In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.
Answer:
A rational number can be written as the ratio of two integers.
Step-by-step explanation:
Fractions (1/2), whole numbers (7 7/1), terminating decimals (2.33) repeating decimals (.222 repeating) square root of a perfect square (V-25 = 5/1) Integers (1 -2)
A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees. If only 18 inches of the wiper cleans the windshield, what is the area (in exact form) of the windshield that is wiped during each swing? 468π inches squared 156π inches squared 160π inches squared 108π inches squared
Answer: 108π inches squared
Step-by-step explanation:
Formula : Area of sector = [tex]\dfrac{\theta}{360^{\circ}}\times\pi r^2[/tex]
where , r= radius and [tex]\theta =[/tex]
Given : A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees.
If only 18 inches of the wiper cleans the windshield, then we take radius of the range of wiper cleaining = 18 inches
The area of the windshield that is wiped during each swing = Area of the sector made by wiper of with a central angle of 120 degrees.
[tex]=\dfrac{120}{360}\times\pi (18)^2\\\\=\dfrac{18^2}{3}\pi=\dfrac{18\times6}{1}\pi=108\p\text{ inches}^2[/tex]
Hence, the area (in exact form) of the windshield that is wiped during each swing is 108π inches squared.
can you please help me.
Answer:
Answer is D.
6 x 3 =1 8
9 x 3 = 27
11 x 3 = 33
14 x 3 = 42
18 x 3 = 54
c = 3 x w
Step-by-step explanation:
Ricky purchase Shoes for $159.95 and then exchanged them at a buy 1 get 1 half off sale. The shoes that he purchased on his return trip were $74.99 and $68.55. How much did he receive back from the store after his second transaction?
Answer:
50.68
Step-by-step explanation:
The higher priced shoes are full price and the lower priced shoes will be 1/2 price
74.99 + 1/2 (68.55)
74.99 + 34.28
109.27
He had 159.95 in credit
159.95-109.27
50.68 in return
The rectangle below has an area of x^2-6x-7 sq meters and a width of x-7 meters.
What expression represents the length of the rectangle?
Length=______ meters
Answer:
Length = ( x - 1 ) ( m)
Step-by-step explanation:
Area of rectangle is:
A(r) = l*w ( in m² ) where l is the length in m and w is the width in m
If we have: A(r) = x² - 6*x - 7 (m²), as an area of a rectangle, then we can factoring the equation, and get the rectangle dimensions, then:
x² - 6*x - 7 = ( x - 1 ) * ( x - 7 ) = area of the rectangle in m²
As problem statement establishes that ( x - 7 ) ( m) is the width, then
( x - 1 ) ( m) is the length
4 x^{2} -12 x +9 = 0
Rewrite the equation by completing the square.
Answer:
Step-by-step explanation:
[tex]4x^2-12x+9=0\\4*9=36\\6+6=12\\6*6=36\\4x^2-(6+6)x+9=0\\4x^2-6x-6x+9=0\\2x(2x-3)-3(2x-3)=0\\(2x-3)(2x-3)=0\\(2x-3)^2=0[/tex]
Answer:
[tex](x-\frac{3}{2}) ^{2}[/tex]
Step-by-step explanation:
When we complete the square, we take the b value from the equation:
a[tex]x^{2}[/tex] + bx + c = 0, and plug it into [tex](\frac{b}{2})^{2}[/tex] ..
First step is to make the coefficent of x go away. By dividing by 4.
x^2 - 3x + 9/4 = 0
now plug into the equation
(-3/2)^2 = 9/4 <-- because the square is parantheses, the negative goes away. Notice how there is a 9/4 already in our equation, meaning we dont have to do anything and simply can find the answer!
(x - 3/2)^2 = 0
Please help!
You roll a 6-sided die two times.
What is the probability of rolling a number less than 3 and then rolling a 6?
Simplify your answer and write it as a fraction or whole number.
Answer:
number less than 3=1 and 2
so 2/6 = 1/3 in lowest terms
then rolling a 6 =
there is only one 6 so it will be 1/6
I hope I helped
4. Would a 51-foot ladder be long enough to climb a 50-foot wall? Sketch a graph and find your answer using trigonometric functions
Answer:
Yes, it is enough to climb.
