Answer:
irrational
Step-by-step explanation:
it cannot be written as a ratio
The given decimal number is a nonterminating and non-repeating decimal it is irrational.
The given decimal number is 0.828228222822228222228...
We need to identify whether the given decimal number is rational or irrational.
What are rational numbers and irrational numbers?Rational Numbers
The term ratio came from the word ratio which means the comparison of any two quantities and is represented in the simpler form of a fraction. A number is considered a rational number if it can be expressed in the form of a/b where both a (numerator) and b(denominator) are integers. The denominator of a rational number is a natural number(a non-zero number). Integers, fractions including mixed fractions, recurring decimals, finite decimals etc all come under the category of rational numbers.
Irrational Numbers
A number is considered an irrational number if it cannot be able to simply further to any fraction of a natural number and an integer. The decimal expansion of irrational numbers is neither finite nor recurring. Irrational numbers include surds and special numbers such as π. The most common form of an irrational number is pi (π). A surd is a non-perfect square or cube which cannot be simplified further to remove the square root or cube root.
Since the given decimal number is a nonterminating and non-repeating decimal it is irrational.
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In an AP. 19th term is 52 and 38th term is 128. Find the sum of the first 56 terms.
19th term of an AP = 52
38th term = 128
Find:the sum of the first 56 terms
Solution:We know that,
nth term of an AP – a(n) = a + (n - 1)d
Hence,
→ a + (19 - 1)d = 52
→ a + 18d = 52 -- equation (1)
Similarly,
→ a + (38 - 1)d = 128
→ a + 37d = 128 -- equation (2)
Subtract equation (1) from (2).
→ a + 37d - (a + 18d) = 128 - 52
→ a + 37d - a - 18d = 76
→ 19d = 76
→ d = 76/19
→ d = 4
Substitute the value of d in equation (1).
→ a + 18 * 4 = 52
→ a = 52 - 72
→ a = - 20
We know,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ S(56) = 56/2 * [ 2 (- 20) + (56 - 1) * (4) ]
→ S(56) = 28 * [ - 40 + 55 * 4 ]
→ S(56) = 28 * [ - 40 + 220 ]
→ S(56) = 28 * (180)
→ S(56) = 5040
Hence, the sum of first 56 terms of the given AP is 5040.
I hope it will help you.
Regards.
The sum of the first 56 terms of the given AP is 5040.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression. A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series.
Given that in an AP. 19th term is 52 and 38th term is 128.
nth term of an AP – a(n) = a + (n - 1)d
a + (19 - 1)d = 52
a + 18d = 52 -- equation (1)
Similarly,
a + (38 - 1)d = 128
a + 37d = 128 -- equation (2)
Subtract equation (1) from (2).
a + 37d - (a + 18d) = 128 - 52
a + 37d - a - 18d = 76
19d = 76
d = 76/19
d = 4
Substitute the value of d in equation (1).
a + 18 * 4 = 52
a = 52 - 72
a = - 20
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
S(56) = 56/2 * [ 2 (- 20) + (56 - 1) * (4) ]
S(56) = 28 * [ - 40 + 55 * 4 ]
S(56) = 28 * [ - 40 + 220 ]
S(56) = 28 * (180)
\S(56) = 5040
Hence, the sum of the first 56 terms of the given AP is 5040.
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Tell whether the following questions are biased or fair. Rewrite biased questions as fair question.
Do you eat at least the recommended number of servings of fruits and vegetables to ensure a healthy and long life?
Answer:
this aint no math question
Step-by-step explanation:
Answer/Step-by-step explanation:
Biased; How many serving of fruits and vegetable do you eat
~Learn with Lenvy~
What is the value of x in the proportion below?
StartFraction 180 kilometers over 3 hours EndFraction = StartFraction 540 over x EndFraction
6
9
12
60
Answer:
9
Step-by-step explanation:
steps are = to 9
Answer:
What is the value of x in the proportion below?
