The n th term of the series is 3n where n is the term of reference
As we can see that there is constant difference in the terms
12-9=3
9-6=3
6-3=3
We are made sure that it is the arithmetic progression
Common difference is the difference that is constantly subtracted or added to each term after the first term
Thus the common difference 'd' is 3 as per the calculations above
Now the first term is 3
We know that any N th term of arithmetic progression is given by the formula
Tn= a+ (n-1)*d
where a is the first term of the progression and n is the term of reference and d is the common difference
a=3
d=3
Therefore, nth term of the series is = Tn= 3 + (n-1) *3
Tn= 3+3n-3
Tn = 3n
Hence the n th term of the series is 3n where n is the term of reference
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Un coche tarda 9hrs en recorrer un trayecto siendo su velocidad de 85km/h, ¿Cuánto tardará en recorrer el mismo trayecto a 70km/h?
The time taken to travel the distance 70 Km/h is 11 hours.
What is speed distance formula?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.
The formula can be rearranged in three ways:
speed = distance ÷ timedistance = speed × timetime = distance ÷ speedGiven:
time = 9 hours
speed = 85 Km/h
Now, distance
=speed * time
=85 * 9
= 765 km
As, the speed is 70 km/h
time = distance/ speed
time = 765 / 70
time = 10.92
time= 11 hours
Hence, the time taken to travel the distance 70 Km/h is 11 hours.
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The translation of the question is:
A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?
l2x-2l = 8
what are the solutions of the equations
Answer:
x=5
Step-by-step explanation:
The absolute value is positive, so the equation stays the same:
2x-2=8
Add 2 on both sides:
2x=10
Solve:
x=5
Answer:
x=29/12
Step-by-step explanation:
Let's solve your equation step-by-step.
12x−21=8
Step 1: Add 21 to both sides.
12x−21+21=8+21
12x=29
Step 2: Divide both sides by 12.
12x/12 = 29/12
x=29/12
Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
\(-3a=-3(3,2)\text{ = (-9,-6)}\)Also, vector b = (-5, 6), then;
\(2b=2(-5,6)=(-10,12)\)Then, -3a + 2b = (-9, -6) + (-10, 12)
\(\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}\)The answer is (-19,6)
\(G(3)=4^{2}\)
Answer:
G = 5.333
Step-by-step explanation:
Given: G(3) = 4^2
3 times G is 3G:
3G = 4^2
4 squared is 16:
3G = 16
Divide both sides by 3:
G = 5.333
Find the measure of the missing angles.
X= _ degrees Y=_degrees
PLS HELP IEKSKE PLS
What's the product of (3a^2b)*(-2ab^3)
Explanation:
First, we can rewrite:3a2b×−2ab3as(3×−2)(a2×a)(b×b3)⇒−6(a2×a)(b×b3)Next, use this rule for exponents to rewrite the expression:a=a1−6(a2×a1)(b1×b3)Now, use this rule of exponents to complete the multiplication:xa×xb=xa+b−6(a2×a1)(b1×b3)⇒−6a2+1b1+3⇒−6a3b4
-6x +20 >= -11x
solve the inequality
Answer:
x≥-4Step-by-step explanation:
plz i need brailyesit
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed. What is the volume of the sphere?
10 meters cubed
20 meters cubed
30 meters cubed
40 meters cubed
Explain how the sample you collect can affect your understanding of a population.
Use the word representative in your response.
The sample we collect plays a cruciThe sample we collect can significantly affect our understanding of a population,
especially when it comes to making generalizations or drawing conclusions about the entire population based on the sample data. The key aspect in this regard is whether the sample is representative of the population.
A representative sample is one that accurately reflects the characteristics, diversity, and distribution of the population from which it is drawn. When our sample is representative, we can have greater confidence in generalizing the findings from the sample to the larger population. However, if our sample is not representative, our understanding of the population may be biased or limited.
In the provided example, the given data represents different age groups and their reported time spent with friends per day. If we were to collect a sample from this population, it would be crucial to ensure that the sample includes individuals from each age group in proportion to their representation in the population. This would help ensure that our sample accurately reflects the age distribution of the population.
If our sample is not representative, it may lead to inaccurate conclusions. For instance, if we only surveyed individuals from the age group 55-64 and ignored the other age groups, our understanding of the population's time spent with friends would be limited to that specific age group. We wouldn't be able to generalize our findings to the entire population because we would have missed important variations in behavior across other age groups.
To improve the representativeness of our sample, we could use random sampling techniques, such as simple random sampling or stratified sampling, to ensure that individuals from all age groups are included in the sample. By doing so, we can enhance our understanding of the population as a whole and make more accurate inferences.
