The truth value of a is False and after seeing the result of 1st statement b is true.
A mathematical statement like "3 is bigger than 4," "an infinite set exists," or "7 is prime" is referred to as a proposition.
A statement that is presumptively true is known as an axiom. Although there are several exceptions, mathematical logic can typically classify a claim as true or false given enough information (e.g., "This statement is false").
let p(x):x^2<=4
the domain for x is all positive integers (1, 2, 3, . . .).
(a) p(5)
p(5):25 not equal or less than 4
hence the truth value of a is False
(b) negation for x;p(x)
after seeing the result of 1st statement b is true.
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Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank? (1000 cubic cm = 1 liter).
The height of the water tank of the air cooler brought by Anu is 40 cm.
What is the meaning of Height?Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.
given,
Length = 50 cm
Width = 20 cm
Maximum tank volume = 40 liters = 40,000 cm3
Tank height?
Steps,
Tank volume = length x width x height
40,000 = 50 x 20 x height
40,000 = 1000 x height
Tank height = 40,000 : 1000
Tank height = 40 cm
So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.
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What statement describes a key feature of function G if g x equals x - 7
a. Y-intercept at 0, negative 7
b. Range of y < -7
c. Domain of x > -7
d. Horizontal asymptotic of y=-7
The statement that describes a key feature of function g if [tex]g(x)=e^x-7[/tex] is Horizontal asymptote of y= -7.
What is a horizontal asymptote?A horizontal line that is not a part of a function's graph but is essential because it directs the graph's x values is known as a horizontal asymptote.
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.
A line that is asymptotically sloped, vertical, or both has the equation x = a, y = a, or y = ax + b
In this instance, the declaration that enumerates the primary property of the function g if g(x) = [tex]e^x[/tex] - 7 is that the horizontal asymptote of y = -7.
This can be seen from the equation given.
Therefore option (d) is correct
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does the confidence interval provide convincing evidence that the two population proportions are equal? explain your answer. yes. because the interval is based upon two independent random samples, there is convincing evidence that the two population proportions are equal. no. even though 0 (no difference) is a plausible value for the difference there are many other plausible values in the interval that would suggest that the two proportions are not equal. no. because the interval contains 0, there is not convincing evidence that the two population proportions are equal. yes. because the interval contains 0, there is convincing evidence that the two population proportions are equal. no. because the conditions are not met, the interval cannot provide evidence that the two population proportions are equal.
No the confidence interval does not provide convincing evidence that the two population proportions are equal.
No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.
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No the confidence interval does not provide convincing evidence that the two population proportions are equal.
No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.
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Solve the following initial value problem:
dy/dt=t^2+1, t ≥ 0, y = 6 when t=0
The solution of the initial value problem is [tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.
In this case, the differential equation is given by:
dy/dt = t² + 1, t ≥ 0
with the initial value y = 6 when t = 0.
To solve this initial value problem, we can use the method of integrating factor.
We can find the integrating factor for this differential equation by using the formula:
[tex]= > e^{\intP(t)dt,[/tex]
where P(t) = t² + 1
So,
[tex]= > e^{\int P(t)dt} = e^{t^3/3 + t}[/tex]
By the product rule, we have:
[tex]= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})[/tex]
We can evaluate the integral on the right side using standard integration techniques, and we get:
[tex]= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)[/tex]
Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):
[tex]= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
To find the value of C, we can use the initial value y = 6 when t = 0:
6 = Ce⁰
So, C = 6.
Therefore, the solution to the initial value problem is:
[tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
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(a) must it be true that log f(n) = ⇥(log g(n))? prove or disprove.
No, it is not required to be accurate. The growth rates of the two functions can vary.
It's not necessary for log f(n) to equal log g(n). Depending on the equation's constants and the inputs to the two functions, the growth rates of the two functions may differ. For instance, log f(n) = 2 log n and log
g(n) = 3 log n,
which are not equal, if
f(n) = n2 and g(n) = n3.
In this instance, log f(n) is equal to (log n) and log g(n) to (log n3), indicating that the two functions grow at various rates. Likely not equal are log f(n) and log g(n) if
f(n) = n and g(n) = n2,
respectively. Log f(n) is defined as (log n) and log Therefore, the statement "log f(n) = (log g(n)" is not necessarily true.
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What point on the line 3x – y = 4 is closest to the point A(–2, 3)?
The closest point on the line 3x - y = 4 to the point A(-2, 3) is (4, 3).
