Answer:
Ans = 8
Step-by-step explanation:
because -- is + and −−√70 is positive
so square root =8.366600265340757
and 8 is bigger as 8.366600265340757 is a decimal number.
At the grocery store, students measure the weight of three drinks in ounces. How many more ounces are the of water than orange juice?
Orange juice 7.9
Water 13.4
Milk 8.5
Answer:
2
Step-by-step explanation:
literally just 2 it's quite simple
in the school cafeteria 6 people can sit together at 1 table. if 2 tables are placed together end to end in a row 10 people can sit together. if 3 tables are placed together in a row how many can be seated? if 4 tables are placed together in a row how many people can be seated? if 5 tables are placed together in a row how many people can be seated? what patterns do you notice?
write an equation that would help find the number of people seated for any number of tables. show all your mathematical thinking giving 40 points and brainliest plss helpp
Answer:
First, we can use the information given to find out how many people can be seated at one table:
One table can seat 6 peopleNext, we can use the information given to find out how many people can be seated in a row of tables:
Two tables can seat 10 peopleTherefore, one row of tables can seat 5 people per tableUsing this information, we can find out how many people can be seated in a row of any number of tables:
Let x be the number of tables placed together in a rowOne row of x tables can seat 5x peopleSo, if 3 tables are placed together in a row, 15 people can be seated. If 4 tables are placed together in a row, 20 people can be seated. If 5 tables are placed together in a row, 25 people can be seated.
The pattern we notice is that the number of people seated in a row of tables increases by 5 for each additional table added.
To summarize, the equation that would help find the number of people seated for any number of tables is:
Number of people seated = 5x, where x is the number of tables placed together in a row.
Answer:
we are given that
6 people can sit together at 1 rectangular table.
2 tables are placed together, 10 people can sit together.
14 people can sit if three tables are put together.
It mean we get a sequence
6,10,14..........
So its making an arithmetic progression, where
First term=a=6
Common difference
Number of terms=number of table
As we know the nth term is given by the formula
Hence 402 people can sit
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2(2x-5)=-18 solve the equation algebraically. show all work
Answer:
Step-by-step explanation:
2(2x-5) = 18 (FOIL)
4x-10=18
4x = 28
x= 7
Answer:
x = -2
Step-by-step explanation:
2(2x - 5) = -18
Divide both sides by 2.
2x - 5 = -9
Add 5 to both sides.
2x = -4
Divide both sides by 2.
x = -2
To solve the problem using these steps, what are the dimensions of the rectangle he should draw? on a coordinate plane, parallelogram a b c d has points (1, negative 1), (3, 2), (1, 3), and (negative 1, 0). 2 units by 4 units 3 units by 2 units 4 units by 4 units 5 units by 6 units
As per the given coordinates, dimensions of the rectangle are √13 x √13.
One way to do this is to find the distance between two parallel sides of the parallelogram. In this case, we can look at sides AB and CD, which are parallel to each other.
The distance between points A and B is the
=> √((3-1)² + (2-(-1))²) = √13
which simplifies to the square root of 13. Similarly, the distance between points C and D is the
=> √((1-(-1))² + (3-0)²) = √13.
Therefore, the length of the rectangle is the distance between sides AB and CD, which is the square root of 13.
Therefore, the width of the rectangle is 2 units. So the dimensions of the rectangle are 2 units by the square root of 13 units.
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Answer:
4 units by 4 units
Step-by-step explanation:
i got it correct on edg :)
NEED HELP PLEASE HELP
Answer: B --3/2
Step-by-step explanation:
-4,8 TO -2,5
You would go down -3 steps first
Then you would go 2 steps.
Not sure if this is right but hopefully it works :D
consider using a z test to test h0: p 5 .6. determine the p-value in each of the following situations. a. ha:p..6,z51.47 b. ha:p,.6,z522.70 c. ha:p?.6,z522.70 d. ha:p,.6,z5.25
a) P-value = P(z<1.47) = 0.9292.
b) P-value = P(z>2.70) = 0.0036.
c) P-value = 2 × P(z>2.70) = 0.0072.
d) P-value = P(z>2.5) = 0.0062.
Z-test is a statistical test for the null hypothesis, which refers to the population mean, where the population standard deviation is known. P-value represents the probability value for any hypothesis, where a small p-value indicates that the null hypothesis is less accurate.
P-value, for the given values of z-test is calculated as follows: a) For ha: p < .6, z=1.47The p-value for this hypothesis test is calculated as follows: P-value = P(z<1.47) = 0.9292. Therefore, the P-value is 0.9292. b) For ha: p > .6, z=2.70The p-value for this hypothesis test is calculated as follows.
P-value = P(z>2.70) = 0.0036. Therefore, the P-value is 0.0036.c) For ha: p ≠ .6, z=2.70The p-value for this hypothesis test is calculated as follows: P-value = 2 × P(z>2.70) = 0.0072.
Therefore, the P-value is 0.0072.d) For ha: p > .6, z=2.5The p-value for this hypothesis test is calculated as follows: P-value = P(z>2.5) = 0.0062. Therefore, the P-value is 0.0062.
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The perimeter of a rectangular map of the world is 270 cm. It is 90 cm in height. How wide is it?
Answer:
The perimeter of a rectangle is given by:
P = 2(L + W)
where P is the perimeter, L is the length, and W is the width.
In this case, we know that P = 270 cm and L = 90 cm, so we can solve for W as follows:
270 = 2(90 + w)
Divide both sides by 2:
135 = 90 + w
Subtract 90 from both sides:
w = 45
Therefore, the width of the map is 45 cm.
Step-by-step explanation:
Solution of inequality 1/(x - 5) < 3 is
Step-by-step explanation:
1/(x - 5) < 3
1 < 3(x - 5)
1/3 < x - 5
1/3 + 5 < x
5 1/3 = 16/3 = 5.33333... < x
or
x > 5 1/3
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
To find the perimeter of a polygon, we add up the lengths of all the sides. In this case, we have a quadrilateral with sides of length y+8, y+7, y+7, and y+8.
Perimeter = (y+8) + (y+7) + (y+7) + (y+8)
Simplifying by combining like terms, we get:
Perimeter = 4y + 30
Therefore, the perimeter of the quadrilateral is 4y + 30.
Answer:
4y + 30
Step-by-step explanation:
To find:-
The perimeter of the given figure.Answer:-
Perimeter is simply the sum of all sides of any figure. Since here it is a quadrilateral, perimeter would be the sum of all four sides of it .
The four sides given to us are , y+7 , y+8 , y+7 and y+8. We can add them to find out the perimeter as ,
Perimeter = y+7 + y+8 + y+7 + y+8
Perimeter = 4y + 30
Hence the perimeter of the given figure is 4y+30 .
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 17 births.
The value of the mean is μ=_____ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is σ=____(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 15 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result ____ is not. is. significantly high, because 15 girls is greater than. less than. equal to _______ __ girls. A result of 15 girls would suggest that the method _______ is effective. is not effect.
The suggest that the method is effective.
Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:
a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.
b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.
c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.
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In Problems 1 through 6 you are given a homogeneous system of first- order linear differential equations and two vector-valued functions, X(1) and x(2) a. Show that the given functions are solutions of the given system of differential equations. b: Show that X = Cx(T) + C2x(2) is also a solution of the given system for any values of C1 and C2. C. Show that the given functions form a fundamental set of solutions of the given system.
The given functions form a fundamental set of solutions of the given system.
The solution of the given system of differential equations is shown below.a) To prove that the given functions X(1) and x(2) are the solutions of the given system of differential equations, we must substitute these functions into the given system to show that they satisfy the equations.In the given system, we have the following equations:
X_1' (t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4X_1 (t) - 2X_2 (t)
Now, let's substitute the given vector-valued functions X(1) and x(2) into the above equations and check if they satisfy these equations.
a. For X(1) = [1, 2]e^2t
Substituting X(1) into the given system, we get:
X_1' (t) = [1, 2] * 2e^2t = 2X_1 (t) - X_2 (t)
X_2' (t) = [1, 2] * 4e^2t = 4X_1 (t) - 2X_2 (t)
Therefore, the given function X(1) is a solution to the given system of differential equations.
b. To prove that X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2, we need to X into the given system of equations and check if it satisfies the equations.
So, we have:
X = C_1[1, 2]e^2t + C_2[1, -1]e^-t
X_1 = C_1e^2t + C_2e^-t
X_2 = 2C_1e^2t - C_2e^-t
Differentiating X_1 and X_2 with respect to t, we get:
X_1' = 2C_1e^2t - C_2e^-t
X_2' = 4C_1e^2t + C_2e^-t
Substituting X_1 and X_2 into the given system, we get:
X_1' (t) = 2(C_1e^2t - C_2e^-t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4(C_1e^2t + C_2e^-t) = 4X_1 (t) - 2X_2 (t)
Therefore, the given function X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2.
c. To show that the given functions form a fundamental set of solutions of the given system, we need to prove that they are linearly independent and that their Wronskian is non-zero.
We know that the vectors [1, 2] and [1, -1] are linearly independent, therefore the functions x(1) and x(2) are also linearly independent.
Also, the Wronskian of x(1) and x(2) is given by:
W(x1, x2) = | x1 x2 |
| x1' x2' |
Substituting x(1) and x(2) into the above equation, we get:
W(x1, x2) = | e^2t e^-t |
| 2e^2t -e^-t |
Simplifying the above equation, we get:
W(x1, x2) = 3e^(3t) ≠ 0
Therefore, the given functions form a fundamental set of solutions of the given system.
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Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned
The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.
Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.
In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.
Sick Days:
Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.
In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.
To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.
In 2019, the cost of compensated absences was 58 x $6 = $348.
In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.
Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
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Find the value of 2 - 3x when x = 7
2 - 3x is a(n)__________.
Therefore, when the equation x = 72 - 3x, the value of 2 - 3x is -52.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.
Here,
When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:
x + 3x = 72
Combining like terms, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now that we know x = 18, we can substitute this value into the expression 2 - 3x:
2 - 3x = 2 - 3(18)
2 - 3x = 2 - 54
2 - 3x = -52
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The data in the table below shows the number of passengers and number of suitcases on various airplanes.
The line of best fit for the data is approximately y=-1.98x+7.97.
a) True
b) False
The line that best fits the data has a value of around y=-1.98x+7.97 is False.
Define straight lineA line is defined as a straight, one-dimensional figure that extends infinitely in both directions. It is a basic geometrical object that has no thickness or width, and can be defined as the set of all points that are equidistant from two fixed points, called the endpoints. It is represented by y=mx+c.
given y=-1.98x+7.97
Taking first caseNumber of passenger=75
Number of Suitcases=159
75=-1.98×159+7.97
75=-305.26
Hence, the line does not satisfy the data.
The line that best fits the data has a value of around y=-1.98x+7.97 is False.
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Find the area of the figure. Use 3.14 for . 8 in 9 in OA. 97.2 in² OB. 86.24 in² O C. 61.12 in² O D. 122.24 in²
The area of the figure is option (C) 61.12 in².
What is the Area of a TriangIe?The area of a triangIe is the region encIosed within the sides of the triangIe. The area of a triangIe varies from one triangIe to another depending on the Iength of the sides and the internaI angIes. The area of a triangIe is expressed in square units, Iike, m2, cm2, in2, and so on.
What is the Area of CircIe?The area of a circIe is the amount of space encIosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the totaI number of square units inside that circIe. Area of CircIe = πr2 or πd2/4 in square units, where
(Pi) π = 22/7 or 3.14.
r = radius of the circIe
d = diameter of the circIe
Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.
Area of triangIe = ½ x B x H
Given Height = 8 in
Given Breath = 9 in
Area of TriangIe = ½ x 8 x 9 = 36 in²
Area of haIf circIe = ½ (pi x r²)
= ½ (3.14 x 16)
= (½ x 50.24) in²
= 25.12 in²
Area of the figure wiII be 36 in² + 25.12 in² = 61.12 in²
Option C wiII be the correct option.
