Answer:
[tex]a_{14}=\dfrac{52}{3}[/tex]
Step-by-step explanation:
General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.Given terms of an arithmetic sequence:
[tex]a_4=14[/tex][tex]a_{10}=16[/tex]Substitute the values into the general formula to create two equations:
[tex]\sf\underline{Equation \:1}\\\begin{aligned}a_4 & = 14\\\implies a+(4-1)d & = 14\\a + 3d & = 14\end{aligned}[/tex]
[tex]\sf\underline{Equation \:2}\\\begin{aligned}a_{10} & = 16\\\implies a+(10-1)d & = 16\\a + 9d & = 16\end{aligned}[/tex]
Subtract Equation 1 from Equation 2 to eliminate a:
[tex]\begin{array}{l r l}& a+9d & = 16\\- & a+3d & = 14\\\cline{2-3}&6d & = \:\:2\end{array}[/tex]
Solve for d:
[tex]\begin{aligned}\implies 6d & = 2\\\dfrac{6d}{6} & = \dfrac{2}{6}\\d & = \dfrac{1}{3} \end{aligned}[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\begin{aligned}a + 3d & = 14\\ \implies a+3 \left(\dfrac{1}{3}\right)&=14\\a+1&=14\\a+1-1&=14-1\\a&=13\end{aligned}[/tex]
Substitute the found values of a and d into the general formula to create an equation for the nth term of the arithmetic sequence.
[tex]\implies a_n=13+(n-1)\dfrac{1}{3}[/tex]
[tex]\implies a_n=13+\dfrac{1}{3}(n-1)[/tex]
To find the 14th term, simply substitute n = 14 into the equation:
[tex]\begin{aligned}a_n & = 13+\dfrac{1}{3}(n-1)\\\implies a_{14}& = 13+\dfrac{1}{3}(14-1)\\&=13+\dfrac{1}{3}(13)\\ & = \dfrac{39}{3}+\dfrac{13}{3}\\&=\dfrac{52}{3}\end{aligned}[/tex]
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find the x and y intercept
6.8x+8.8y+9.8=0
From the given equation 6.8x+8.8y+9.8=0 the value of x-intercept is -98/68 and value of y-intercept is -98 /88.
As given in the question,
Given equation :
6.8 x +8.8 y +9.8= 0
To get x -intercept substitute y =0 in the equation :
6.8 x+ 8.8 (0) + 9.8=0
⇒6.8x= -9.8
⇒x= 98 /68
To get y -intercept substitute x =0 in the equation :
6.8 (0)+ 8.8y + 9.8 =0
⇒8.8y= -9.8
⇒ y= 98 /68
Therefore, from the given equation 6.8x+8.8y+9.8=0 the value of
x-intercept is -98/68 and value of y-intercept is -98 /88.
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What is the solution set to the inequality m-7>-2(m+0.5)?
Select a ray. Move the point on the ray to the correct place on the number line.
The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.
What is real numbers?Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.
This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.
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If 6 is added to the square of a positive number, the sum is 31. Find the number.
Answer:
The number is 5.
Step-by-step explanation:
Given: If 6 is added to the square of a positive number, the sum is 31. Find the number.
Step-by-step solution:
Step 1: Formula
We know that the square of a positive number plus 6 is equal to 31. In a formula, it would look like [tex]\sqrt{x}[/tex] + 6 = 31 where x replaces the positive number.
Step 2: Subtract 6
We need to get x by itself to find the number. Subtract 6 on both sides to cancel it out and move it to the left
so, [tex]\sqrt{x}[/tex] + 6 -6 = 31 -6 = [tex]\sqrt{x}[/tex] = 25
Step 3: Square Root of 25
The Square Root of 25 is 5. We know this because 5*5 = 25.
Therefore, the number is 5.
Lori ran 5/3 miles Monday, 15/4 miles Tuesday, 9/2 miles Wednesday,
3/5 on Thursday and 2/5 miles on Friday. What is the average number of miles
Lori ran per day this week?