Step-by-step explanation:
Let suppose that wall is vertical and perpendicular to surface, a right-angled triangle is formed after using the ladder against the wall. (See attachment)
Ladder is useful only if its length is greater than wall length and trigonometrically speaking, the ratio of wall length to ladder length must be less than 1, associated with the definition of sine. That is:
[tex]\sin \theta = \frac{50\,ft}{51\,ft}[/tex]
[tex]\sin \theta = 0.980[/tex]
In a nutshell, the 51-foot ladder is useful to clime a 50-foot wall.
The lines below are perpendicular. If the slope of the green line is ą, what is
the slope of the red line?
Answer:
See below
Step-by-step explanation:
If i recall right when two slopes are perpendicular one slope is supposed to be the negative reciprical of the other slope, because of this I think your answer should be B. -\frac{2}{3}
Hope this helps
The lines are perpendicular and the slope of the red line is m₂ = -2/3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m₁ = 3/2
So , the slope of the green line is m₁ = 3/2
Since the lines are perpendicular to each other , the product of their slopes will be equal to -1
And , m₁ x m₂ = -1
So , ( 3/2 ) x m₂ = -1
Multiply by ( 2/3 ) on both sides , we get
m₂ = ( -2/3 )
Therefore , the slope of the red line is ( -2/3 )
Hence , the slope of the red line m₂ = ( -2/3 )
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The complete question is attached below :
The lines below are perpendicular. If the slope of the green line is 3/2 what is the slope of the red line?
The mean of 2,4,6,8,10
Answer:
6
Step-by-step explanation:
to find the mean, you must add all the numbers together and divide by the amount of numbers. for example, 2+4+6+8+10=30. next, you divide 30 by the amount of numbers, which is 5. if you count there are five numbers. so 30÷5=6 :)
Find the area of the circle below.
12 cm
Answer:
About 113.1
Step-by-step explanation:
Area of a circle= πr2
Radius= 6
6x6=36
36π= About 113.1
Answer:
work is shown and pictured
Please someone help me I’m confused
Answer:
a2 =14
a4 = 22
a11 = 50
Step-by-step explanation:
an = 10 + (n-1) *4
n is the term number
Let n =2
a2 = 10 +(2-1)*4 =10 +(1)*4 = 14
Let n =4
a4= 10 + (4-1)*4 = 10 *3*4 = 10+12 = 22
Let n = 11
a11 = 10 +(11-1)*4 = 10 *10*4 = 10+40 = 50
Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?
if four out of ten people vote, then in a town with two hundred thousand people how many will vote?
Answer:
80,000 people would answer in a town of 200,000 people
Answer:
80,000 people.
Step-by-step explanation:
Let's use a ratio:
voters : people overall
4 : 10
80 : 200
80,000: 200,000
80,000 out of 200,000 people voted.
For a field trip 5 students rode in cars and
the rest filled ten buses. How many students
were in each bus if 215 students were on the
trip?
Answer:
21
Plz mark me brainliest
Step-by-step explanation:
Answer:21 students were on each bus.
Step-by-step explanation:
215-5=210
210/10=21 the number of students divided by the number of buses
Today is your lucky day! You have just won a contest, and they can pay you your prize in two different ways.
Option one is to pay you $10,000 every 10 days, for 30 days.
Option two is a prize of a penny that doubles every day, for 30 days.
Which option would you choose?
Answer:penny
Step-by-step explanation:
Answer:
I would choose option two. Option one will make me a total of $30,000. Option two will make a total of $5,368,709.12.
A cylinder has a base radius of 5 centimeters and a height of 17 centimeters. What is its volume in cubic centimeters, to the nearest tenths place?
The slope of the graph of the equation y = 2 x minus 2 is 2. What is the y-intercept? y-intercept =
Answer:
(0, -2)
Step-by-step explanation:
y= 2x - 2
To find the y-intercept, or where the graph hits the y-axis, you plug 0 in for x
y= 2(0) - 2
y= -2
because 2 times 0 is 0, then 0 - 2 is -2
If they ask for just the value, it is -2
If they ask for the coordinate, it is (0, -2)
Answer:
the answer is -2
Step-by-step explanation:
What is important to keep in mind when selecting a sample?
a. The sample should be chosen based on specific criteria, such as the youngest students in the
class.
b. The sample should be chosen at random so that it is fair.
c. The sample should consist of every person in the population being studied.
d. The sample size should always be exactly one person or piece of data.
