Yes ,inclination in between 4in / 15 in < 4in / 18 in
What is incline?An inclined plane, also known as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other. It can be used to lift or lower a load.
What is horizontal and vertical?The horizontal line in coordinate geometry is the line perpendicular to the x-axis, and the vertical line is the line perpendicular to the y-axis. Horizontal lines and vertical lines will be parallel to the x-axis and the y-axis, respectively. As a result, lines that share at least one point are perpendicular to one another when they are drawn.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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Yes, inclination in between 4in / 15 in < 4in / 18 in
What is incline?A flat supporting surface that is inclined at an angle from the vertical direction with one end higher than the other is referred to as an inclined plane or a ramp. A load may be raised or lowered using it.
What is horizontal and vertical?In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis. Vertical and horizontal lines will be perpendicular to the x- and y-axes, respectively. As a result, when lines are drawn, they are perpendicular to one another if they share at least one point.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6 feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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Two real numbers are defined as: a=0444444444444 b=0.354355435554 Determine whether each number is rational or irrational. Is the product of a and b rational or irrational? Justify your answers. Enter your answers and your justifications in the box provided.
The a is rational , b is irrational and product of a and b is rational.
The number a=0.444444444444 is rational
Because it can be expressed as the ratio of two integers.
a = 4/9
The number b=0.354355435554 is irrational
Because it cannot be expressed as the ratio of two integers.
It has an infinite non-repeating decimal expansion.
To determine whether the product of a and b is rational or irrational, we can simply multiply them together:
a × b = (4/9) × 0.354355435554
= 0.158919191574
This product is a rational number, because it can be expressed as the ratio of two integers.
Hence, a is rational , b is irrational and product of a and b is rational.
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9. A classroom table has a mass of 24 kg. Pulling with a force of 36 N, a student moves the table to the other side of the classroom. How much did the table accelerate? Record your answer and fill in the bubbles. Be sure to use the correct place value.
The acceleration of this classroom table is equal to 1.5 meter per seconds square.
How to calculate the acceleration of this classroom table?From Newton's Second Law of Motion, the force exerted on the classroom table is modeled or represented by this mathematical equation (formula):
F = ma
Where:
F represent the force.m represent the mass.a represent the acceleration.By making "acceleration" the subject of formula, we have the following:
Acceleration, a = force/mass
Acceleration, a = 36/24
Acceleration, a = 1.5 meter per seconds square.
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A. Find the average rate of change over the interval (-1, 2] for each function. Show all steps and work for credit.
B. Which function has the greatest average rate of change over the interval [1, 2]
the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2
what is function and average rate?A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.
According to given informationFor the function f(x) = 2x + 3:
Let x1 = -1 and x2 = 2
f(x1) = 2(-1) + 3 = 1
f(x2) = 2(2) + 3 = 7
The average rate of change is:
[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2
Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.
For the function g(x) = x^2 - 1:
Let x1 = -1 and x2 = 2
g(x1) = (-1)^2 - 1 = 0
g(x2) = 2^2 - 1 = 3
The average rate of change is:
[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1
Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.
For the function h(x) = 2^x + 1:
Let x1 = -1 and x2 = 2
h(x1) = 2^(-1) + 1 = 1.5
h(x2) = 2^2 + 1 = 5
The average rate of change is:
[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)
Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.
b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.
Let's assume the functions are f(x), g(x), and h(x).
The average rate of change for f(x) over the interval [1, 2] is:
[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2
The average rate of change for g(x) over the interval [1, 2] is:
[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2
The average rate of change for h(x) over the interval [1, 2] is:
[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2
Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.
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Dave is buying popcorn and sodas for his son and his five friends that he brings to the movies (Six kids total). The needs to buy at least one of the two items for each of the six. Popcorn costs $2. 50 per bag and sodas cost $4. 00 each. Dave can spend at most $40. Lets represent the number of sodas he buys and p represent the number of bags of popcorn he buys
The system of equations that models this scenario is:
p + s ≥ 62.50p + 4.00s ≤ 40How can it be modeled using a system of equations?Let p be the number of bags of popcorn.
Let s be the number of sodas Dave buys.
Since Dave needs to buy at least one of each item for all six kids, we have:
p + s = 6 -----(1)
Given:
The cost of a bag of popcorn is $2.50.
The cost of a soda is $4.00.
The total cost of Dave's purchase can be expressed as:
2.50p + 4.00s = C -----(2) where the C is the total cost of Dave's purchase.
Since Dave can spend at most $40, we have:
2.50p + 4.00s ≤ 40 -----(3).
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At a company a copy machine prints 175 pages in 5 minutes. if the number of pages printed is proportional to the time in minutes what is the unite rate
Answer:
The unit rate is 35 pages per minute.
