n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1
What is Remainder?
The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.
As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.
As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.
[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]
[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).
The remainder will be n= (K+1)^3
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When 9 is multiplied by 2/3 the product will be between 2/3 and 9
The required product will be 6 when 9 is multiplied by 2/3.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
We have to determine whether the product will be between 2/3 and 9
As per the given question, we have
2/3 and 9
⇒ 2/3 × 9
Apply the multiplication operation,
⇒ 18/3
Reduce the above fraction into the simplest form, and we get
⇒ 6
Thus, the required product will be 6 between 2/3 and 9.
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The point g(2,1) is translated 3 units left. What are the coordinates of the resulting point, g'?.
The coordinates of the resulting point, g' is :
(-1,1)
Given:
The coordinate plane allows for the translation of any object both horizontally (left/right) and vertically (up/down).
Rules are:
Replace x with x - k when the form is moved k units to the left.Replace x with x + k when the form is moved k units to the right.Replace y with y + k when the form is raised by k units.Change y to y - k when the form is shifted down by k units.The point g(2,1) is translated 3 units left.
we are asked to find the coordinates of the resulting point, g'.
By translating 2 units left, it means the x-axis value is made more negative by 2 units
So we are going to subtract two from the x-coordinate
So we have;
(2-3,1)
= (-1,1)
Hence we get the required coordinates.
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Solve for x. x = -x
not possible
0
1
-1
a cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. the base of the can has an area of 75 \text{ cm}^275 cm 2 75, start text, space, c, m, end text, squared, and the height of the can is 10 \text{ cm}10 cm10, start text, space, c, m, end text. if 110 \text{ cm}^3110 cm 3 110, start text, space, c, m, end text, cubed of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?
The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
Given that,
Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
We have to find which of the following comes closest to the total volume of the fruit pieces in the can if 110 cm³ of syrup is required to fill the can completely.
We know that,
Total volume of the cylinder can is equal to the sum of the total volume of fruits and total volume of Syrup.
So,
The total volume of the fruits is we have to find take x
The total volume of the cylinder is base× height=75×10
The total volume of the syrup is 110
So,
75×10=x+110
x=750-110
x=640
Therefore, The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
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5. For problems A-E, write the converse, inverse, and contrapositive statements based on the given
conditional statement.
A. If I own a dog, then I own an animal.
Converse:
Inverse:
Contrapositive:
B. If I go to be early, then I sleep well.
Converse:
C.if this is Thursday, then I do not go to church.
Converse:
Inverse:
Converse:
D. If today is Wednesday, then yesterday was Tuesday.
Converse:
Inverse:
Converse:
E. If 5X equals 10, then X equals two.
Converse:
Inverse:
Answer:
Step-by-step explanation:
Conditional Statement: If it is a beagle, it is a dog.
Converse: If it is a dog, it is a beagle. This is a false statement, since a dog can be any other breed (ex. Pomeranian).
Inverse: If it is not a beagle, it is not a dog. Again a false statement, since if it is a different breed, it is a dog despite not being a beagle. For example, it could be a Pomeranian.
Contrapositive: If it not a dog, it is not a beagle. This is true, since if something is not a dog, it won't be any particular breed of dog either (and it won't be a beagle).
Which expression makes the equation true for
the values of x?
16x16= 4(?)
a. 4x - 4
b. 4x - 16
C. 2x - 2
d. 12x -12
Answer:
Step-by-step explanation:
answer is c
An artist frames his rectangular artwork. The length of his art is 3 times the
vidth, w. How can he represent the perimeter of the art? Draw a line to match
ach reason on the left to the expression it describes.
Provides a relationship between length and width
Provides a sense of the entire perimeter
Provides a description of the amount of framingmaterial for length and for width separately
3w
8w
2(w +3w)
4(3W)
6w+2w
Answer:
See attached worksheet
Step-by-step explanation:
which is the solution to dis system of equations
x+y=3
x-y=-3
Answer:
Step-by-step explanation:
You are going to want to use the substitution method to solve. Substitute the given value of x (which is x=-3+y) into the equation x+y=3. Now solve the equation for y.You get y = 3. Plug in 3 for x in the other equation. You get x-3=-3 ---> x = 0.
So x = 0, y = 3
What is the answer to 2+2?
A- 4
B- 5
C- 22
D- 8
Determine the value of x in the following triangle.
Answer:
the value of x is 9
Step-by-step explanation:
the sum of all angles of a triangle is 180
one side is 90 so,
90+7x+3x = 180
10x = 180-90
10x = 90
x=9
what is the product of 5/6 x 2/3
A product sells at a regular price of $150 which is on sale for 60% off the regular price. Find the sale price.
The new sale price of the product after the deduction of discount is $60
What is the sale price?Based on the given task content; percentage is the concept that can be used to solve for the new sale price.
Regular price of the product = $150Percentage discount = 60%New price of the product = Regular price of the product - (Percentage discount × Regular price of the product)
= 150 - (60% × 150)
= 150 - (0.6 × 150)
= 150 - 90
= $60
Consequently, new selling price of the product is $60
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Find the equation of the line that passes through the point (-4, 11) and is perpendicular to the following line.
y= -2/3x -7
The equation of a line perpendicular to y = (-2/3)x - 7 is y = (3/2)x + 17.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines perpendicular to each other have slopes that are negative reciprocals of each other.
So, the slope of the perpendicular line to the given line y = (-2/3)x - 7 is (3/2)
which passes through the point (-4, 11) is,
11 = (3/2)(-4) + b.
b = 11 + 6.
b = 17.
∴ y = (3/2)x + 17 is our required line.
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brayden was a 60% free throw shooter last season. he practiced all through the off-season and has made 12 of the first 16 free throws this season. based on his performance and the results of the simulation, is there convincing evidence that brayden has improved his free-throw percentage? explain.
Yes , there is convincing evidence that Brayden has improved his free-throw percentage when compared to previous year.
Brayden made 60 % free throws last year
P(Making free throw last year) = 0.6
This year,
X% of 16 = 12
X/100 * 16 =12
75%
therefore, this year
P(Making free throw this year) = 7.5
This clearly shows that he improved his free throw percentage compared to last year.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.
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should I eat a cough drop?
Answer: Yes
Step-by-step explanation: Because that candy will help your throat feel better!
1. Which of the following describes this function?
OIt is a linear function, and it is decreasing.
O it is not a linear function, and it is constant.
OIt is not a linear function, and it is decreasing
It is a linear function, and it is increasing
Solve the quadratic equation: 3x2 − 3x − 3 = 0
Leggings are on sale for 10% off the
original price. What is the sale price of
leggings with an original price of $45?
C.$40.50
d. $41.50
a. $35
b. $4.50
Answer:
Your answer is C) $40.50
Step-by-step explanation:
[tex]0.1[/tex] × [tex]45 = 4.5[/tex]
[tex]45 - 4.5 = 40.50[/tex]
Answer: C) $40.50
Step-by-step explanation:
You buy a stock for $100. In one year its price rises to $114, and it pays a $1 dividend. Your capital gains yield is _____
Answer:
Step-by-step explanation:
$13
A clothing store offers customers a holiday sale of 30% off the price of x items. A customer then has an additional 15% off coupon that can be used whe checking out. Which of the following functions represents the final price Px) of the items purchased?
a. P(x) = 0.045x b. P(x) = 0.45X c. P(x) = 0.595x
d. P(x) = 0.15x
A clothing store offers customers a holiday sale of 30% off the price of x items. A customer then has an additional 15% off coupon that can be used when checking out then the function is P(x) = 0.595x
Original price = x
Sale price = 30% off:
x - 30% =
x - 0.3x =
0.7x
Further discount 15% off:
0.7x - 15% =
0.7x - 0.7x*0.15 =
0.7x - 0.105x =
0.595x
The function is:
P(x) = 0.595x
Correct choice is C
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Write the equation of the line that passes through the points (7, 4) and (-5, 4). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answer:
y = 4
Step-by-step explanation:
note that the y- coordinates of the 2 points are equal, both 4
This indicates that the line passing through them is horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through ), then
y = 4 ← equation of line
Ayana lives 900 meters from his school in India Eva lives 2000 feet from her school in United States who lives closer to their school
Ayana lives 2952 feet away from his school and Eva lives 2000 feet away, Thus Eva lives closer to school.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
In India, Ayana lives 900 meters from his school,
And in United Sates Eva lives 2000 feet from her school.
Since,
1 meter = 3.28 feet
900 meter = 2952 feet
Here, distance of Ayana from her school is 2952 feet and distance of Eva from her school is 2000 feet.
Therefore, Eva lives closer to their school.
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How do you multiply powers with different bases but the dame exponent?