Answer: b. The sample should be chosen at random so that it is fair.
Step-by-step explanation:
Looking at the options:
a. The sample should be chosen based on specific criteria, such as the youngest students in the class.
This is false. Choosing a sample size based on specific criteria may skew the data unfairly. For example, in a survey on students' studying habits, choosing only the students with lowest grades would be an inaccurate representation of the data.
b. The sample should be chosen at random so that it is fair.
This is true. Randomizing a sample eliminates any bias, whether intended or unintended.
c. The sample should consist of every person in the population being studied.
Although it is ideal to survey every person in order to get the most accurate data, doing so is often impossible given the scope of a data set. Doing a survey on high schooler's study habits cannot possibly get data from every person in the population, as there are high school students across the world.
d. The sample size should always be exactly one person or piece of data.
One person's data is not a survey, it is just an opinionated study. Sample size should always be large enough to eliminate any accidental bias.
The correct choice is B.
Correct answers only please!
To the nearest cent, how much will she have in 3 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$125.97
Step-by-step explanation:
They have given you everything you need.
p = 100
r = 0.08
t = 3
B = final amount
B = 100(1 + 0.08)^3
B = 125.9712
since you're dealing with money you have to round to the nearest cent
B = $125.97
Please brainlist if I helped
The average mark of candidate in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are 148, 102,152. What is the average of the extracted scores t hat are extreme values (outliers)?
Answer:
Step-by-step explanation:
Given that : The average marks of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102 and 152.
The objective here is to determine the average of the extracted scores that are the extreme values (outliers)
NOW:
The average marks of candidates in an aptitude test was 128.5
i.e the Mean = 128.5
Standard Deviation = 8.2
outlier will be outsides;
then the range will be Mean ± 3 × SD
= 128.5 ± 8.2 × 3
= 128.5 ± 24.6
Range is ( 103.9 , 153.1)
102 is outside this range
Hence, the average of the extracted scores that are extreme values (outliers) will be 102 only
% of 10 = 10
I need help with this
Answer:
100 percent
Step-by-step explanation:
if x of y is y....
x is always 100!
Use the remainder theorem to determine whether x - 2 is a factor of
f(x) = x3 + 3x2 - x - 18
A)
Yes, x - 2 is a factor of f(x) because f(2) = 0
B)
No, x - 2 is not a factor of f(x) because f(2) = 0
C)
Yes, x - 2 is a factor of f(x) because f(-2) = -12
D)
No, x - 2 is not a factor of f(x) because f(-2) = -12
Answer:
A
Step-by-step explanation:
To determine if (x - 2) is a factor of f(x)
Evaluate f(2) and if equal to zero then (x - 2) is a factor
f(2) = 2³ + 3(2)² - 2 - 18
= 8 + 12 - 2 - 18
= 0
(x - 2) is a factor of f(x) because f(2) = 0 → A
The answer to the question "Use the remainder theorem to determine whether x - 2 is a factor of [tex]f(x) = x^3+3x^2-x-18[/tex]" is option A: Yes, x - 2 is a factor of f(x) because f(2) = 0
The given function is:
[tex]f(x) = x^3+3x^2-x-18[/tex]
The function [tex]f(x) = x^3+3x^2-x-18[/tex] is divided by x - 2
x - 2 will be a factor of [tex]f(x) = x^3+3x^2-x-18[/tex] only if f(2) = 0
Substitute x = 2 into [tex]f(x) = x^3+3x^2-x-18[/tex]
[tex]f(2) = 2^3 + 3(2)^2 - 2 - 18\\\\f(2) = 8 + 3(4) - 2 - 18\\\\f(2) = 8 + 12 - 20\\\\f(2) = 20 - 20\\\\f(2) = 0[/tex]
Since f(2) = 0, then we can conclude that x - 2 is a factor of [tex]f(x) = x^3+3x^2-x-18[/tex]
Learn more here: https://brainly.com/question/22237647
Help NEEDED asap if you dont know atleast comment
Item 11
MODELING REAL LIFE The stem-and-leaf plot shows the number of confirmed cases of a virus in 15 countries.
A stem and leaf plot. A vertical line separates each stem from its first leaf. The first row has a stem of 4 and leaves 1, 1, 3, 3, and 5. The second row has a stem of 5 and leaves 0, 2, 3, and 4. The third row has a stem of 6 and leaves 2, 3, 3, and 7. The fourth row has a stem of 7 and leaf 5. The fifth row has a stem of 8 and no leaves. The sixth row has a stem of 9 and leaf 7. The key shows 5 vertical bar 0 is equal to 50 cases.