StartFraction 180 kilometers over 3 hours EndFraction = StartFraction 540 over x EndFraction Option B
(B) 9 100% Answer
Step-by-step explanation:
Answer in picture please solve
Answer:
n=-6
Step-by-step explanation:
2(n+5)=-2
2n+10=-2 (distribute the 2)
2n=-12 (subtract 10 from left, add it to right)
n=-6
Alfredo bought a fishing pole for 60%
off its original price of $97. If the tax
was 4% (of the sale price), how much
did Alfredo pay for the fishing pole?
Don't forget to round to the nearest cent!
Answer:
$40.35
Step-by-step explanation:
the pole is 60% off so we only pay 40% of the pole
97*.40=38.80
38.80*.04=1.55 <---tax
38.80+1.55=40.35
Jacki evaluated the expression below. 2 cubed (3 minus 1) + 4 (8 minus 12) = 2 cubed (2) + 4 (4) = 8 (2) + 16 = 16 + 16 = 32. What was Jacki's error?
Answer:His error lies in the subtraction of 12 from 8 , he wrote 4 instead of -4 , as 8-12 gives -4 instead of 4.
Step-by-step explanation:
Step 1
Rewriting this to a mathematical expression 2 cubed (3 minus 1) + 4 (8 minus 12) and solving correctly gives
2³(3-1)+ 4(8-12)
=8(2) + 4(-4)
= 16 +(-16)
16-16=0
Step 2-----Jacki's evaluation
2³(3-1)+ 4(8-12)
= 2³(2) +4(4)
= 8(2) +16= 16+ 16 =32
His error lies in the subtraction of 12 from 8 , he wrote 4 instead of -4 , as 8-12 gives -4 instead of 4.
Answer:
C
Step-by-step explanation:
I took the test ;)
3.6 X 1.5m/s^2 I will give you brainiest but explain
Answer:
mx x 5.4 over s2
Step-by-step explanation
You have to multiply the fraction then
multiply the numbers.
Another term for a possible "rule" of a pattern it is called
Answer:
A sequence
Step-by-step explanation:
A sequence is a collection of things arranged such that there is order or form in the collection. The components of a sequence are called elements or terms
The pattern in a sequence is achieved by the implementation of well defined rules, such that a term more than one space from a known term can be calculated
An example of a sequence is the following numbers;
1, 6, 11, 17, 22, 28,...
It can be observed that each subsequent term of the sequence is larger than the previous term by 5, therefore, 5 is known as the common difference, and the sequence is known as an arithmetic progression.
Can these three side lengths make a triangle? (Hint: use the Triangle
Inequality Theorem)*
Answer:
No
Step-by-step explanation:
Triangle inequality theorem : Any side of a triangle must be shorter than the other two sides added together.
Let's check if this theorem holds good with these side lengths
3< 9+5 (holds good)
5< 9+3 (holds good)
9< 5+3 (does not hold good)
So, these 3 sides cannot make a triangle
I WILL GIVE BRAINLIEST IF YOU ANSWER THIS QUESTION CORRECTLY
The answer is $3971. There are 209 members and each one gets one of each item. Add the costs of one of each item to get $19 per person. Then multiply $19 by 209 people and you get $3971 for everyone.
It is $17 for each person. ($10 + $3 + $2 + $2 = $17) So you do 17 x 209 = $3,553. So the answer is $3,553 dollars to pay for everyone.
What’s the slope?
( “M”only)
Answer:
slope (m) = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Find the slope by using the following equation:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let:
([tex]x_1 , y_1[/tex]) = (1 , 2)
([tex]x_2 , y_2[/tex]) = (7 , 7)
Plug in the corresponding numbers to the corresponding variables:
slope (m) = [tex]\frac{7 - 2}{7 - 1} = \frac{5}{6}[/tex]
slope (m) = [tex]\frac{5}{6}[/tex]
~
[tex] \LARGE{ \underline{ \purple{ \bf{Required \: answer:}}}}[/tex]
We can find the slope (m) by using the formula:
[tex] \rm{m = \dfrac{y2 - y1}{x2 - x1} }[/tex]The points given to us:
(x1 , y1) = (1 , 2)(x2 , y2) = (7 , 7)Plugging the given values of x1, y1, x2 and y2 to find the slope:
[tex] \rm{m = \dfrac{7 - 2}{7 - 1} }[/tex]
This is equals to,
[tex] \rm{m = \dfrac{5}{6} }[/tex]
And this is our required result....