Answer:
Step-by-step explanation:
First, multiply the bases together. Then, add the exponent. Instead of adding the two exponents together, keep it the same. This is because of the fourth exponent rule: distribute power to each base when raising several variables by a power.
for the following 3 questions: a study obtained data on the amount of time 28 randomly selected high school students and 31 randomly selected college students spend on their cell phones each day. the investigator is interested in determining whether there is evidence that the amount of time students spend on their cell phone is different between high school and college Let H= time spent on phone by high school students; C= Time spent on phone by college students; and d=H−C
The data are not paired because: o All of these are true o Each element in a sample is measured once: time spent on cell phone o The conclusion pertains to the difference of two independent population means o There are two samples
The correct answer is
H₀ : μh - μc = 0
H₀ : μh - μc ≠ 0
Given that,
Regarding the subsequent 3 inquiries: A study collected information on how much time 28 randomly chosen high school students and 31 randomly chosen college students spent each day on their cellphones. The researcher is interested in learning whether there is proof that students use their phones for varying amounts of time in high school and college.
Because the samples of college and high school students are independent, the independent samples t-test should be utilized.
The study's research (Claim) aims to ascertain whether students' cell phone usage patterns alter between high school and college.
For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,
H₀ : μh - μc = 0
H₀ : μh - μc ≠ 0
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The proper null and alternative hypotheses are
[tex]H_{0}[/tex] : μh = μc
[tex]H_{A}[/tex] : μh - μc
The study's research wants to ascertain whether difference between the time spent by high school students and college students.
The actual test begins by considering two hypothesis i.e. null hypothesis and alternative hypothesis.
Let, H= time spent on the phone by high school students;
C= Time spent on the phone by college students; and
d=H−C
For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,
[tex]H_{0} :[/tex] μh = μc (time spent by high school students is equal to college students)
[tex]H_{A} :[/tex] μh - μc (difference between the time spent by high school students and college students)
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Maya worked 41 hours this week at a local hospital. She makes $12. 00 per hour. Anytime over 40 hours is paid at time and half or 1. 5 times her hourly wage. How much will maya earn for her 41 hours of work this week?.
We know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
What do we mean by mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, earnings of Maya when she works for 41 hours are:
We know that Maya works for $12.00 per hour.
She's paid 1.5 times her hourly income when she works for more hours after 40 hours.
That will be: 12 × 1.5 = $18
Hence, Maya's income for 41 hours will be:
40 hours + 1 hour (Extra hour)
(12 × 40) + 18
480 + 18
$498
Therefore, we know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
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two trains leave stations miles apart at the same time and travel toward each other. one train travels at miles per hour while the other travels at miles per hour. how long will it take for the two trains to meet? do not do any rounding.
Time taken for the both train to meet each other is 1.8 hours
The distance between two stations = 360 miles
The speed of one train = 95 miles per hour
The speed of the second train = 105 miles per hour
The relative speed of the trains = 95 + 105
Add the numbers
= 200 miles per hour
We know
Speed = Distance / Time
The time = Distance / Speed
The time taken for the two trains to meet = Distance / relative speed
Substitute the values in the equation
= 360 / 200
= 1.8 hours
Therefore, both trains will meet each other after 1.8 hours
I have answered the question in general, as the given question is incomplete
The complete question is:
Two trains leave stations 360 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 105 miles per hour. How long will it take for the two trains to meet?
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Please Help!!!! Hurry!!
Answer:b e and g
Step-by-step explanation:
because between e and g it increases the most
The value of a house has been increasing by $5000 each year. Write an equation to show how the value will have changed x years from now.
y=(?)x
Answer: y=(1x)^x + 5000
Step-by-step explanation:
So the original equation is y=mx + b
And we know that each year the house increase by 5000, so the b is 5000
For the x which is the slope, we don't know what the slope is so we just say it as x and the ^x is for the number of years, let's say 3 years then it is ^3 and keep increasing like that up.
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Which of these tables (if any) represent a proportional relationship?
please help!!
None of the tables represent a proportional relationship.
What is a proportional relationship?Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
To determine whether a relationship is proportional, examine the ratios between the two variables. The relationship is proportional if the ratio is always the same. The relationship is not proportional if the ratio changes.
Fir the first table, the ratio varies. Also, the second table isn't constant.
Therefore, none has a proportional relationship.
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Find the ditance from the point A(-2,3) to the line y =1/2x1. Round your anwer to the nearet tenth
The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
We will comprehend the slope-finding method and its applications in this article.
According to our question-
10/√5 *√5/√5*105/√5
Hence, The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.
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