In conclusion, the sample we collect plays a crucial role in shaping our understanding of a population. A representative sample enables us to make valid generalizations and draw reliable conclusions about the entire population. It ensures that the characteristics and diversity of the population are properly reflected in the sample, allowing for more accurate insights and informed decision-making.al role in shaping our understanding of a population
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julio bought 4 pounds of carrot sticks and 3 pounds of celery sticks for the school potluck. he had 6 bowls for serving vegetables. he wants to put an equal amount of carrots and celery in each bowl. how many pounds of vegetables would be in each bowl
Answer:2
Step-by-step explanation: 4 times 3 equals 12 and 12 divided by 6 is 2
There are 1(1/6) pound of vegetables in each bowl.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of bowls = 6
Number of carrot sticks = 4 pounds
Number of celery sticks = 3 pounds
The number of carrots in each bowl.
= 4/6
= 2/3 pounds
The number of celery sticks in each bowl.
= 3/6
= 1/2 pounds
The number of pounds of vegetables in each bowl.
= 2/3 + 1/2
= (4 + 3)/6
= 7/6
= 1(1/6) pounds
Thus,
There are 1(1/6) pound of vegetables in each bowl.
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An artist is going to cut four similar right triangles from a rectangular piece of paper like the one shown to the right. What is BE to the nearest tenth when AC=13
The measurement of altitude BE is 4 unit.
What is an altitude?As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.
As ABCD is rectangle
AD = BC = 12
ΔABC = ΔBCD
BE = FD
5² = 3²+BE²
AE = 3
BE = √(5²-3²)
BE = 4
Thus, The measurement of altitude BE is 4 unit.
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Shannon drove 475 miles. Which expression shows the miles per gallon obtained by her car if she used g gallons of gas on the trip?
A.
475 - g
B.
475 × g
C.
475 + g
D.
475 ÷ g
Answer:
D
Step-by-step explanation:
gallon/miles
In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to 2:21. Find the number of teachers who joined the school.
Answer:
50 Teachers
Step-by-step explanation:
To solve this problem, we first need to find the number of teachers before the new teachers were added. To do so, I created Model 1. On the bottom of the ratios, we have students. On the top, is teachers. The X is the number of teachers we are trying to find. Following the model, I multiplied 2,100 x 1 (2,100) and divided it by 14 to get 150 teachers. Then, I set up a similar model with the new student-teacher ratio (Model 2). From there, I multiplied 2,100 x 2 (4,200) and divided it by 21 to get 200 teachers. Now I have the original number of teachers and the new number of teachers. Subtract the new by the original to find the teachers added and you get the answer of 50 teachers added.
What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
y−1=611(x−4)
y+1=67(x+4)
y+1=611(x+4)
y+4=116(x+1)
Answer:
3rd choice
Step-by-step explanation:
Answer:
it's c
Step-by-step explanation:
Peter creates balloon animals for different events. He has 644 balloons. He wants to use
the same number of balloons for each of 28 events. How many balloons can Peter use at
each event?
Answer:
He uses 23 balloons for each of the 28 events.
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
I divided 644 by 28. There are 644 balloons and you want to split
(divide) into the same number of balloons with none left over. Look for those key words to tell you what type of math your doing. Hope this helps!
due in 5 min
help me plss
Answer:
What is the question asking for??
Step-by-step explanation:
area of the square=7*10=70cm2
area of the semi circle=πr^2/2
=22/7*5*5/2
. =39.25cm2
total area=39.25+70=109.25cm2
If the door to the library is at (2, 4), the door to the mall is at (8, 2), and one
square unit equals one square mile, the approximate distance between the library
and the mall is
miles, when measured door to door.
Answer:
6 miles
Step-by-step explanation:
The distance formula is expressed as;
D = √(x2-x1)²+(y2-y1)²
D = √(2-4)²+(8-2)²
D = √(-2)²+(6)²
D = √4 + 36
AD = √40
AD = 6.32
Hence the approximate distance between the library and the mall is 6 miles
A group of 75 math students were asked whether they
like algebra and whether they like geometry. A total of
45 students like algebra, 53 like geometry, and 6 do
not like either subject.
Algebra vs. Geometry
Likes Algebra
Does Not
Like Algebra
Total
Likes
Geometry
Mark this and return
a
3
53
Does Not
Like Geometry
b
6
e
Total
45
P
75
What are the correct values of a, b, c, d, and e?
a 16, b = 29, c = 22, d = 30, e = 24
a = 29, b = 16, c = 30, d = 22, e = 24
a 16, b = 29, c = 24, d = 22, e = 30
H
a = 29, b = 16, c = 24, d = 30, e = 22
The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.
For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:
We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.
75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)
Simplifying this equation, we have:
75 = 98 + 6
75 = 104
This equation is incorrect, so we can eliminate options c and d.
Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.
Using the correct values for a and b, we have:
16 + b = 6
b = 6 - 16
b = -10
Since we can't have a negative value for the number of students, option a is also incorrect.
The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.
Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)
Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)
Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)
Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)
All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.
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not every linearly independent set in set of real numbers r superscript ℝn is an orthogonal set. T/F?
The given statement is true.
Consider linearly independent vectors of \(R_{n}\)
Where n = 2
\(V = \[\begin{array}{ccc}4&\\2\end{array}\right]\)
\(U = \[\begin{array}{ccc}5&\\6\end{array}\right]\)
Now product of these vectors
UV = 4x5 + 2x6
= 32
Hence these vectors are not orthogonal.
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Help pleanbehehdhddhdhdhdhdhdhdhhd
Answer:
Step-by-step explanation:
h
------ - 1 = -3
6
To solve for h, first add 1 to both sides to isolate h/6:
h
---- = -2
6
Now isolate h by multiplying both sides by 6:
h = -12
Answer:
h is -12
..... .. . . . . .. . . .
The daily dinner bills in a local restaurant are normally distributed with a mean of $30 and a standard deviation of $5.
What is the probability that a randomly selected bill will be at least $39.10?
a. 0.9678
b. 0.0322
c. 0.9656
d. 0.0344
The probability of a randomly selected bill being at least $39.10 is approximately option (d) 0.0344
To solve this problem, we need to standardize the given value using the standard normal distribution formula
z = (x - mu) / sigma
where:
x = $39.10 (the given value)
mu = $30 (the mean)
sigma = $5 (the standard deviation)
z = (39.10 - 30) / 5
z = 1.82
Now, we need to find the probability of a randomly selected bill being at least $39.10, which is equivalent to finding the area under the standard normal distribution curve to the right of z = 1.82.
Using a standard normal distribution table or calculator, we can find that the probability of a randomly selected bill being at least $39.10 is approximately 0.0344.
Therefore, the correct option is (d) 0.0344.
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Which type of parent function is f(x) = x2? O A. Square root O B. Linear O C. Cube root O D. Quadratic
Answer: D. quadratic
Step-by-step explanation:
I will mark you brainiest if you can answer this
Answer:
9 buses
12 cars
(Step-by-step explanation:
x=bus x+y=21 --> y=-x+21
30x+4y=318 --> y= -30x/4 + 318/4
y=car
x= 9
y=12
:) hope this help
What’s the answer 4(x+4)=24+6x
Answer:
x = -4
Step-by-step explanation:
used app by google called Socratic, it can solve a ton of problems
Answer:
x = -4
Explanation:
[ Step 1: Simplify both sides of the equation ]
4(x + 4 ) = 24 + 6x
(4)(x) + (4)(4) = 24 + 6x (Distribute)
4x + 16 = 24 + 6x
4x + 16 = 6x + 24
[ Step 2: Subtract 6x from both sides ]
4x + 16 − 6x = 6x + 24 − 6x
−2x + 16 = 24
[ Step 3: Subtract 16 from both sides ]
−2x + 16 − 16 = 24 − 16
−2x = 8
[ Step 4: Divide both sides by -2 ]
-2x / -2 = 8 / -2
x = -4
Given: ΔABC, AC = BC, AB = 3 CD ⊥ AB, CD = √3 Find: AC
Answer:
\(\boxed{AC = 2.3}\)
Step-by-step explanation:
AD = BD (CD bisects AB means that it divides the line into two equal parts)
So,
AD = BD = AB/2
So,
AD = 3/2
AD = 1.5
Now, Finding AC using Pythagorean Theorem:
\(c^2 = a^2+b^2\)
Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)
\(AC^2= (1.5)^2+(\sqrt{3} )^2\)
\(AC^2 = 2.25 + 3\)
\(AC^2 = 5.25\)
Taking sqrt on both sides
\(AC = 2.3\)
Answer:
\(\boxed{2.29}\)
Step-by-step explanation:
The length of AB is 3 units.
The length of CD is \(\sqrt{3}\) units.
D is the mid-point of points A and B.
AD is half of AB.
\(\frac{3}{2} =1.5\)
Apply Pythagorean theorem to solve for length of AC.
\(c=\sqrt{a^2 +b^2 }\)
The hypotenuse is length AC.
\(c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }\)
\(c=\sqrt{2.25+3 }\)
\(c=\sqrt{5.25}\)
\(c= 2.291288...\)
enter the fraction as a product of a whole number and a unit fraction: 4/5 = blank times blank
A unit fraction is a fraction with the numerator equals 1.
So, in order to have the fraction 4/5, we can multiply the number in the numerator by a unit fraction with the same denominator:
\(\frac{4}{5}=4\cdot\frac{1}{5}\)So the first blank space is filled with 4 and the second one with 1/5.
PLEASE HELP ME ASAP WILL GIVE BRAINLIEST
Answer:
7.)44 degrees
8.)133 degrees
9.)I think it is 15 degrees
10.)46 degrees
Step-by-step explanation:
7.)79-35=44
8.) 179-46=133
9.) I'm not actually sure
10.)X+55+x+115=152
A.)2x + 170 = 152
B.)2x = -18
C.)X=-9
D.)(-9)+55=46
How to reduce decimals to fractions.
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.
What is the opposite of –16?
HELP PLEASE FAST!!!!
Answer:
Domain = (-5,1,3)
Range = ( -4,-2,0,2,4)
This is not a function
Step-by-step explanation:
Domain = (-5,1,3)
Range = ( -4,-2,0,2,4)
Since one x value gives two points for y
this is not a function