Step-by-step explanation:
Divide 175 by 5, or 175/5 to get the unit rate, which is 35.
Given: Circle with center D.
Construct: Equilateral triangle ABC so that points A, B, and C are on circle D.
The circle with equilateral triangle is constructed.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Here we need to construct the circle with center D.
Now we know that in equilateral triangle , side length of the all sides are equal.
Then, AB=BC=CA.
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A rectangle is seven times as long as it’s width. One way to write an expression to find the perimeter would be m+7m+m+7m. Write the expression in two other ways.
Step-by-step explanation:
Perimeter = 2 m + 2 * 7m
Perimeter = 2 ( m + 7m)
Perimeter = 2m + 14m
Perimeter = 16 m Pick any of them
dont understand what m supposed to do at the radius = diameter/2 part
Step-by-step explanation:
Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle
the average score of 100 students taking a statistics final was 70, with a standard deviation of 7. assuming a normal distribution, what test score value separates the top 2.5% of the students from the rest of the students? (show your work)
The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.
To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.
z = (x - μ) / σ
To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.
Presently ready to utilize the z-score equation to unravel for x:
1.96 = (x - 70) / 7 Increasing both sides by 7, we get:
x - 70 = 13.72
Including 70 to both sides, we get:
x = 83.72
Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.
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please help me IXL have to achieve a smart score of 80 part 1
The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.
What is a linear equationA linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.
given the slope m = -3/5 and y intercept b = 6, we can write the equation as;
y = (-3/5)x + 6
y = -3x/5 + 6.
Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.
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Suppose On a Sunny Day the Temperature decreases 5.4 F° for each 1,000- foot rise in elevation. If the temperature at the base of a 3,000 foot mountain is 27 F°, what is the temp at the mountain summit?
GUYS PLS EXPLAINNN
Therefore, the temperature at the summit of the 3,000-foot mountain on a sunny day is estimated to be 10.8 F°.
What is equation?In mathematics, an equation is a statement that indicates the equality of two expressions. An equation typically contains one or more variables, which are placeholders for unknown values or quantities. The variables can take on different values, and the goal is often to find the values that satisfy the equation.
Here,
Let's start by calculating the rate of change of temperature with respect to elevation:
=-5.4 F° / 1,000 ft
This means that for every 1,000-foot increase in elevation, the temperature will decrease by 5.4 F°.
Next, we can calculate how much the temperature will decrease from the base of the mountain to the summit:
3,000 ft / 1,000 ft = 3
This means that the elevation difference between the base of the mountain and the summit is 3,000 - 0 = 3,000 ft.
So, the temperature decrease from the base to the summit is:
-5.4 F° / 1,000 ft * 3,000 ft = -16.2 F°
This means that the temperature at the summit will be:
27 F° - 16.2 F° = 10.8 F°
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What is the equation of the trend line in
the scatter plot?
Use the two yellow points to write the
equation in slope-intercept form. Write
any coefficients as integers, proper
fractions, or improper fractions in
simplest form.
Answer:
y= 7/3x -7
Step-by-step explanation:
Slope is 7/3 (rise/run or up seven over 3) and when you continue the graph the line will eventually hit your y-intercept at -7
A piece of metal with a mass of 611 g is placed into a graduated cylinder that contains25.1 mL of water, raising the water level to 56.7 mL. What is the density of the metal?A) 2.70 g/cm3 B) 7.13 g/cm3 C) 8.96 g/cm3 D) 10.5 g/cm3 E) 19.3g/cm3
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
The given mass of the metal is 611 g and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal volume can be evaluated by subtracting the initial volume from the final volume of water released by the metal.
Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL
Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
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What is the surface area of this composite solid? Show your work.
According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.
What is the surface area of the composite solid?To calculate the surface area of the composite solid we have to perform the following procedure:
Sides (a) area
4 * 3 = 1212 * 2 = 24Sides (b) area
7 * 3 = 2121 * 3 = 63Face (c) area
3 * 4 / 2 = 66 * 2 = 12Base area
4 * 7 = 28
Total surface area
To calculate the total surface area we have to add the value of each face as shown below:
28 + 12 + 63 + 24 = 127According to the above, the surface area of this solid would be 127.
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please solve and explain
LaTisha's calculation of the distance for the brake anchor placement is incorrect because she didn't take into account the height at which the cable is attached to the starting tree.
What is the correct distance ?The bungee cord is attached 16 feet above the ground, which will also contribute to the length of the cable needed to reach the ending tree.
To correctly calculate the distance, we can use the Pythagorean theorem, considering the height (16 feet) and the length of the stretched bungee cord (24 feet + 18 feet = 42 feet). Let's denote the horizontal distance from the base of the ending tree to the brake anchor as 'd'. We have:
d² + 16² = 42²
Now, we can solve for d:
d² + 256 = 1764
d² = 1508
d = √1508 = 38.8 feet (rounded to one decimal place)
The brake anchor should be placed approximately 38.8 feet from the base of the ending tree.
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Q3. (Calculator)
Abox contains only red, blue and green pens.
The ratio of red pens to blue pens is 5:9.
The ratio of blue pens to green pens is 1:4.
Calculate the percentage of pens that are blue.
The percentage of pens that are blue =18%
Let's assume that r represents the red pens, b represents the blue pens and g represents the green pens.
From the statements we can observe that the blue appears in both ratio.
The ratios are,
r:b=5:9 and b:g=1:4
Consider ratio b:g,
b:g
= 1:4
= (1×9) : (4×9)
=9:36
i.e., b:g = 9:36 and r:b = 5:9
So, we can conclude that, b=9, g=36, r=5
so, the total number of pens would be,
n = b + g + r
n = 9 + 36 + 5
n = 50
Now we need to find the percentage of pens that are blue.
Using percentage formula,
p = (b/n) × 100
p = (9/50) × 100
p = 18%
Hence, the percentage of blue pens are 18%.
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refer to exercise 3.91. in this exercise, we determined that the mean and variance of the costs necessary to find three employees with positive indications of asbestos poisoning were and , respectively. do you think it is highly unlikely that the cost of completing the tests will exceed ?
The probability that the cost will exceed $600 is approximately 0.057, or 5.7%. which is relatively small, so it is highly unlikely that the cost of conducting the test will exceed $600.
we need to use the information provided to calculate the probability that the test execution cost will exceed a certain value.
Let X be the cost of conducting a test to find three of her employees with positive signs of asbestos poisoning. From the information provided, we can see that:
E(X) = $550
Var(X) = $500
Using these values, we can standardize X to a standard normal distribution.
Z = (X - E(X)) / sqrt(Var(X))
= (X - $550) / square meters ($500)
Accepting that the costs take after an ordinary conveyance, able to utilize the standard ordinary conveyance to compute the likelihood that the fetched surpasses a certain esteem. For case, to find the likelihood that the taken toll surpasses $600, we are able to compute:
P(X > $600) = P(Z > ($600 - $550) / square meters ($500))
= P(Z > 1.58)
Using a standard normal table or calculator, we find that P(Z > 1.58) is approximately 0.057. hence, the probability that the cost will exceed $600 is approximately 0.057, or 5.7%.
This likelihood is generally little, so it is profoundly impossible that the fetch of conducting the test will surpass $600.
Be that as it may, the precise limit for what is considered exceedingly improbable may change depending on the setting and the particular criteria utilized.
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The graph of EFG is shown. Graph the image of EFG after translation of 3 units left 1 unit down write the coordinates of the image
The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).
How to translate an image ?To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.
To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.
For point E (1, 4):
E' = (1 - 3, 4 - 1) = (-2, 3)
For point F (-1, 1):
F' = (-1 - 3, 1 - 1) = (-4, 0)
For point G (2, -1):
G' = (2 - 3, -1 - 1) = (-1, -2)
The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).
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put on pair of brackets into each calculation to make it correct
a. 6×7-5 +4= 16
b. -2[tex]x^{2}[/tex]+24÷12-4=2
(a) The simplified and correct expression is (6×7)-(5 +4) = 16
(b) The simplified and correct expression is (-2x²) + (24÷12)-4 = 2
What is the simplified expression?
a. 6×7-5 +4= 16
In this calculation, we need to use brackets to ensure the correct order of operations, which is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).
Without brackets, the calculation would be evaluated as follows:
6×7-5 +4 = 42-5 +4 (applying multiplication first)
= 37 +4 (applying subtraction)
= 41 (applying addition)
However, the desired result is 16. To achieve this, we can use brackets to group the addition and subtraction operations together, like this:
(6×7)-(5 +4) = 42 - 9 (applying addition within the brackets first)
= 33 (applying subtraction)
b. -2x²+24÷12-4=2
Similarly, in this calculation, we need to use brackets to ensure the correct order of operations.
Without brackets, the calculation would be evaluated as follows:
-2x²+24÷12-4 = -2x²+2-4 (applying division first)
= -2x²-2 (applying addition and subtraction)
However, the desired result is 2. To achieve this, we can use brackets to group the division and subtraction operations together, like this:
-2x²+(24÷12)-4 = -2x²+2-4 (applying division within the brackets first)
= -2x²-2 (applying addition and subtraction)
By adding brackets to each calculation to ensure the desired order of operations, we arrive at the correct results of 16 and 2, respectively.
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PLEASE HELP!!!
