The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.
In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.
Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.The integers are typically shown as lines of specially chosen, evenly spaced dots. Even though the image only shows the integers from -3 to 3, as well as values that are in between the integers, the product contains all real numbers, going forever in both directions. When teaching the very foundations , addition and subtraction with negative numbers, it is widely used as a teaching technique.We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.
Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.
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you are given the set of letters {a, b, c, d, e}. what is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters a and b are next to each other?
The probability in a random 5-letter string that the letters A and B will be next to each other is 0.4
For A and B to be next to each other in the string of letters, consider the AB combination as a single letter. Then there are 4 letters AB, C, D, E.
There are 4! number of ways to arrange these 4 letters.
4!= 24 ways
We know AB can be arranged in 2 ways ( AB or BA)
Thus there are 2*4! = 2 * 24 = 48 ways of arranging the letters such that AB are next to each other in the random Five-letter string
The total number of letters in the set is 5 and hence the total number of ways the letters can be arranged without A and B necessarily being next to each other is 5!= 120
The probability that in the random five-letter string( in which each letter appears only once with all such strings equally likely) the letters A and B are next to each other= 48/120 = 0.4
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Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes. If she continues at the same rate, how many hours will it take for Selena to make 264 more pancakes?
Selena needs 4 more hours to prepare 264 more pancakes.
What is unitary method?Unitary method is a process of finding the value of a single unit, and use this value to find the value of the required number of units.
Given is Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes.
We have -
The rate at which Selena is making pancakes = 132 pancakes in 2 hours.
Number of pancakes left to be made = 264
Now, in 2 hrs she makes 132 pancakes
Then, in 1 hr she will make (132/2) or 66 pancakes.
Now, she makes 66 pancakes in 1 hour.
So, she will make 1 pancake in (1/66) hours
Therefore, she will make 264 pancakes in (264/66) or 4 hours.
Therefore, she will need 4 more hours to prepare 264 more pancakes.
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The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x-2, y+3), give the vertices of △A′B′C′.
Answer:
A' = (0, 0)
B' = (-5, -2)
C' = (2, 4)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x - 2, y + 3)
This notation tells you that the x-coordinate is translated 2 units to the left, and the y-coordinate is translated 3 units up.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 - 2, -3 + 3) = (0, 0)
⇒ B' = (-3 - 2, -5 + 3) = (-5, -2)
⇒ C' = (4 - 2, 1 + 3) = (2, 4)
how do I right this in numeral formsix thousand, five hundred eighty-two ten-thousandths
Riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
The triangle QRS with points Q(8, -4), R(-1, 2), and S(3, 7). After the triangle is reflected across Y axis, then the coordinates of vertex Q are (-8, -4).
How to determine reflection coordinates?
These are the specified parameters:
Q(8, -4), R(-1, 2), and S(3, 7)
Determine the reflected of Q(8, -4) across Y-axis
A(a, b) ⇔ A' (-a, b)
Q(8, -4) ⇔ Q' (-8, -4)
Determine the reflected of R(-1, 2) across Y-axis
A(a, b) ⇔ A' (-a, b)
R(-1, 2) ⇔ R' (1, 2)
Determine the reflected of S(3, 7) across Y-axis
A(a, b) ⇔ A' (-a, b)
S(3, 7) ⇔ S' (-3, 7)
The coordinates of vertex Q after the triangle is reflected across the y-axi are (-8, -4).
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f(x) = 4x3 + 6x2 – 3x – 4g(x) = 4x – 3Find (f - 9)(x).A. (f - g)(x) = 4x3 + 6x2 + x - 1B. (f - g)(x) = 4.23 + 6x2 – 7x – 7c. (f - g)(x) = 4x3 + 6x2 + x - 7O D. (f - g)(x) = 4x3 + 6x2 – 7x - 1SUBMIT
Step1:
You are to subtract g(x) from f(x)
Step2:
Simplify and collect like terms
therefore,
[tex]\begin{gathered} \\ (f-g)x=4x^3+6x^2\text{ - 3x - 4 - (4x - 3)} \\ =4x^3+6x^2\text{ - 3x - 4 - 4x + 3} \\ \text{Next add like terms} \\ =4x^3+6x^2\text{ -7x - 1} \end{gathered}[/tex]Option D is the correct answer