#CarryOnLearning
Hi! If you know geometry well can you tell me if I am correct before I continue? I chose 3.5 because the length of both lines seem congruent.
Answer:
yes you are correct
Step-by-step explanation:
ANSWERS ASAP!!
Howdy everyone! I need help with these 3 math problems by just filling the numbers 4-19!! I'm sorry but I really need help!! Please don't answer random dumb questions for the points, be kind and actually help me!
Answer:
4. 2a
5. 3
6. 10
7. 2
8. 2
9. 5
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
there
WILL GIVE 15 POINTS FOR THE CORRECT ANDWER PLEASE I NEED HELP
Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they will each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.
Estimate the total cost that each friend will have to pay for gas and hotels. Explain and show your work on how you got your answer. Here are some figures that may help you out:
• Tony's car can travel 28 miles for each gallon of gas.
• The average fuel cost at the time of their trip is $3 per gallon.
• They plan to drive about 650 miles each day.
• They estimate the average cost of a hotel each night is $85.
• They will drive approximately 2,240 miles to get from Albuquerque to Boston
When I did the problem i got 2,445
I'm nit exactly sure how to solve this anyone got a clue
Answer:6
Step-by-step explanation:
23=5x-7
Rewrite the point-slope form of the equation y − 725 = 12( x −50 ) in slope-intercept form. What does the y-intercept represent in terms of the situation? Explain.
Answer:
Point-slope form
y-b = m(x-a)
y- 725 = 12(x -50)
y -725 = 12x -600
+725 +725
Slope Intercep form
y = mx + b
y = 12x + 125
Step-by-step explanation:
The slope- intercept form is y = 12x + 125 and the y- intercept is 125.
What is slope- intercept ?The slope-intercept form of a line is a way of writing the equation of a line so that the slope of the line and the y-intercept are easily identifiable.
Given:
y − 725 = 12( x −50 )
Now, arranging in the form of slope- intercept form
y- 725 = 12 x - 600
y = 12x - 600 + 725
y = 12x + 125
as, the slope intercept form is
y= mx + b
Hence, the y- intercept is 125
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The and age of each child in a random sample of children was recorded The value of the correlation coefficient between height and the children in the sample was 0.8 . Based on the line created from the data to the height of a child based on age which of the following is a correct statement ?
Options :
A.) On average, the height of a child is 80% of the age of the child.
B.) The least-squares regression line of height versus age will have a slope of 0.8.
C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
D.) The least-squares regression line will correctly predict height based on age 80% of the time.
E.) The least-squares regression line will correctly predict height based on age 64% of the time.
Answer:
C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
Step-by-step explanation: from the scenario stated above, The correlation Coefficient R = 0.8, which shows the strength of relationship between age and height of children. From the value of correlation Coefficient Given, we can obtain the Coefficient of determination (R²) which gives the percentage of Variation which can be explained by the regression model.
Hence the Coefficient of determination (R²) = 0.8² = 0.64. Hence, the proportion of variation in height of children which can he due to age is 0.64 while 0.36 can be based on other factors.
Based on the line created from the data to the height of a child based on age the correct statement is given by: Option C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
How can we get to know the variability of one variable to other from correlation coefficient?For that, we can use the coefficient of determination.
The coefficient of determination is square of correlation coefficient and thus, ranges from 0 to 1.
The coefficient of determination tells for unit variation in one variable will lead to how much variation in other variable and vice versa.
Let we take:
X = age of children of the sample considered
Y = height of children of the sample considered
Then, as it is given that:
[tex]r(X, Y) = 0.8[/tex]
Thus, the coefficient of determination is: [tex]r^2 = 0.8^2 = 0.64[/tex]
Thus, we get that 0.64 of the variation in the height is explained by the age of the children.