Is 14 a factor of 3,024
Answer:
Yes, 14 × 216 = 3024
Step-by-step explanation:
the base is of this pyramid is a square. how do you find the area of a square.
Answer:
If you're just looking for the area of the square, then it's 49m. If you want the surface area of the whole pyramid, it's 189.
Step-by-step explanation:
For just the square, it's easy: Multiply the side lengths. 7x7 is 49.
For the surface area, find the area of the square (49) and the four triangles. To find the areas of the triangles, multiply the base (bottom, here it's the side length of the square) by the height (in this case 10m) and divide by 2. 7x10=70 and 70/2=35. Now since there are 4 triangles, multiply that by 4. 35x4=140, and now add the area of the square; 140+49=189. I don't think you wanted the surface area though, but I hope this helps!
complete exercises 22 - 24.
X
h(x)
-3
-24
-2
0
-1
8
0
6
1
0
2
-4
4
18
13. Two of the zeros of h(x) are listed in the table. Between which two values of x does the Intermediate
Value Theorem guarantee that a third value of x exists such that h(x) = 0? Explain your reasoning.
Answer:
send the image of the exercise
A travel agent is booking trips for tourists who travel from New York to Chicago. Tourists have three choices for how to travel from New York to Chicago. They can take an airplane for $350, a bus for $150, or a train for $225. Once they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. If each option is equally likely to occur, what is the probability that a tourist will spend more than $250 on these 2 legs of the trip?
From the calculation below, the probability that a tourist will spend more than $250 on the 2 legs of the trip is 2/3.
How do we calculate the amount spent using probability?From the question, the number of possible options available and their total amount is as follows:
Airplane and Van = $350 + $60 = $410
Airplane and Cab = $350 + $40 = $390
Bus and Van = $150 + $60 = $210
Bus and Cab = $150 + $40 = $190
Train and Van = $225 + $60 = $285
Train and Cab = $225 + $40 = $265
From the above, it can be observed that we have a total number of 6 different options available and 4 of the options are more than $250.
Therefore, we have:
Probability of spending more than $250 = Number of options that are more than $250 / Total number of different options = 4/6 = 2/3
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Two in-line skaters, Nell and Kristin start from the same point and skate in the same direction.Nell skates at 8 mile per hour and Kristin skates at 10 miles per hour. if they can keep up the pace for 4.5 hours, how far apart will they be at the end of the time?
At the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.
Here, we are given that Nell and Kristin start from the same point and skate in the same direction.
Speed of Nell = 8 miles per hour
Time for which he skates = 4.5 hours
Thus, the distance travelled by Nell will be-
Distance = Speed × time
= 8 × 4.5
= 36 miles
Similarly, Speed of Kristin = 10 miles per hour
Time for which he skates = 4.5 hours
Thus, the distance travelled by Kristin will be-
= 10 × 4.5
= 45 miles
Thus, the distance between them will be-
45 - 36 = 9 miles.
Thus, at the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.
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Nell and Kristin, two inline skaters, begin at the same location and move in the same direction. While Kristin skates at 10 miles per hour, Nell skates at 8 miles per hour. 5 miles apart will they be at the conclusion of the 4.5 hours if they maintain their current rate.
Distance =Rate x time ....... d=rt
The difference in the distances traveled will be how far apart they are 12(2.5)-10(2.5)=2(2.5)=5 miles apart
Note that you can find their individual distances and subtract those to get the same answer:
Nell: distance =10(2.5)=25 miles
Kristin: distance =12(2.5)=30$ miles
30-25=5 miles apart
Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
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Guys this is an important question do NOT PUT A RANDOM ANSWER OR WRITE RANDOM THINGS
It’s annoying man
Answer: 1/7
Step-by-step explanation:
The total amount of cars that had AC problems is 30+20=50. The total amount of cars is 30+20+200+100=350. 50/350 = 1/7
Ian measures 9 kg of rice. One kilogram is approximately equal to 2.2 pounds. Which measurement represents the number of pounds of rice?