The point on the line closest to point A can be found by finding the line that is perpendicular to the line 3x - y = 4 and passes through A, then finding the point of intersection between the two lines.
To find the perpendicular line, we can use the slope-point form of a line, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. The slope of a line perpendicular to the line 3x - y = 4 is the negative reciprocal of the slope of the line, which is undefined since the line 3x - y = 4 is a vertical line. Hence, the perpendicular line is a horizontal line with slope 0, and it passes through the point A(-2, 3). So, the equation of the line is y = 3.
The point of intersection of the two lines is the point closest to A. Solving the equations 3x - y = 4 and y = 3, we get the intersection point (x, y) = (4, 3).
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If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room? (5 points) a Length = 16 feet, width = 12 feet b Length = 10 feet, width = 8 feet c Length = 32 feet, width = 24 feet d Length = 14 feet, width = 12 feet
The correct option is C. Length = 24 feet, width = 18 feet
How to find the Length of a room?To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.
The calculation is as follows:
Since 2cm = 6 feet
So,
The length is = 4(6) = 24 feet
And, the width be = 3(6) = 18 feet
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A scale drawing of Julie's living room is shown below:
A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.
If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?
A)Length = 16 feet, width = 12 feet
B)Length = 10 feet, width = 8 feet
C)Length = 32 feet, width = 24 feet
D)Length = 14 feet, width = 12 feet
Solved If sin (????)=8/17, where 0 < ???? < pi/2 and cos (????)=5/13 |
The value of θ is approximately equal to 0.92729522.
What do you mean by sine?The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.
The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.
If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.
θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).
So, the value of θ is approximately equal to 0.92729522.
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The value of θ is approximately equal to 0.92729522.
What do you mean by sine?The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.
The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.
If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.
θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).
Therefore, the value of θ is approximately equal to 0.92729522.
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If the dot indicates the center of the circle, which equation must be true?
The true equation is m∠A + m∠B = 180°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Here, we have
Given: the dot indicates the center of the circle.
we have to find which equation is true.
"The angle formed by a diameter at the circumference is always a right angle (that is 90 degrees).
We concluded that the true equation is m∠A + m∠B = 180°
Hence, the true equation is m∠A + m∠B = 180°
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Unit 4 Mid Unit Assessment - Grade 6
Avery made a large pot of soup and she plans to divide the soup equally into smaller containers. If
the pot contains 30 cups of soup, describe one way to interpret 302 = 3 in this context.
(on the next question, you will be asked for a second interpretation)
Interpretation 1
Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.
Avery can interpret 302 = 3 by understanding that 30 is the total amount of soup to be divided, and 2 represents the number of equal parts she wants to divide the soup into. This means that Avery can divide the 30 cups of soup into 3 equal containers, each containing 10 cups of soup.
Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.
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find the length of AB
remember to write your awnser in 1 decimal place
Answer:
this can be solved using trigonometry
Find out the length of segment GF?
Answer:
8
Step-by-step explanation:
Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).
So 12 = 4+x, and x = 8.
Bob used these steps to evaluate 3m - 3 ÷ 3 for m = 8.
Complete the explanation about his error.
3 x 8 - 3 ÷ 3 = 24 - 3 ÷ 3
= 21 ÷ 3
= 7
"He did not apply the order of operations correctly. He should have performance the subtraction before the division. The correct answer is 23, not 7."
Bob did not apply the order of operations correctly. He should have performed the subtraction (3 - 3) before the division (÷ 3). The correct order of operations is to perform any calculations inside parentheses first, then perform any exponents, then perform any multiplication or division (from left to right), and finally perform any addition or subtraction (from left to right).
Applying the correct order of operations to the expression 3m - 3 ÷ 3, we get:
= 3 x 8 - 3 ÷ 3 = 24 - 1= 23Therefore, the correct answer is 23, not 7.
It is important to always apply the order of operations correctly in mathematical expressions to ensure that the correct answer is obtained. Failure to follow the correct order of operations can lead to incorrect answers and misunderstandings.
This question should be provided as:
Bob used these steps to evaluate 3m - 3 ÷ 3 for m = 8. Complete the explanation about his error.
3 x 8 - 3 ÷ 3 = 24 - 3 ÷ 3= 21 ÷ 3= 7He did not apply the order of operations correctly. He should have performance the _______ before the ______. The correct answer is _____, not 7.