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The area of the figure will be 36 in² + 25.12 in² = 61.12 in². Option C will be the correct option.
What is the Area of CircIe?
The area of a circIe is the amount of space enclosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the total number of square units inside that circle.
Area of CircIe = πr2 or πd2/4 in square units, where
(Pi) π = 22/7 or 3.14.
r = radius of the circIe
d = diameter of the circIe
Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.
Area of triangle = ½ x B x H
Given Height = 8 in
Given Breath = 9 in
Area of TriangIe = ½ x 8 x 9 = 36 in²
Area of haIf circIe = ½ (pi x r²)
= ½ (3.14 x 16)
= (½ x 50.24) in²
= 25.12 in²
Therefore, Area of the figure will be 36 in² + 25.12 in² = 61.12 in²
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NEED HELP DUE TODAY!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangle DEF is twice the size of the triangle ABC and the triangles are similar triangles
How do the sizes of the circles compare?Given the triangles ABC and DEF
From the figure, we have
AB = 1
DE = 2
This means that the triangle DEF is twice the size of the triangle ABC
Are triangles ABC and DEF similar?Yes, the triangles ABC and DEF are similar triangles
This is because the corresponding sides of DEF is twice the corresponding sides of triangle ABC
How can you use the coordinates of A to find the coordinates of D?Multipliying the coordinates of A by 2 gives coordinates of D
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I need help with this question
Answer: the answer is c I think
Please helppp grid question
0.1 for the top left, 0.2 for bottom middle
Pls help!!! Asap
Possible answers
Al m=5. L0=14, NO-12
B) m=7, 10= 14, NO= 14
C m=7, LO=12, NO= 12
D) m=4, L0=13, NO = 14
E) m=5, LO= 14, NO= 15
Answer:
C
m= 7 LO= 14 MO= 14
Step-by-step explanation:
LO and NO are going to be the same length
m + 7 = 2m
to get the variable alone subtract m from both sides
7 = m)
plug 7 into both equations
7 + 7 = 14
2 x 7 = 14
4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
an insurance policy is written to cover damage to a luxury sports car. the amount of damage is uniformly distributed between $0 and $46000. in order to decrease the insurance premium, the insurance company decides to charge an ordinary deductible, d, so that the expected insurance payment with the deductible is 60 % of the expected insurance payment without the deductible. determine the value of the deductible, d.
In order to decrease the insurance premium, the insurance company should charge an ordinary deductible of $18,400.
The expected insurance payment without a deductible is the full value of the damage, or $46,000.
With a deductible.
The expected insurance payment would be 60% of that, or $27,600.
To find the value of the deductible, d, subtract the expected insurance payment with a deductible from the expected insurance payment without a deductible. This gives us d = $46,000 - $27,600 = $18,400.for such more questions on Statistics
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i have no clue what to do
Answer:
Step-by-step explanation:
you are going to give more info ?????
Yesterday, Eve ran a mile in 15 minutes. Today, she ran a mile in 5 minutes. What is the percent decrease in the time it takes her to run a mile? Round to the nearest whole number.
Eve now completes a percent mile in about 67% less time than she did previously.
How does math define a percent?In essence, percentages are fractions with a denominator of 100. The cent symbol (%) is placed next to a number to indicate that it is a percentage. As an illustration, if you answered 75 of 100 questions correctly on an examination (75/100), then would have received a score of 75% percent drop (original value − new value) / initial value x 100%).
Let's use "t1" for yesterday's time and "t2" for today.
t1 = 15 minutes, t2 = 5 minutes.
Using the equation, we obtain:
percentage decrease equals (t1 - t2) / (t1 x 100%) percentage decrease equals (15 - 5) / (15 x 100%) percentage decrease equals 10 / (15 x 100%) percentage decrease equals 0.666... x 100% percentage decrease equals 67%
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A point A lies on the circle with the equation x^2 + y^2 = 20 and has y-coordinate -4
A point B lies on the circle and has x-coordinate √10
A tangent line set at A intersects the tangent at B at point C
As per the coordinate, the equation of the tangent line is y = (-1/2)x - 3.
In this problem, we are given the equation of a circle, x² + y² = 20, which represents all the points on the plane that are equidistant from the origin (0,0) with a distance of √20 or a radius of
=> √20/2 = 2√5.
Now, let's consider point A. We know that it lies on the circle, so it must satisfy the equation x² + y² = 20. Additionally, we are told that its y-coordinate is -4. Using this information, we can substitute y=-4 into the equation of the circle to get
=> x² + (-4)² = 20,
which simplifies to x² = 4.
Thus, point A has coordinates (±2, -4), and we can determine which one is correct by looking at the circle's equation.
Next, let's consider point B. We are told that its x-coordinate is √10. Since point B lies on the circle, it must also satisfy the equation
=> x² + y² = 20.
Using this equation, we can substitute x=√10 to get
=> (√10)² + y² = 20,
which simplifies to y² = 10. Thus, point B has coordinates (√10, ±√10).
To find the y-intercept, we can use the fact that point A lies on the tangent line. Substituting the coordinates of point A into the equation of the tangent line, we get -4 = (-1/2)(±2) + b, which simplifies to b = -3. Thus, the equation of the tangent line at point A is y = (-1/2)x - 3.
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Complete Question:
A point A lies on the circle with the equation x² + y² = 20 and has y-coordinate -4
A point B lies on the circle and has x-coordinate √10
A tangent line set at A intersects the tangent at B at point C
Find the equation of the tangent line.
What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.
what is Combination?In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.
The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:
[tex]nCk = n! / (k! *(n-k)!)[/tex]
where n! denotes the factorial of n, i.e., the product of all positive integers up to n.
by the question.
Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:
[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]
Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]
Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).
Since a_i >= 4 for i=1, we have:
[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]
Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:
[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]
This gives us:
[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]
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What part of an hour passes from 1:35 P. M. To 2:15 P. M. ?
Answer:
2/3 rd or 0.667th part of an hour passes from 1:35 P.M to 2:15 P.M
To determine the fraction of an hour that passes from 1:35 P.M. to 2:15 P.M., we need to calculate the elapsed time between the two times and express it as a fraction of an hour.
The elapsed time between 1:35 P.M and 2:15 P.M is 40 minutes. To convert minutes to fractions of an hour, we can divide the number of minutes by 60.
40 minutes / 60 minutes per hour = 2/3 hours = 0.67 hours
Therefore, the fraction of an hour that passes from 1:35 P.M. to 2:15 P.M. is 0.67. This means that approximately two-thirds of an hour, or 67% of an hour, has passed between these two times.
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6. If x is an integer, what is the solution set of 3 < x≤ 6?
a) {3, 4, 5}
b) {4, 5, 6}
(c)(3, 4, 5, 6}
d) {4, 5}
Answer:
B
Step-by-step explanation:
4, 5, and 6 are greater than 3 and they are also less than or equal to 6.
An equation is given.
x² + 9 = 6x
What is one solution to the equation?
x=
Step-by-step explanation:
x²-6x+9=0
using the almighty formula where a=1 , b=-6 , c=9
What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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Lily has an inspirational board on her bedroom wall.The number of photos on lilys inspiration board is 4 more than twice the number of quotes on her board.she has a combined total of 37 quotes and photos on her board.How many quotes are on lily inspiration board? How many pho are on lily inspiration board
In response to the stated question, we may state that As a result, Lily has equation 26 images on her inspiration board.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation consists of two sides separated by an algebraic equation (=). For instance, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Assume there are x quotations on Lily's board.
According to the issue, the quantity of photographs on Lily's board is four times more than the number of quotes. As a result, the number of photographs may be expressed as 2x + 4.
We also know that there are 37 quotations and photographs on Lily's board. So let us create an equation:
x + (2x + 4) = 37
3x + 4 = 37
3x = 33
x = 11
So Lily's inspiration board contains 11 quotations.
To calculate the number of images, enter x = 11 into the equation we discovered earlier:
2x + 4 = 2(11) + 4 = 26
As a result, Lily has 26 images on her inspiration board.
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