By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
We are given that:
1 kg of rice = 2.2 pounds of rice.
We need to find the number of pounds of rice in 9 kg of rice.
So, we will use the operation of multiplication to covert the units from kg into pounds.
So, we get that:
9 kg of rice = 2.2 × 9 pounds of rice
9 kg of rice = 19.8 pounds of rice.
Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
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No
5) Determine if the list of numbers is an arithmetic sequence by choosing Yes or No. If Yes
then choose the option with the correct common difference "d."
18, 16, 14, 12, 10,...
Yes, d= -2
Yes, d = -3
Yes, d = 2
Helppp!!
The option yes, d = -2 is correct
The arithmetic sequence or progression is a sequence of numbers such that the difference between the consecutive terms is constant.
The formula of an arithmetic sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
Here the sequence is 18, 16, 14, 12, 10...... which is in arithmetic sequence as there is a common difference between them.
Now we have to find the common difference between the two consecutive terms of the series,
common difference (d) = 16- 18 = 14 - 16 = -2
Therefore the series is an arithmetic sequence and the common difference between them is -2.
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I have a few math problems I need help with so they're all in picture form (and in separate questions). I'd appreciate it if they were explained to me, but it is not a requirement.
Answer:
In those questions you asked, we can use equation to find the answer but the 1st question's x did not get an exact value so you can do no solution. Thank you
Which system of inequalities represents the graph?
y−6≤−11x
y+3x≤−4
−2x+3y<15
y−6≤−11x
y+3x≥−4
−2x+3y>15
y+11x≥6
y+4≥−3x
−2x+3y>15
y+11x≥6
y+4≤−3x
−2x+3y<15
The system of inequalities that represents the graph are:
y−6≤−11x
y+3x≥−4
−2x+3y>15
Option B
This is further explained below.
What is a system of equalities?Generally, The term "set of simultaneous equations" refers to a finite collection of equations in the subject of mathematics, all of which are looking for the same solution.
A system of equations or an equation system is a name that is sometimes used to refer to this kind of collection of equations.
In conclusion,
y−6≤−11x
y+3x≥−4
−2x+3y>15
represents the graph
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HELP PLEASE!! I WILL GIVE BRAINLYEST
8. Mrs. Shin has a piece of lumber that is 11- inches wide. She plans to split the width of lumber into 3 equal pieces. How wide will each piece be?
the answer is 8
Step-by-step explanation:
just minus 11by 3
What type of number is √14? (square root of 14) Multiple answers can be selected.
A. Rational
B. Irrational
C.Natural
D. Whole
F. Integer
Answer:
B. Irrational
Step-by-step explanation:
The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.
Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.
Help me solve this question
Answer:
x = -26
Step-by-step explanation:
[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]
This is in the domain of the equation, and is thus a solution.
7. y = x + 5
8. y=x-7
9. y=x-b
Solve for x: ax + b = c.
Han's younger sister is riding her tricycle in a straight line. After 3 s, her speed is 0.5 m/s. After 5 s, her speed is 1.5 m/s. what is her acceleration during this time?
The acceleration during this time will be 0.5 m/s².
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Han's younger sister is moving straight ahead on her tricycle. Her speed is 0.5 m/s after 3 seconds. Her speed is 1.5 m/s after 5 seconds.
We know that the first equation of motion is given as,
v = u + at
The information is given below.
v = 1.5 m/s, u = 0.5 m/s, and t = 2 s. Then the value of the acceleration will be
v = u + at
1.5 = 0.5 + 2a
2a = 1
a = 1/2
a = 0.5 m/s²
The acceleration during this time will be 0.5 m/s².
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Explain how negative powers of 10 can be
helpful when writing and comparing small
numbers.
Negative powers of 10 helpful when writing and comparing small numbers.
Small numbers (numbers between 0 and 1) are written with a negative power of ten. The specific power of 10 indicates just how big or how small the number is. You can compare two numbers written in scientific notation by looking at their powers of 10. The number with the greater power of 10 will be the greater number.