4. Round the number 5,997 to the nearest hundred.
Answer:
6,000
Step-by-step explanation:
A book has 250 pages.how many digits have been used to print page no.s of book
Answer: 642 Digits have been used to print 250 Pages
Step-by-step explanation:
A book has 250 pages
1 - 250 Numbers will be used
Single Digit number - 9 ( 1- 9)
Two Digit Numbers 90 ( 10 - 99)
Three Digit Numbers 151 ( 100 - 250)
Number Of Digits used = 9 * 1 + 90 * 2 + 151 * 3
= 9 + 180 + 453
= 642
642 Digits have been used to print 250 Pages
Please help CORRET ANWSERS ONLY!
Answer:uhh
Step-by-step explanation:
Use the factor theorem to find all real zeros and one factor.
f(x) = 2x³-9x² + 13x - 6; x - 1
Answer:
x = {1, 1.5, 2}Step-by-step explanation:
GivenPolynomial f(x) = 2x³ - 9x² + 13x - 6, One of the factors x - 1.Factorize the polynomial using the given details.
Since one of the factors known, try to factor it out and futher:
2x³ - 9x² + 13x - 6 = 2x³ - 2x² - 7x² + 7x + 6x - 6 = 2x²(x - 1) - 7x(x - 1) + 6(x - 1) = (x - 1)(2x² - 7x + 6) = (x - 1)(2x² - 3x - 4x + 6) = (x - 1)[x(2x - 3) - 2(2x - 3)] =(x - 1)(x - 2)(2x - 3)Find its zero's:
x - 1 = 0 or x - 2 = 0 or 2x - 3 = 0x = 1 or x = 2 or x = 1.5Answer:
[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=2x^3-9x^2+13x-6[/tex]
Sum the coefficients:
[tex]\implies 2-9+13-6=0[/tex]
As the sum of the coefficients is zero, (x - 1) is a factor.
Therefore:
[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]
[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]
Compare the coefficients with the given polynomial.
As the coefficient of the leading term of the polynomial is 2:
[tex]\implies a=2[/tex]
As the coefficient of the term in x² is -9:
[tex]\implies b-a=-9[/tex]
[tex]\implies b-2=-9[/tex]
[tex]\implies b=-7[/tex]
As the constant of the given polynomial is -6:
[tex]\implies c=6[/tex]
Substitute the found values of a, b and c into the factored form of the polynomial:
[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]
Factor the quadratic:
[tex]\implies 2x^2-7x+6[/tex]
[tex]\implies 2x^2-4x-3x+6[/tex]
[tex]\implies 2x(x-2)-3(x-2)[/tex]
[tex]\implies (2x-3)(x-2)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]
To find the zeros, set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.
solve the systems using equal values.y= 2xy= -3x + 5
x+6x-5x=x+114 Please help.
if a number decreases by 8, the result is -21.What is the number?
Answer: it would be -13
Step-by-step explanation: -13-8=-21
PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
Step-by-step explanation:
This should be the right solution.
Complete the table and use the results to find the indicated limit.
Given the function:
[tex]k(x)=\frac{x^3-x-6}{x-2}[/tex]when x = 1.9
[tex]k(x)=\frac{1.9^3-1.9-6}{1.9-2}=\frac{-1.041}{-0.1}=10.41[/tex]when x = 1.999
[tex]k(x)=\frac{1.999^3-1.999-6}{1.999-2}=\frac{-0.0109944}{-0.001}=10.994001[/tex]When x = 2.001
[tex]k(x)=\frac{2.001^3-2.001-6}{2.001-2}=\frac{0.011006}{0.001}=11.006[/tex]When x = 2.1
[tex]k(x)=\frac{2.1^3-2.1-6}{2.1-2}=\frac{1.161}{0.1}=11.61[/tex]so, the limit of the function k(x) = 11
The answer is option A. 11
I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.