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Average movie prices in a be united states, are in general lower than in other countries. it would cost $77.75 to buy three tickets in Japan plus 2 tickets in switzerland. Three tickets in switzerland plus two tickets in japan would cost $73.75. how much does an abt movie ticket cost in each of these countries?
The cost of Japan and Switzerland tickets are 17.15 dollars and 13.15 dollars respectively.
How to find the cost of each ticket in each country?it would cost $77.75 to buy three tickets in Japan plus 2 tickets in Switzerland. Three tickets in Switzerland plus two tickets in japan would cost $73.75.
Using system of equation,
let
x = cost of each ticket in Japan
y = cost of each ticket in Switzerland
Therefore,
3x + 2y = 77.75
2x + 3y = 73.75
Multiply equation(ii) by 1.5
3x + 2y = 77.75
3x + 4.5y = 110.625
subtract the equations
2.5y = 32.875
y = 32.875 / 2.5
y = 13.15 dollars
Hence,
3x + 2y = 77.75
3x = 77.75 - 2y
3x = 77.75 - 2(13.15)
3x = 77.75 - 26.3
x = 51.45 / 3
x = 17.15 dollars
Therefore,
cost of Japan ticket = 17.15 dollars
cost of Switzerland ticket = 13.15 dollar
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The _______ is responsible for absorbing the most UV radiation.
a.
troposphere
b.
stratosphere
c.
mesosphere
d.
thermosphere
Answer:
b. stratosphere
Step-by-step explanation:
The ozone layer, located in the stratosphere is responsible for absorbing the most UV radiation. This is because the ozone molecule (O3) is able to absorb UV radiation due to its molecular structure, specifically the presence of three oxygen atoms which allows it to efficiently absorb the UV-C radiation (the most damaging to living organisms). This protects life on Earth from harmful effects of UV radiation, such as DNA damage, skin cancer and other harmful impacts on plants and marine life.
Determine whether the following relation repreent y
a a function of x
5x3y=15
The given equation does not represent y as a function of x.
A relation is a function if for every unique x value, there exists only one unique y value. The equation 5x³y = 15 does not define a unique value for y for a given value of x, and therefore does not represent y as a function of x.
Function Of X, Y OutputThe equation 5x³y = 15 does not represent y as a function of x. A function must have exactly one output value for each input value, but this equation doesn't have the unique output restriction.
The equation 5x³y = 15 represents a 3-dimensional surface in the x-y-z plane, where z = 5x³y. It does not define y as a function of x, because for a given x there can be multiple values of y that satisfy the equation. To define y as a function of x, additional information, such as an equation that relates y and x in a one-to-one manner, is needed.
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Need the answer ASP
A bird flew 3/5 of a mile in one quarter of an hour. At this rate how far will the bird fly in 2 1/2
hours?
Answer:
60 miles
Step-by-step explanation:
We know
3/5 = 0.6
one-quarter of an hour = 15 minutes
So, we know
0.6 mile in 15 minutes
2 1/2 hours = 150 minutes
0.6 times 10 = 60 miles
So, the bird flies 60 miles in 2 1/2 hours.
Find x.
A) 1.6
B) 1
C) 0.9
D) 2
option:-
[tex] \boxed { \blue{\rm{D ) \: 2 \: }}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{8x - 1 = 3x +9}[/tex][tex] \: [/tex]
[tex] \rm{8x - 3x = 9+1}[/tex][tex] \: [/tex]
[tex] \rm{5x = 10}[/tex][tex] \: [/tex]
[tex] \rm {x = \cancel{ \frac{10}{5} }}[/tex][tex] \: [/tex]
[tex] \underline {\boxed{ \rm {\red{ \bold{{x = 2}}}}}}[/tex][tex] \: [/tex]
hope it helps!:D
Triangle ABC is graphed on a coordinate plane, as shown.
The coordinates of the pre-image are A(2,2) B(4,4) and C(-4,2). If the triangle was dilated by a scale factor of 2 with a center of dilation at the origin what are the coordinates of the vertices of ΔA′B′C′?
The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)
What is center of dilation?
A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.
The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.
A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)
B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)
C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)
So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).
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Surveys have become an integral part of our lives. Because it is so important that every citizen have the ability to interpret survey results, surveys are the focus of this project.
The Gallup Poll recently conducted a survey of 2,558 U. S. Adults and found that 46% of those surveyed have dealt with substance abuse in their families
The minimum sample size required will be 231.
What is Sample Size?
The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.
The sample size(n) is 2558.
p = 46%
= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives
1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).
Hence, the confidence interval is given by
= [0.46 ± 0.02]
= [0.44, 0.48]
As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48
2) Margin of error = E
= 0.02
3) Null hypothesis 0.4 percent of US people have dealt with substance misuse in their families.
P = 4/10
= 0.4
Alternative hypothesis More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.
P > 0.4
95% confidence interval is - [0.44, 0] 48]
We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)
As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.
As a result, the newspaper could make the assertion.
4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.
5) The required minimum sample size is given by:
P is the specified value of population proportion under the null hypothesis = 0.4
= (1.96/0.02)² (0.4) (1 - 0.4)
= [tex]98^{2}[/tex] (0.4) 0.6
= 230.5
So, the minimum sample size required will be 231.
Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.
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The minimum sample size required will be 231.
What is Sample Size?
The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.
The sample size(n) is 2558.
p = 46%
= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives
1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).
Hence, the confidence interval is given by
= [0.46 ± 0.02]
= [0.44, 0.48]
As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48
2) Margin of error = E
= 0.02
3) Null hypothesis 0.4 percent of US people have dealt with substance misuse in their families.
P = 4/10
= 0.4
Alternative hypothesis More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.
P > 0.4
95% confidence interval is - [0.44, 0] 48]
We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)
As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.
As a result, the newspaper could make the assertion.
4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.
5) The required minimum sample size is given by:
P is the specified value of population proportion under the null hypothesis = 0.4
= (1.96/0.02)² (0.4) (1 - 0.4)
= (0.4) 0.6
= 230.5
So, the minimum sample size required will be 231.
Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.
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A 19,000 car has been reduced inpri by 4%. what is the new price of the car
The new price of the car after the 4% reduction is $18,240
What is the new price of the car?Percentage is simply number or ratio expressed as a fraction of 100.
Given that,
Initial price of the car = $19,000Percentage of reduction = 4%New price of the car = ?To determine the new price of the car after reduction;
New price = Initial price × ( 100% - 4% )
New price = Initial price × ( 96% )
Note that 96% is the same as 96/100
New price = $19,000 × 96/100
New price = $19,000 × 0.96
Multiply $19,000 and 0.96
New price = $18,240
Therefore, the new price is $18,240.
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Sum of Rational Numbers
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
Which expression is modeled by the number line?
The expression modeled by the number line: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 is the sum of the first ten negative integers. The expression can be written as $-1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10$
What is rational number ?Any number that can be written as a ratio of two integers, the numerator and the denominator, is said to be rational.The denominator cannot be equal to zero, and the ratio must be reduced to its lowest terms. For example, the fraction 2/4 can be reduced to 1/2, so 1/2 is a rational number. Decimal representation of a rational number is either finite or repeating. Rational numbers include both positive and negative fractions, as well as integers. They can be added, subtracted, multiplied, and divided just like any other number. All rational numbers form a dense set on the number line, meaning that between any two rational numbers, there is always another rational number. The set of rational numbers is a subset of the set of real numbers, which also includes irrational numbers like √2 or π.It represents the sum of the first ten negative integers from -1 to -10.To learn more about rational number refer:
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Gillian has a board that is 2 meters long. She cuts the board into 5 equal pieces, and then measures them with a tape measure that only measures in customary units. To the nearest inch, what is the length of each piece?
The length of each piece to the nearest inch is 16 inches.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that,
Total length of the board = 2 meters
Gillian cuts the board into 5 equal pieces.
Length of each piece of the board in meters = 2 / 5 = 0.4 meter
We know that,
1 meter = 39.37 inches
0.4 meter = 39.37 × 0.4
= 15.748 inches
≈ 16 inches
Hence the length of each piece of the board is approximately 16 inches.
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How To Convert 36.5 °C to °F?
The 36.5 °C when converted to Fahrenheit it is equal to 97.7 °F.
How to convert Celsius to Fahrenheit?When measuring temperature, different units of measurement, such as Celsius and Fahrenheit, can be used. Celsius (°C) is a unit of measurement in the metric system, which is widely used in many countries worldwide, whereas Fahrenheit (°F) is a unit of measurement in the imperial system, which is primarily used in the United States.However, the conversion requires the following expression:Temperature in degrees Fahrenheit = [Temperature in degrees Celsius * 1.8] + 32As a result, we can use the expression to convert a 36.5 °C temperature to a Fahrenheit temperature;Temperature (degrees Fahrenheit) = (36.5 * 1.8) + 32°F temperature = 65.7 + 32= 97.7
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Nagma runs around a rectangular park 180m long and 120m wide at the rate of 7. 5km/hr. In how much time will she complete five rounds?
pls answer my question as I have my exam tomorrow
The time that Nagma takes to complete five rounds is 0.4 hours or 24 minutes.
What is the meaning of Time?Travel time is the total time required to pass a certain length of road.
Given,
Length = 180m
Width = 120 m
Speed = 7.5 km/hr
Time of five rounds?
Steps,
The first step that must be done is to find the travel time for one round
Distance of one round = 2(length + width)
Distance of one round = 2(180 + 120)
Distance of one lap = 3 (300)
Distance of one round = 600 m = 0.6 km
Time needed to reach 5 rounds
Time = 5 (distance : speed)
Time = 5 (0.6 : 7.5)
Time = 0.4 hours = 24 minutes
So, the time needed to complete five rounds is 0.4 hours or 24 minutes.
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a freight train is leaving from hanford is 14 mph slower than the passenger train which also leaves from hanford. the passenger train travels 400 miles in the same amount of time that the freight train travels 330 miles. what is the speed of the passenger train?
The speed of the passenger train is 80 mph.
Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.
Therefore, we can write the equation:
400/p = 330/f
Expanding the second term and substituting "p" for "f" + 14:
400/p = 330/(p - 14)
Cross multiplying and simplifying:
400 * (p - 14) = 330 * p
Expanding both sides:
400p - 5600 = 330p
Subtracting 330p from both sides:
70p = 5600
Dividing both sides by 70:
p = 80 mph
So the speed of the passenger train is 80 mph.
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The speed of the passenger train is 80 mph.
Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.
Therefore, we can write the equation:
400/p = 330/f
Expanding the second term and substituting "p" for "f" + 14:
400/p = 330/(p - 14)
Cross multiplying and simplifying:
400 * (p - 14) = 330 * p
Expanding both sides:
400p - 5600 = 330p
Subtracting 330p from both sides:
70p = 5600
Dividing both sides by 70:
p = 80 mph
So the speed of the passenger train is 80 mph.
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How do I solve (x^2 + 4x + 8)(2x - 1) Please do step by step explanation. So I can learn
The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(x^2 + 4x + 8)(2x - 1)
now, we know,
(a+c)*b = ab+cb
so, we get,
⇒2x^3+8x^2+16x-x^2-4x-8
⇒2x^3+7x^2+12x-8
Hence, The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.
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How do you convert 1500 Meter (m) to Mile US (mil)?
Utilize the following formula to convert metres to miles: m/1,609.344=mi (meters divided by 1,609.344 equals miles).
Is the 1500m the equivalent to the mile?Since 1896, the Summer Olympics have featured the event, and since 1983, the World Championships in Athletics have included it. It is equivalent to 15 to 16 miles or 1.5 kilometres.To convert a mile's worth into metres, all you have to do is multiply it by 1609.344. That simple, indeed.The statutory mile, which has a length of 5,280 feet, is one example of a mile (1.609 km). Its original unit of measurement was the mille passus, or "thousand paces," which was equivalent to 5,000 Roman feet.For instance, if it's 11 a.m. Eastern Daylight Saving Time in Washington, D.C., it means it's 1500 hours in Zulu time/UTC. See the legend in the following paragraph.To learn more about metres refer to:
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Here are the ingredients to make strawberry trifle for 4 people
Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.
How to find the amount of ingredients for three people?To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:
1. We must make a rule of three to find the exact amounts of each ingredient as shown below:
4 - 120g strawberry jelly3 - ?3*120g/4=90g strawberry jelly.4 - 83 - ?3 * 8 / 4 = 6 sponge fingers4 - 420 ml custard3 - ?3*420ml/4=315ml custard.4 - 180g tinned fruit3 - ?3 * 180g / 4 = 135g tinned fruitAccording to the above, the following ingredients are needed for this recipe:
90g strawberry jelly.6 sponge fingers315 ml custard135g tinned fruitNote: This question is incomplete because there is some information missing. Here is the complete information:
120g strawberry jelly
8 sponge fingers
420ml custard
180 g tinned fruit
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I need help with this math equation. It is Comparing Functions.
1. B has the greater rate of change.
2. A has the greater rate of change.
3. B has the greater rate of change.
How to obtain the rate of change?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the initial value assumed by the output variable.For the rate of change, we must look at the slope of each function.
From the graph or from a table, the slope is given dividing the change in y by the change in x.
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