When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then
if the powers of 10 are the same in compared numbers are the same, just compare the numbers which are multiplied by these powers of 10. For example, 3.6× 10∧-6 is greater than 2.6× 10∧-6 because powers are the same (-6) and 3.6 is greater than 2.6if the powers are different, then the smaller is power, the smaller is number (number with the smaller negative power has more places after decimal point). For example,3.6× 10∧-6 is greater than 2.6× 10∧-7 because -6 > -7.10 to the power of negative 7 is equal to 0.0000001.For example- 0.00003450000
3.45 x 10 -5
3.450000 x 10 -5
0.345 x 10 -4
0.3450000 x 10 -4
Hence it is prooved that negative powers of 10 helpful when writing and comparing small numbers.
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Match the solution to its expression.
3/4*1/4 = 3/16
3/7*1/2 = 6/7
In an effort to keep low-wage workers' salaries commensurate with the cost of living, a number of states have amended their constitutions to allow the minimum wage to be adjusted with inflation.
You are the accountant for a company that owns a chain of 16 fast food restaurants in a state which adjusts the minimum wage for inflation. Each restaurant employs 55 workers, each averaging 20 hours per week at the current federal minimum wage, $7.25 per hour.
(d)
How much in "additional wages" will the company have to pay out next year at the adjusted rate (in $)? (Round your answer to the nearest dollar.)
The "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.
What is the inflation-adjusted pay rate?The inflation-adjusted pay rate is the rate after adjusting for inflation.
Data and Calculations:The number of fast-food restaurants = 16
The number of workers per restaurant = 55
Average weekly hours per worker = 20 hours
The number of weeks per year = 52
The current federal minimum wage per hour = $7.25
The total hours worked by the workers = 915,200 hours (16 x 55 x 20 x 52)
Total current wages = $6,635,200 (915,200 x $7.25)
Inflation rate = 7.5%
Inflation-adjusted wage rate = $7.79 ($7.25 x 1.075)
Total wages for next year = $7,129,408 ($7.79 x 915,200)
Additional wages next year = $494,208 ($7,129,408 - $6,635,200)
Thus, the "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.
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Which of these is NOT a rational number?
0.54225422...
0.55555555...
0.3434343...
0.61166117...
0.61166117... is not an rational number as it has no regularly repeating digit or group of digits.
What is rational number?A rational number is one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero. Every integer, including 3/7 (3 = 5/1) and 7 is a rational number.
Boldface Q is typically used to represent the field of rationals, also known as the field of rational numbers, the set of all rational numbers, or "the rationals."
Real numbers are those that make sense. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for example, 3/4 = 0.75), or eventually starts to repeatedly repeat the same finite sequence of digits (for instance, 9/44 = 0.20454545).
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Find the product of 2(5) and (2) in simplest form. Also, determine whether the result is irrational or rational and explain
The product of 2√5 and √2 is 2√10.
And, The result is an irrational number.
Here,
We have to find the product of 2√5 and √2.
And, also determine the result is a rational or irrational number.
What is Irrational number?
A number which cannot be written in the form of fraction p/q, is called an Irrational number.
Now,
The product of 2√5 and √2 is;
⇒ 2√5 * √2 = 2√5*2 = 2√10
Hence, The product of 2√5 and √2 = 2√10.
Since, √10 is an irrational number because it cannot be written in the form of fraction.
Hence, 2√10 is an irrational number.
Therefore, The product of 2√5 and √2 is 2√10.
And, The result is an irrational number.
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The correct question is this;
Find the product of 2√5 and √2 in simplest form. Also, determine whether the result is irrational or rational and explain
Rochelle had an important swim meet coming up, so she made a schedule for herself for extra practice. She practiced for 609 minutes over a 3-week time span to get herself ready. She spent the same amount of time practicing each week. What is the constant of proportionality (k) between the number of minutes Rochelle practiced (m) and the number of weeks she spent practicing (w)?
Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.