The angle x of the triangle is 60 degrees.
How to find the angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.
A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.
Therefore, the angle x of the triangle can be found as follows:
x + x + x = 180
3x = 180°
divide both sides of the equation by 3
3x / 3 = 180 / 3
x = 180 / 3
x = 60 degrees.
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Answer:
the person below or above me is the answer. Yeah
Step-by-step explanation:
Find the indicated measure. Assume that all segments that appear to be tangent are tangent.
We are asked to determine the arc length of HJ. To do that we will use the following formula:
Given two secant lines that intercept outside a circle as follows:
We have the following relationship:
[tex]\angle x=\frac{1}{2}(\text{mCD-mAB)}[/tex]Substituting the values we get:
[tex]29=\frac{1}{2}(96-\text{mHJ)}[/tex]Now, we multiply both sides by 2:
[tex]58=96-mHJ[/tex]Now, we subtract 96 from both sides:
[tex]58-96=-\text{mHJ}[/tex]Solving the operations:
[tex]-38=-\text{mHJ}[/tex]Now, we multiply both sides by -1:
[tex]38=\text{mHJ}[/tex]Therefore, the measure of the arc length of HJ is 38.
A triangle has sides with lengths of 20 cm, 15 cm, and 10 cm. Substitute these values into the Pythagorean Theorem to determine if the sides form a right triangle.
Answer:
10^2 + 15^2 = 20^2
100+225≠400
so no, it's not a right angled triangle
:)
Find the mean and population standar deviation for each data set.
Hours slept
Mean of given set is 7.8
Define mean.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value." It is a statistical idea with significant financial implications.
Given,
Mean:
Formula:
Sum = 118.25
Total = 15
[tex]\frac{sum}{total}[/tex]
[tex]\frac{6.75 + 6.5 + 7 +8 +7+8.75+7.25+5.75+9.25+7.75+7+7.5+8+7.5+8+6.25}{15}[/tex]
= [tex]\frac{118.25}{15}[/tex]
= 7.8
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what is 16 divided by 3,482
Answer:217.625
Step-by-step explanation:
What is the equation to this graph? pls help
Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2
Three t-shirts for $10. find the unit rate
Answer:
Step-by-step explanation:I don’t know
33% of millennials rely on blogs before making a purchase and eight
out of 10 millennials never buy anything without reading a review first.In a sample size of 75 Millennials, how many people use blogs to make a purchase?In a sample size of 75 Millennials, how many people never buy anything without reading a
review first?
24 millennials will use blogs to make a purchase and 60 millennials will never buy anything without reading a review first.
Here, we are given that 33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first.
a. If there is a sample of 75 Millennials, out of these 33% will use blogs to make a purchase.
Thus,
33% of 75
= 33/100 × 75
= 33/4 × 3
= 99/4
= 24.75
Since, the number of millennials cannot be a decimal number, we approximate it to the lowest integer, that is, 24.
Thus, 24 millennials will use blogs to make a purchase.
b. Now, if there is a sample of 75 Millennials, out of these 8 out of 10 will never buy anything without reading a review first.
8 out of 10 in percentage terms will be-
8/10 × 100
= 80%
Thus,
80% of 75
= 80/100 × 75
= 80/4 × 3
= 20 × 3
= 60
Thus, 60 millennials will never buy anything without reading a
review first.
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write each percent as a fraction in simplest form. 20%
Answer:
1/5
Step-by-step explanation:
"percent" means "per hundred"
(because cent means hundred like years in a century or cents in a dollar)
anyway
20% means
20 per 100
write it as 20/100
Now simplify it.
20/100
= 2/10
= 1/5
Alexis can run 5/2 miles in 1/4hrs. What is her speed in miles per hour?
Solution
We are given
Distance = 5/2 miles
Time = 1/4 hours
Answer:
The speed would [tex]10~\text{mph}[/tex].
Step-by-step explanation:
Step 1: State the formulas required
The formula for speed is:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Step 2: Substitute the values into the formula
The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].