A principal of $4200 is invested at %8 interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$10,244.14 after 12 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
A = the final amount of the investment
P = the principal amount ($4200 in this case)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (once annually in this case)
t = the number of years the money is invested (12 years in this case)
Substituting the given values into the formula, we get:
A = 4200(1 + 0.08/1)^(1*12)
A = 4200(1.08)^12
A = 4200(2.44140625)
A = $10,244.14 (rounded to the nearest cent)
1/4 exponent 4 equal to in fraction form
Answer:
(1/256)
Step-by-step explanation:
[tex](\frac{1}{4})^{4} = \frac{1^{4} }{4^{4} } = \frac{1}{256}[/tex]
Using laws of exponents I distributed the exponent to the fraction and solved.
Is 409  greater or less than 1.008
Answer:
409 > 1.008
Step-by-step explanation:
409 is greater than 1.008
A population has a mean μ=135 and a standard deviation Ï=28. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=57.
A population has a mean μ=135 and a standard deviation Ï=28.
The mean of the sampling distribution of sample means is equal to the population mean, that is 135.
The standard deviation of the sampling distribution of sample means can be calculated by using the formula
SE = Ï /[tex]\sqrt{n}[/tex]
Where Ï is the population standard deviation and n is the sample size.
By putting the given values we get
SE = 28 / [tex]\sqrt{57}[/tex] = 3.7
Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.
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PLEASE HELP ME ITS URGENT MY GRADE NEEDS HELP! THIS IS MULTIPLE CHOICE QUESTION!
Which ordered pairs are solutions to the inequality 2x+3y≥−1?
Select each correct answer.
Responses
(0, −1)
begin ordered pair 5 comma negative 1 end ordered pair
(−2, 1)
begin ordered pair negative 2 comma 1 end ordered pair
(0, 1)
begin ordered pair 0 comma 1 end ordered pair
(−6, 0)
begin ordered pair negative 6 comma 0 end ordered pair
(2, −1)
Answer:
b, c, d, f
Step-by-step explanation:
Which ordered pairs are solutions to the inequality?
2x+3y≥−1?
a≥b means that A must be equal to or greater than B.
Let's do this the long, but easy way, by plugging it in!
(x,y)
a. (0,-1) -> -3≥-1 -> false
b. (5,-1)-> 7≥-1 -> true
c. (-2,1) -> -1≥-1 -> true
d. (0,1) -> 3≥-1 -> true
e. (-6,0) -> -12≥-1 - > false
f. (2,-1) -> 1≥-1 -> true
Let me know if it is incorrect!
- a friendly 8th grader :)
WHAT IS THE RANGE OF THIS PIECEWISE FUNCTION?
The given piecewise function has a range of:
Range = {46, 48, 50, 52, 54, 56}.
What is range of a function?The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.
It is, in other words, the entire set of values that the function is capable of returning as its result.
From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.
These values correspond to the y-intercepts of each of the line segments in the graph.
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can someone js help me w these questions
Answer:
a=60 (12*5=60)
b=7 (45/9=5 5+2=7)
c=62
d=25 (11*5=55 55-30=25)
Change the subject of each formula to the letter given in brackets.
Here he formula for v is:
v = √(2gh)
What is meant by the term formula?
A formula is a mathematical relationship or rule that is expressed using symbols and mathematical operations. It is used to represent a relationship between quantities or to calculate a value based on given variables or inputs. Formulas are often used in various branches of mathematics, science, and engineering.
According to the given information
To change the subject of the formula mgh = (1/2)mv² to v, we need to isolate v on one side of the equation.
First, we can multiply both sides of the equation by 2 to eliminate the fraction:
2mgh = mv²
Next, we can divide both sides of the equation by m:
(2mgh) / m = v²
Simplifying the left side, we get:
2gh = v²
Finally, we can take the square root of both sides of the equation to solve for v:
v = √(2gh)
Therefore, the formula for v is:
v = √(2gh)
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If Joanne has three hours and 45 minutes before swim practice, she wants to go to the store which will take 220 minutes. She also wants to take her brother to the park for 230 minutes which activity does Joanne have time to do before practice
please help asap!! i need the help
Answer:
Step-by-step explanation:
angle L is 106 degrees
x= 2
angle LMK is 37 degrees
its equal, you can check by adding up all the angles to 360 degrees
Think of a number. The L C M of this number and 42 is 126. If the number lies between 60 and 70, what is the number
The LCM of 63 and 42 is 126 where 63 is the required number lying in between 60 and 70.
Let the missing number be x.
The number x lies in between 60 and 70.
The LCM ( Least Common Multiple) refers to the least value that is divisible by any two (or more) numbers.
Here LCM of x and 42 is 126.
Simplifying 126 we can write it as,
126 = 2*3*21
Thus, one of the number having 126 is as multiple is 42 (as already given).
The other number, that is x, having 126 as multiple lying between 60 and 70 is,
x = 3*21 = 63
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