Given that,
Rochelle planned out additional practice because she was getting ready for a big swim meet.
Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.
We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).
3 week =609 minutes
3w=609m
1w=609m/3
1w=203m
For 1 week she practiced 203 minutes.
Now,
Constant of proportionality is
m=kw
203=k(1)
k=203
Therefore, the constant of proportionality is k=203.
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3. A car can accelerate at a rate of 0.5 meters per second squared if it is already moving forwards at an initial velocity of 6 meters per second.
a. Write a differential equation for velocity. Write an initial condition for the velocity.
b. Solve the initial value problem you wrote in (a) to find a formula for velocity.
c. Use the formula for the velocity you found in (b) to write an initial value problem for the car’s position. Assume that the car is initially at position 0.
d. Solve the initial value problem you wrote in (c) to find a formula for the position of the car.
e. How fast is the car going after 30 seconds?
Using the relation between acceleration, velocity and distance, it is found that:
a) The differential equation for the velocity is: [tex]\frac{dV}{dt} = 0.5[/tex]
b) The formula for the velocity is given by: V(t) = 0.5t + 6.
c) The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]
d) The formula for the position of the car is S(t) = 0.25t² + 6t.
e) The car is at a velocity of 21 m/s after 30 seconds.
What is the relation between acceleration, velocity and distance?We have that:
The velocity is the integral of the acceleration.The position is the integral of the velocity.For item a, we have that the acceleration is constant of 0.5 m/s², hence the differential equation for the velocity is:
[tex]\frac{dV}{dt} = 0.5[/tex]
For item b, we apply separation of variables, and find the velocity as follows:
[tex]\frac{dV}{dt} = 0.5[/tex]
[tex]\int dV = \int 0.5 dt[/tex]
V(t) = 0.5t + v(0).
v(0) is the initial velocity and is the constant of integration, hence:
The formula for the velocity is given by: V(t) = 0.5t + 6.
For item c, we have that the position is the integral of the velocity, hence:
The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]
For item d, applying separation of variables, we have that:
[tex]\frac{dS}{dt} = 0.5t + 6[/tex]
[tex]\int dS = \int (0.5t + 6) dt[/tex]
S(t) = 0.25t² + 6t + s(0).
Since s(0) = 0, we have that:
The formula for the position of the car is S(t) = 0.25t² + 6t.
The velocity after 30 seconds is of:
v(30) = 6 + 0.5(30) = 21.
The car is at a velocity of 21 m/s after 30 seconds.
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Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that
there is more than one correct answer.)
31, 27, 23, 19, 15,
Answer:
pattern: numbers decrease by 4next number: 11Step-by-step explanation:
You want the next number in the sequence 31, 27, 23, 19, 15, ... such that it follows the same pattern.
Sequence patternsIt is often useful to look at the differences between successive terms of a sequence. This can quickly reveal a pattern if the sequence is polynomial or exponential.
Here, the differences are ...
27 -31 = -4
23 -27 = -4
19 -23 = -4
15 -19 = -4
It appears reasonable to assume that the pattern is that each term is 4 less than the previous one.
Next termThe number that is 4 less than 15 is ...
15 -4 = 11
The next number in the pattern is 11.
eight more than the quotient of a number and 4 is equal to 2
The algebraic expression from the given statement is 8+x/4=x
Given the statement is the "eight more than the quotient of a number and 4 is equal to 2."
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
Lat us assume the number be x.
In the given statement the quotient of a number and 4 means x/4.
And eight more than the quotient of a number and 4 means 8 is the sum of quotient of a number and 4 and it can be written as
8+x/4 ......(1)
As given in the statement eight more than the quotient of a number and 4 is equal to 2 means we want to equate equation (1) with 2 and written as
8+x/4=2
Hence, the algebraic expression from the given statement "eight more than the quotient of a number and 4 is equal to 2" is 8+x/4=2.
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probability from a two way table
Answer:
82% or 23/28
Step-by-step explanation:
2+3+18=23
2+3+18+6=28
23/28=