Find the mean, median, mode, range, and interquartile range of the data. Round your answers to the nearest tenth, if necessary.
The mean is
.
The median is
.
The modes from least to greatest are
,
, and
.
The range is
.
I tried to do it and this is what i got
mean - 4.19
median - 3 or 4
Modes L to G - 0,1,1,2,2,3,3,3,3,3,4,4,5,5,5,6,7,7,7,8,9 and the most occuring number is 3
Range - 9
I tried i hope this can help, i'm sorry if not.
As always i would appreciate a brainliest
2006-1-2-3-4-...-48-49-50
Answer: What is the "..." for?
Step-by-step explanation:
Nine times a number is -63
Answer:-7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
Please help me now plz I promise I will mark you brainliest
Answer:
It should be 72 degrees
Step-by-step explanation:
angle j and h are the same so you just add 63 to 45 and once you get 108, just subtract that from 180 degrees which is the full measure of the triangle.
A biologist tags 25 birds with a band on their foot and lets them go back into the wild. The next year 100 total birds are captured and 5 of them have the foot bands. Enter an estimate of the total bird population. 20
Answer:
We can estimate a population of 500 birds.
Step-by-step explanation:
We can estimate the total bird population using a rule of three with the information given:
If we find 5 birds with the foot band among 100 birds captured, how many birds there are in total if inicially we put foot bands in 25 birds?
5 birds with foot band -> 100 birds captured
25 birds with foot band -> X total birds
X * 5 = 25 * 100
X = 25 * 100 / 5 = 500 birds
We can estimate a population of 500 birds.
An aluminum can is a right cylinder. Find the amount of paper needed for the can's label and the total
amount of aluminum needed to make the can. Round to the nearest tenth.
7 cm
12 cm
The amount of paper needed for the can's label is
1 cm?
The total amount of aluminum needed to make the can is
cm?
Please help put a bunch of points for this question do
Answer:
Label: About 527.9 square centimeters
Aluminum: About 835.7 square centimeters
Step-by-step explanation:
Amount of paper needed for the label:
You can imagine taking off the label and unrolling it, forming a rectangle. The height of this rectangle will be the height of the cylinder, while the length of the rectangle will be the circumference of the cylinder. Therefore, the area of that rectangle will be [tex]2\pi r h= 2 \cdot \pi \cdot 7 \cdot 12\approx 527.9[/tex].
Amount of aluminum needed for the can:
This time, you need to add in the top and bottom of the can as well, which each have area [tex]\pi r^2[/tex]. Together, they have area [tex]2\pi r^2=2\cdot \pi \cdot 7^2\approx 307.9[/tex]. Adding this to the area of the sides, you get a total of about 835.7 square centimeters.
Hope this helps!
Someone please help me this will be a lot of points and I will follow u and Mark u the brainiest
Answer:
Reindeer runs in 3 hrs = 20×1/4 miles
Reindeer runs in 1 hr = 81/4 × 1/3 = 6 × 3/4 miles (option 2)
*WILL GIVE BRAINLIEST* the following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x)=0.05x^2-7x+300
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
0.6 899.58
0.8 899.52
1 899.50
1.2 899.52
1.4 899.58
Based on the given information, determine which company has a lower minimum and find the minimum value.
a.) f(x) at (1, 899.50)
b.) g(x) at (70, 55)
c.) f(x) at (70, 55)
d.) g(x) at (1, 899.50)
Answer:
C.
Step-by-step explanation:
By analyzing the functions f(x) and g(x), we can see that they are both quadratic relations.
To find the minimum value, we want to find the y-coordinate of the vertex.
In f(x), by using the formula (-b/2a), we get the x-coordinate of the vertex, 70. When we substitute 70 into the function, we get 55 as our minimum.
In h(x), we can see that the lowest y-coordinate in the given points is 899.52. So (1, 899.50) is our vertex.
This means that in f(x), the minimum production cost is $70. In contrast, in h(x), the minimum production cost is $899.50. Therefore f(x) has a lower minimum, with its minimum value at (70, 55), our vertex.
Answer:
The Answer is C. f(x) at (70, 55)
Hope This Helps!