Substitute these values into the formula:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]
Step 3: Calculate
[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]
So, the speed is [tex]10~\text{miles per hour}[/tex] or [tex]10~\text{mph}[/tex].
our football team has members, of which only are strong enough to play offensive lineman, while all other positions can be played by anyone. in how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?
By using Permutation, the total number of ways in which we can choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver is 1512.
Permutation is defined as the arrangement of items in a specific or a particular order.
Since there are 3 choices for the position of offensive lineman, and for the next position there are 9 choices, similarly 8 choices for the next position and 7 choices remain for the last position.
So we get, 3x9x8x7 =1512, by the concept of Permutation.
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Arianys is driving to a concert and needs to pay for parking. There is
an automatic fee of $11 just to enter the parking lot, and when she
leaves the lot, she will have to pay an additional $3 for every hour she
had her car in the lot. How much total money would Arianys have to
pay for parking if she left her car in the lot for 4 hours? How much
would Arianys have to pay if she left her car in the lot for t hours?
Cost of parking for 4 hours:
Cost of parking for t hours:
Pls help me
Answer:
c = 3t + 11
t = time in the lot
c = total cost
4 hours the cost will be $23
Step-by-step explanation:
Cost for 4 hours.
c = 3t + 11
c = 3(4) + 11
c = 12 + 11
c= $23
Round your answer to the nearest hundredth.A = 8.4 in²Calculate the diameter of the circle.O 3.27 inO 4.20 inO 1.75 inO2.89 in
The area of a circle can be calculated as follows:
[tex]A=\pi r^2[/tex]Using the area given in the problem and solving for the radius r:
[tex]\begin{gathered} A=8.4 \\ 8.4=\pi r^2 \\ \frac{8.4}{\pi}=r^2 \\ \sqrt{\frac{8.4}{\pi}}=r \\ 1.635=r \end{gathered}[/tex]Finally, the diameter is twice the radius:
[tex]\begin{gathered} d=2r \\ d=2*1.635 \\ d=3.27\text{ in} \end{gathered}[/tex]Then the answer is the first option 3.27 in
Malik's car used \frac{1}{48}
48
1
of a gallon to travel \frac{1}{4}
4
1
of a mile. How many miles can the car go on one gallon of gas?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
The number of miles that the car can go on one gallon of gas is:
12 miles.
How to calculate the rate of miles per gallon?The rate of miles per gallon is given by the number of miles divided by the number of gallons, according to the equation presented as follows:
miles per gallon = miles / gallon.
In the context of this problem, the measures are found as follows:
Miles = 1/4 = distance traveled.Gallon = 1/48 = amount of fuel used to travel the given distance.Hence the rate is given as follows:
miles per gallon = (1/4) / (1/48)
For a division of fractions, we multiply the inverse of the denominator by the numerator, hence:
miles per gallon = 48 x 1/4 = 48/4 = 12 miles.
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the teacher wants to select 6 students from this class. the first selected student will be a media helper, the second one will be a pledge/flag helper, the third one will be a pencil sharpener, the fourth one will be attendance taker, the fifth one will be a board eraser and the sixth one will be a calendar helper. from this class of 13 students, how many different ways can this selection be done?
From this class, the teacher wishes to selected six students. 2,2,2,2,2,3 different ways are there to selected from this class of 13 students.
Given that,
From this class, the teacher wishes to selected six students. The first chosen student will assist with media, the second will assist with pledges and flags, the third will sharpen pencils, the fourth will take attendance, the fifth will wipe the board, and the sixth will assist with the calendar.
We have to find how many different ways are there to selected from this class of 13 students.
For 13 students,
We divide like 2,2,2,2,2,3.
The first 2 student will be a media helper,
The second 2 students will be a pledge/flag helper,
The third 2 students will be a pencil sharpener,
The fourth 3 students will be attendance taker,
The fifth 2 students will be a board eraser and
The sixth 2 students will be a calendar helper.
Therefore, This many ways we can selected the students.
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