Thus, the true statement is:
Option C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
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The first step in solving the equation 5+|2x−4|=9 is to isolate the absolute value expression. What is the first step to isolate the absolute value expression? Divide both sides of the equation by 2. Subtract 9 from both sides of the equation. Subtract 5 from both sides of the equation. Add 4 to both sides of the equation.
Answer:
Subtract 5 from both sides of the equation.
Step-by-step explanation:
Given the function:
[tex]5+|2x-4|=9[/tex]
First step to solve the above equation is to isolate the absolute value function i.e. one side(either Left Hand Side or Right Hand Side) of equation must contain the terms containing the absolute function only.
In Left Hand Side, we have the absolute value function added to 5.
If we subtract 5 from both the sides, we get:
[tex]5+|2x-4|-5=9-5\\\Rightarrow |2x-4|=4[/tex]
So, after "subtracting 5 from both sides of the equation", the absolute function gets isolated on the left hand side of the equation i.e. Left Hand Side contains the absolute value function only.
Answer:
I just finished the Quiz and the Correct answer is "Subtract 5 from both sides of the equation"
Step-by-step explanation:
If there are 60000 pies on the counter and peter eats 90 of them how much pies will be left on the counter and please actually answer! :(
A - 52648
B - 9038
C - 59910
D - 10009
Answer:
C or 59910 I hope you get it right
Step-by-step explanation
The scale on a map is 5cm=25miles. Kyle measured the distance from his house
to the store and it was 13cm. How many miles away is the store from Kyle's
house?
Answer:
65 cm
Step-by-step explanation:
The unit rate of the scale is 1cm=5miles
so you would multiply 13 cm by 5 miles to get 65cm
Answer:
65 miles
Step-by-step explanation:
25 divided by 5 = 5
13 x 5 = 65
order the following number from least to greatest 0.85, 0.92, 8/9
Answer:
0.85, 8/9, .92
Step-by-step explanation:
8/9 = .88
Find the slope of the line.
On a coordinate plane, a line goes through (2, 0) and (6, 1).
a.
4
c.
One-fourth
b.
Negative one-fourth
d. 4
Answer: C 1/4
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge 2021
f(a) = – 3a – 2,
for a = -7
Answer:
7
Step-by-step explanation:
What is the y-intercept of the function f(x)= - 2/9x + 1/3
Answer:
y intercept is 1/3
Step-by-step explanation:
pleaseee!! i need help.
Answer:
n can be all numbers.
Step-by-step explanation:
Expand 3(n-2)+14
3n+8-8=3n+8-8
Simplify
3n=3n
Subtract 3n from each side
3n-3n=3n-3n
Simplify
0=0
All numbers work for n.
Hope this helped! :)
4hours and 12mins - 1hr and 26mins plz help i need a anwser
We know,
1 hour = 60 minutes
Then 4 hours = 4×60= 240 minutes
So 4 hour and 12 minutes := 240+ 12 mins
= 252 minutes
1 hour 26 minutes=60 + 26 minutes
= 86 minutes
Now we're ready to subtract!!!
252 minutes- 86 minutes=166 minutes
= [tex]\huge{\red{\bold{\boxed{2hour\:46minutes}}}}[/tex]
1.Yesterday, there were 10 problems assigned for math homework. Sedrick did 80%
of them correctly. How many problems did Sedrick get right?
Answer:
8
Step-by-step explanation:
[tex] \frac{80}{100} \times 10 = 8[/tex]
find the value of z and z plus 45
Answer:
Z=54 And Z+45=99
Step-by-step explanation:
What would be the gravity in relation to Earth of a planet with 3.4 times the gravity of Mercury
Answer:
t is 3.055.<-not a decimal just a period
Step-by-step explanation:
plz help with this -5/7x - 8/21x + 1/3x
Answer:
-68
Step-by-step explanation:
