the doctor on 1 March, we add 120 days to that date:
1 March + 120 days = 30 June
Therefore, the next date when they will all go to the doctor on the same day is 30 June.
To find the time when the bell and whistle are blown at the same time again, we need to find the LCM of the intervals: 15 minutes and 18 minutes.
LCM of 15 and 18 is 90 minutes.
Since the bell rang and the whistle blew at 8:00 am, we add 90 minutes to that time:
8:00 am + 90 minutes = 9:30 am
Therefore, the bell will ring and the whistle will be blown at the same time again at 9:30 am.
Anthony takes 65 seconds to run a loop, and Joseph takes 75 seconds to run the same loop. We need to find the LCM of these two times to determine when they will be at the same point again.
LCM of 65 and 75 is 975 seconds.
It will take 975 seconds for Anthony and Joseph to be at the same point on the circular track again.
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Danielle is trying to solve the equation 25^x+ 3 =176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
The value of x is 1.601.
What are logarithms?In Mathematics, logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation.
Given that:
The equation is: [tex]\bold{25^{x+3}=176}[/tex]Simplify the equation then,
[tex]\sf 25^{x+3}=176[/tex]
[tex]\sf 25^x=176-3[/tex]
[tex]\sf 25^x=173[/tex]
[tex]\sf 5^{2x}=173[/tex]
Taking ln both sides then,
[tex]\text{In}\sf \ 5^{2x}=\text{In}\sf \ 173[/tex]
Use logarithmic property
[tex]\text{In}\sf \ \text{a}^{\text{b}}=\text{b In a}[/tex]
Then the value is:
[tex]\text{In}\sf \ 5^{2x}=\text{In}\sf \ 173[/tex]
[tex]\sf 2\text{x} \ \text{In} \ 5=\text{In} \ 173[/tex]
[tex]\sf 2\text{x}=\dfrac{\text{In} \ 173}{\text{In} \ 5}[/tex]
[tex]\sf \text{x}=\dfrac{\text{In} \ 173}{2 \ \text{In} \ 5}[/tex]
The value of "x" is:
[tex]\sf \text{x}=\dfrac{\text{In} \ 173}{2 \ \text{In} \ 5}[/tex]
[tex]\sf \text{x}=\dfrac{5.1533}{2\times1.6094}[/tex]
[tex]\sf \text{x}=\dfrac{5.1533}{3.2189}[/tex]
[tex]\bold{x\thickapprox1.601}[/tex]
Hence, the value of x is 1.601.
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The operation is define by a+b=ab-ab
Evaluate
8 *(-4)
The answer is:
-32
Work/explanation:
Remember the integer rule:
[tex]\blacktriangleright\phantom{333}\sf{a\times(-b)=-ab}[/tex]
In other words, we multiply a positive times a negative which results in a negative product.
Therefore,
8*(-4) = -32
Hence, the answer is -32.The commission rate for a a sale of property by auction are 5% on the first $12000, 3% on the next $15000 and 1% on the remainder of the selling price. Find the total commission paid on the sale property for $45000.
To find the total commission paid on the sale property for $45,000, we can break down the selling price into different ranges and calculate the commission for each range separately.
First, let's calculate the commission for the first range, which is 5% on the first $12,000:
Commission for the first range = 5% of $12,000 = 0.05 * $12,000 = $600
Next, let's calculate the commission for the second range, which is 3% on the next $15,000:
Commission for the second range = 3% of $15,000 = 0.03 * $15,000 = $450
Finally, let's calculate the commission for the third range, which is 1% on the remainder of the selling price:
Commission for the third range = 1% of ($45,000 - $12,000 - $15,000) = 0.01 * $18,000 = $180
Now, we can find the total commission by adding up the commissions from each range:
Total commission = Commission for the first range + Commission for the second range + Commission for the third range
Total commission = $600 + $450 + $180 = $1,230
Therefore, the total commission paid on the sale property for $45,000 is $1,230.
what would figure 106 be?
any help would be greatly appreciated!!!!
The value of x for the hypotenuse PQ of right triangle PQR is equal to 16 using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
OP and OQ are radius of the circle O, so OP = 9
OR = PR - OP
OR = 16 - 9 = 7
Considering the right triangle ORQ;
RQ = √[(OQ)² - (OR)²] {Pythagoras rule}
RQ = √(9² - 7²)
RQ = √32
For right triangle PQR;
x² = 16² + (√32)² {Pythagoras rule}
x² = 256 + 32
x² = 256
x = √256
x = 16
Therefore, the value of x for the hypotenuse PQ of right triangle PQR is equal to 16 using the Pythagoras rule.
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What is the function of the graph?
Answer: The function of the graph is f(x) = √X - 2
Step-by-step explanation:
The graph is clearly a square root function. The parent square root function is √x = f(x). Due to the fact that the displayed function has a lowered y-axis of two units it means that the parent function is subtracted by two units in order to display what is shown in the graph.
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
if angle ABD=65 degrees, angle EBC=70 degrees, and angle ABC=115 degrees, find angle EBD
The measure of angle EBD is 65 degrees.
1. Start by noting the given angles: angle ABD = 65 degrees, angle EBC = 70 degrees, and angle ABC = 115 degrees.
2. Recognize that angle ABC can be expressed as the sum of angles ABD and EBD: angle ABC = angle ABD + angle EBD.
3. Substitute the given values into the equation: 115 degrees = 65 degrees + angle EBD.
4. Simplify the equation: angle EBD = 115 degrees - 65 degrees.
5. Perform the subtraction: angle EBD = 50 degrees.
Therefore, the measure of angle EBD is 50 degrees.
6. However, we still need to find the value of angle EBD. To do so, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
7. Recall that in triangle ABC, the sum of angles ABD, EBC, and angle ABC is equal to 180 degrees.
8. Substitute the known values: angle ABD + angle EBC + angle ABC = 180 degrees.
9. Plug in the given angle measures: 65 degrees + 70 degrees + 115 degrees = 180 degrees.
10. Add the values: 250 degrees = 180 degrees.
11. This equation is not valid since the sum of the angles is greater than 180 degrees.
12. To resolve this discrepancy, we realize that angle EBD must be an exterior angle of triangle ABC formed by extending side BD.
13. The sum of an interior angle and its corresponding exterior angle is always 180 degrees.
14. Therefore, angle EBD + angle ABC = 180 degrees.
15. Plug in the given values: angle EBD + 115 degrees = 180 degrees.
16. Subtract 115 degrees from both sides: angle EBD = 180 degrees - 115 degrees.
17. Calculate the subtraction: angle EBD = 65 degrees.
Hence, the measure of angle EBD is 65 degrees.
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the gas tank of a car has a volume of 74.8dm find how many kilometers of gas would it take to completely fill the gas tahk.
It would take 1122 kilometers of gas to completely fill the gas tank of the car if the fuel efficiency of the car is 15 kilometers per liter.
To find out how many kilometers of gas would it take to completely fill the gas tank of a car, we need to know the fuel efficiency of the car in kilometers per liter.
This information can be found in the car's owner's manual or by checking the manufacturer's website.
Let's assume that the fuel efficiency of the car is 15 kilometers per liter.
To find out how many liters of gas it would take to fill the tank, we need to convert the volume of the gas tank from cubic decimeters (dm3) to liters.
To do this, we can use the conversion factor: 1 dm3 = 1 L
So, the volume of the gas tank in liters is:74.8 dm3 x 1 L/dm3 = 74.8 L
Now we can calculate how many kilometers of gas it would take to fill the gas tank:74.8 L x 15 km/L = 1122 km
Therefore, it would take 1122 kilometers of gas to completely fill the gas tank of the car if the fuel efficiency of the car is 15 kilometers per liter.
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tis
3. What is the measure
of ZXYZ?
Y
Z
V
274⁰
Answer:
∠ XYZ = 137°
Step-by-step explanation:
the tangent- chord angle XYZ is half the measure of the intercepted arc XVY , that is
∠ XYZ = [tex]\frac{1}{2}[/tex] × 274° = 137°
Graph the equation to find the solutions to the system
The solution to the systems of equations are (5.854, 4.854) and (-0.854, -1.854)
Solving the systems of equations graphicallyFrom the question, we have the following parameters that can be used in our computation:
y = x - 1
y = 1/3(x + 2)(x - 4)
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection
The coordinates in the solution to the systems of equations are (5.854, 4.854) and (-0.854, -1.854)
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648 is a perfect cubes or not
Answer:
After grouping the prime factors in triplets, one factor 3 is left without grouping. Thus, 648 is not a perfect cube
Find the indicated probability using the standard normal distribution. P(z>−1.54) Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... Question content area bottom Part 1 P(z>−1.54)= enter your response here (Round to four decimal places as needed.)
P(z > -1.54) is approximately 0.9332.
To find the indicated probability using the standard normal distribution, we need to calculate the area under the standard normal curve to the right of the given z-value of -1.54.
Using the standard normal table, we can locate the closest z-value to -1.54, which is approximately -1.55. The table provides the area to the left of the z-value, so we need to find the complement of this area to get the area to the right.
From the table, the closest z-value is -1.5, and the corresponding area to the left is 0.0668. The next closest z-value is -1.6, and the corresponding area to the left is 0.0548.
Since -1.54 is closer to -1.5, we will use the area corresponding to -1.5, which is 0.0668.
To find the area to the right of -1.54, we subtract the area to the left of -1.5 from 1:
Area to the right = 1 - Area to the left = 1 - 0.0668 = 0.9332.
Therefore, P(z > -1.54) is approximately 0.9332.
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What is the value of in the equation 4.8 = 30 + 1.8 ?
Answer:
To find the value of "in" in the equation 4.8 = 30 + 1.8, we need to isolate the variable "in" on one side of the equation.
Let's simplify the equation step by step:
4.8 = 30 + 1.8
First, we can simplify the right side of the equation:
4.8 = 31.8
Now, we have a simple equation with a single variable. The value of "in" can be determined by noting that both sides of the equation are already equal. Therefore, the value of "in" in this equation is 4.8.
Step-by-step explanation:
Please help with math giving brainliest 10 points!
Answer:
x< 2/2 and u can put it as a 1 too
Step-by-step explanation:
ok so
x/2 + 3/2 < 5/2
x/2< 5/2 - 3/2
x/2< 2/2
x/2< 1
if im wrong correct me please thanks
this is the 1. pic
question in the picture
Answer:
a) 34 students scored below an 81%
b) Interval 81-100
c) 34.6 rounded to 35% of students scored no higher than 60%
d) 38.4% of students scored at least 81%
Step-by-step explanation:
a) the frequency refers to the number of students and each of the bars shows how many students got into a certain range of scores. So you would count the frequency for 4 of the ranges except for the last one.
b) interval 81-100 contained the most scores as it has the highest frequency
c) 2+4+12= 18 students scored no higher than 60%, the total number of students is 52 students. So to get the answer you would divide
18/52= 0.346 x 100= 34.6= 35%
d) 20/52= 0.384 x 100= 38.4%
Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 mi slower than the other, If the two cyclists are 86 miles apart after 2 hours, what is the rate of each cyclist?
The rate of the slower cyclist is:
R₁ = 14mi/h
The rate of the other one is:
R₂ = 19mi/h
How to find the rate of each cyclist?We know that they start in the same location, then they travel in opposite directions each one with rates R₁ and R₂, the total distance betweem them after a time t is:
distance = (R₁ + R₂)*t
We know that one travels 5 mi/hour slower than the other, then we can write:
R₁ = R₂ + 5mi/h
And after t = 2 hours, the distance is 86 miles, then:
86mi = (R₂ + 5mi/h + R₂)*2h
Solving for R₂
86mi/2h = (2R₂ + 5mi/h)
43mi/h - 5mi/h = 2R₂
38mi/h = 2R₂
38mi/h/2 = R₂
19mi/h = R₂
Then R₁ is:
R₁ = 19mi/h - 5mi/h = 14mi/h
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NO LINKS!! URGENT HELP PLEASE!!!
What is Arc BD?
Answer:
x=7
Step-by-step explanation:
Central Angle: 124°
Inscribed angle: (7x+13)°
Since, the measure of the central angle that subtends the same arc of any inscribed angle is twice the measure of any inscribed angle that subtends the same arc.
By this :
½*Central Angle = insribed angle.
substituting value
½*124°=(7x+13)°
62°=(7x+13)°
7x=62°-13°
7x=49°
x=49/7
x=7
Now
Inscribed angle=(7*7+13)°=62°
Answer:
x = 7
Inscribed angle: (7x + 13)° = 62°
Step-by-step explanation:
The given diagram shows two chords of a circle where the inscribed angle measures (7x + 13)° and the intercepted arc measures 124°.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:
[tex]\begin{aligned}(7x + 13)^{\circ}&=\dfrac{1}{2} \cdot 124^{\circ}\\\\ (7x + 13)^{\circ}&=62^{\circ}\\\\7x+13&=62\\\\7x+13-13&=62-13\\\\7x&=49\\\\\dfrac{7x}{7}&=\dfrac{49}{7}\\\\x&=7\end{aligned}[/tex]
Therefore, the value of x is 7, and the measure of the inscribed angle is 62°.
CAN SOMEONE PLLSSS HELP
Answer: C
Step-by-step explanation:
The graph has not been translated. Only the slope changed and became less steep.
Originally the slope is m=1 for f(x)
After the slope is m=3/4 for g(x)
If the slope was bigger it would have gotten steeper but the slope is smaller so the slope made the line flatter, which is a rotation clockwise.
C is your answer. It describes all in explanation. It g(x) is less steep and rotated clockwise
Max is 10 years older than tom. in 7 years time, max will be twice as old as tom. find max's age now. (Would appreciate it if done by simultaneous equations)
Answer:
Step-by-step explanation:
M=t+10
M-10=t
---------------
In 7 years
M+7=2t
2t=2m-20
m=2m-20
+20. +20
-m. -m
20=m
(7 years from now_
current age=20-7=13
------------------
Check:
M=13
t=3
In 7 years m=20
t=10
20=2*10
20=20
-----------------
True
Draw the net and calculate the surface area .
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
Find the sum of squares of the deviations from the mean of series of ACT scores listed below 24,27, 16, 30, and 13
Answer:
the sum of the squares of the deviations from the mean is 210.
Step-by-step explanation:
To find the sum of the squares of the deviations from the mean, you first need to find the mean of the series:
Mean = (24 + 27 + 16 + 30 + 13) / 5 = 22
Now, find the deviation of each score from the mean:
24 - 22 = 2
27 - 22 = 5
16 - 22 = -6
30 - 22 = 8
13 - 22 = -9
Next, square each deviation:
2^2 = 4
5^2 = 25
(-6)^2 = 36
8^2 = 64
(-9)^2 = 81
Finally, add up the squared deviations:
4 + 25 + 36 + 64 + 81 = 210
Are there megamillion numbers that have a greater theoretical probability of being drawn? Which ones?
In a standard Mega Millions lottery, the probability of any specific number combination being drawn is the same as for any other combination. Each number has an equal chance of being drawn, regardless of the number itself.
The Mega Millions game involves selecting five numbers from a pool of 1 to 70. In addition, it involves selecting an additional Mega Ball number from a pool of 1 to 25. The order in which the numbers are drawn does not matter.
Therefore, all number combinations have an equal theoretical probability of being drawn. No specific number combinations have the highest theoretical probability of being drawn in the Mega Millions lottery.
Which choices are equivalent to the expression below?
3√8
A. √3.√12
B. √6. √24
C. 72
D. √6. √12
E √3. √24
F. √9. √8
Answer:
D
Step-by-step explanation:
We can manually evaluate all of them using a calculator.
3√8 is approximately 8.5
Now we will evaluate all the others.
A is equal to 6
B is equal to 12
C is 72 which is also not right
D is equal to 8.5
Therefore D is the right answer
The question asks for expressions equivalent to 3√8. After simplifying the expressions down, none of the given choices A, B, D, E, or F are equivalent to 3√8. Therefore, none of the choices are correct.
Explanation:The student's problem involves simplifying a mathematical expression involving square roots. The expression given is 3√8. To compare it against the other choices given, we can first simplify it. 8 can be rewritten as 2^3, so the square root of 8 is √(2^3), which equals 2√2. Therefore, 3√8 simplifies to 6√2.
Next, we can try to simplify the choices in the exact same manner. The expressions characterised by a multiplication between two square roots are equivalent only if their simplified form is the same as 6√2. By following these steps:
A. √3.√12 = √(3*12) = √36 = 6B. √6.√24 = √(6*24) = √144 =12D. √6.√12 = √(6*12) = √72 = 8.48 (approx)E. √3.√24 = √(3*24) = √72 = 8.48(approx.)F. √9.√8 = √(9*8) = √72 = 8.48(approx.)
Comparing these simplified equivalents to the original expression, none of the choices are equivalent to the expression 3√8 (=6√2).
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Please help me with my math assignment. Give brainliest.
Answer:
see explanation
Step-by-step explanation:
(a)
the area (A) of the sidewalk is calculated as
A = area of outer circle - area of inner circle
= πr₂² - πr₁² ( r₁ is the radius of inner circle and r₂ the radius of outer circle
= π × 11² - π × 9²
= 121π - 81π
= 40π cm²
(b)
using π ≈ 3.14 , then
A = 40π ≈ 40 × 3.14 = 125.6 cm²
exact value of tanpi/12
Answer:
0.004569293096
Step-by-step explanation:
Attached is the answer when plugged into a calculator.
Answer:
The value of tan pi/12 in decimal is 0.267949192. . .
Step-by-step explanation:
. Tan pi/12 can also be expressed using the equivalent of the given angle (pi/12) in degrees (15°). ∴ tan pi/12 = tan π/12 = tan(15°) = 2 - √3 or 0.2679491. . .
A baking dish is 6 inches wide and 6 inches long. If LeAnn pours liquid gelitan into the dishto reach a hieght of 2 inches, how many bubic inches of gelitan is that?
The volume of gelatin poured into the dish to reach a height of 2 inches is 72 cubic inches.
To find the volume of gelatin in the baking dish, we need to multiply the length, width, and height of the dish. Given that the dish is 6 inches wide, 6 inches long, and the desired height is 2 inches, we can proceed with the calculation.
The formula for calculating volume is:
Volume = Length × Width × Height
Substituting the given values, we have:
Volume = 6 inches × 6 inches × 2 inches
Multiplying the numbers, we get:
Volume = 36 square inches × 2 inches
Simplifying further:
Volume = 72 cubic inches
Therefore, the volume of gelatin poured into the dish to reach a height of 2 inches is 72 cubic inches.
In summary, to find the volume of gelatin in the baking dish, we multiplied the length, width, and height of the dish. The resulting calculation showed that the volume of gelatin poured into the dish to reach a height of 2 inches is 72 cubic inches.
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how do you workout map distance with given reality distance
The way to workout map distance with given reality distance is:
map distance/ground distance = map scale (1/n)
How to find the Map Distance?Map scale is expressed by reducing the numerator (map distance) to 1. You need to make sure the unit of measure for the distance is the same.
To calculate map distances using a given map scale and ground distance, do the following:
map distance/ground distance = map scale (1/n)
To find the actual distance between two points on a map, simply multiply the distance measured on the map by the scale of the map.
Here's what the scale means:
1:200,000 means:
1 cm on the map is actually 200,000 cm.
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. A box is on a table.
The area of the box in contact with the table is 1500 cm².
The pressure on the table is 28 newtons/m².
Work out the force exerted by the box on the table.
Give your answer correct to the nearest whole number.
Answer: We know that force = pressure * area
Step-by-step explanation:
Given that,
Pressure on the table = 28 Newton/m^2
Area of the box in contact with the table = 1500 cm^2
= 1500/100*100 m^2
= 0.15 m^2
Therefore, as per the formula of force;
Force exerted by the box = 28 Newton/m^2 * 0.15 m^2
= 4.2 Newton
So, force exerted by the box is approximately equal to 4 Newton.
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convert 4(cos(150 dgerees)+isin(150degrees)) into rectangular form
[tex]4( ~~\cos(150^o)+i\sin(150^o) ~~ )\implies 4\cos(150^o)~~ + ~~4i\sin(150^o) \\\\\\ 4\cdot \cfrac{-\sqrt{3}}{2}~~ + ~~4i\cdot \cfrac{1}{2}\implies -2\sqrt{3}~~ + ~~2i\implies \boxed{(-2\sqrt{3}~~,~~2)}[/tex]
