(a) The expression of nth term of arithmetic sequence is [tex]a_n=1+(n-1)6[/tex] and (b) 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
What is arithmetic sequence?
It is a sequence of numbers which have same difference between two consecutive numbers. The common difference can be any positive number or negative number or even it can be 0.
The six terms of the arithmetic sequence are as follows:
1,7,13,19,25,31
Calculate the common difference as follows:
7-1=6
13-7=6
19-13=6
Since it is an arithmetic sequence hence common difference is 6.
Hence, [tex]d=6[/tex].
Now, substitute value of the first term and the common difference in the following expression of the nth term.
[tex]a_n=a+(n-1)d\\a_n=1+(n-1)6[/tex]
Now, the nth term of another sequence is as follows:
[tex]a_n=5n^2\\[/tex]
Substitute n=4 in the above equation.
[tex]a_4=5(4)^2\\=80[/tex]
Hence, (a) the expression of nth term is [tex]a_n=1+(n-1)6[/tex] and 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
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A construction crew is lengthening a road. The road started with a length of 54 mlles, and the crew is adding 4 mlles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 37 days.
Equation:
Total length of the road after 37 days:___miles
The equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles
The length of the road at starting = 54 miles
The rate of lengthening the road per day = 4 miles per day
Where L is the total length of the road in miles
D is the number of days the crew has worked
Then the equation will be
L = 54 + 4D
The number of days = 37 days
Substitute the value of D
L = 54 + 4×37
L = 54 + 148
L = 202 miles
Hence, the equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles
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I drove to my summer home at 75 mph. The next day I drove back, it took me a hour longer because of traffic, and I drove at 50 mph. How long was the drive on the first day?
Answer:
2 hours
Step-by-step explanation:
time it took on the first day = x
speed = d/t
time it took on second day = x + 1
75 = d/x
50 = d/x + 1
75x = d
50 = 75x/(x + 1)
50(x + 1) = 75x
50x + 50 = 75x
50 = 25x
x = 50/25
x = 2
1. Stanley's cat weighs 5 pounds. Stanley's dog weighs 3 3/5 times as much as his cat.
How much does Stanley's dog weigh?
Answer:
18
Step-by-step explanation:
Answer:
18 pounds
Step-by-step explanation:
5x 3 3/5= 18
Compare the scenarios to determine which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the rates in your explanation.
The scenario that represents a greater speed is scenario 1, which is 60 miles per hour.
What is Speed?Speed can be defined as the time it takes a moving object or body to cover a specific distance. In order words, it is calculated as:
Speed = distance/time.
In scenario 1, using one point on the graph, (1, 60), we can find the unit rate which is the speed in miles per hour:
Speed = y/x = distance/time = 60/1
Speed for scenario 1 = 60 miles per hour.
In scenario 2, we are given the equation, y = 55x:
55 is the unit rate which is the speed.
Speed for scenario 2 = 55 miles per hour.
The greater speed is 60 miles per hour.
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19x=y
in standerds form
Answer:
19x − y = 0
__
Find the area of the shape giving
Answer:
49.7
Step-by-step explanation:
FORMULA : A = (b1 + b2)h/2
base 1 = 4.2
base 2 = 10
4.2 + 10 = 14.2
height = 7
14.2 x 7 = 99.4
99.4/2 = 49.7
is it reasonable to use this line of best fit to make the above prediction? select the correct answer below:
The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable. the correct option is (A).
Given that,
The projected amount of time spent with family for someone who spent 36 minutes playing video games is 81.54 minutes, according to the line of best fit.
To find :
Is it appropriate to make the aforementioned forecast using this line of best fit
According to the "line of best fit" it is that along which the sum of squares of deviation is minimum. This means the line of best fit minimizes the deviation or we can say error due to which it gives better estimate than other method.so, the predicted number of minutes spent with family is both reliable and reasonable.
Therefore, the estimate, a predicted time of 81.54 minutes, is both reliable and reasonable
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The question was incomplete. Check below the complete question.
is it reasonable to use this line of best fit to make the above prediction? select the correct answer below:
a. 81.54minutes
b. 50.25minutes
c. 23minutes
d. 36minutes
The length of a rectangle i 12m and the length of it diagonal i 15m.Find
the width of the rectangle.
Answer:
width = 9 m
Step-by-step explanation:
the diagonal divides the rectangle into 2 right triangles.
using Pythagoras' identity on one of the triangles
with legs 12 and width (w) and hypotenuse (diagonal) 15 , then
w² + 12² = 15²
w² + 144 = 225 ( subtract 144 from both sides )
w² = 81 ( take square root of both sides )
w = [tex]\sqrt{81}[/tex] = 9
that is the width of the rectangle is 9 m
A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and represents the number of seconds that have passed since the fuel started
dispensing, then x and y satisfy a linear relationship.
If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?
If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds
The quantity of fuel releases from the container = 5 gallon per second
Consider the fuel remaining in the container = y
Consider the number of seconds that have passed since the fuel started dispensing = x
Then x and y satisfy a linear relationship
The quantity of fuel in the tank at the beginning = 103 gallon
Time taken = 2 seconds
Then the equation will be
y = 103 - 5x
Time taken is x = 2
y = 103 - 5× 2
y = 103 - 10
y = 93 gallon
Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds
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Mr. Ready went to Walmart for some groceries. A large bag of chips is $4 and each
pound of meat is $2. Create an equation that represents the number of bags of chips
and the pounds of meat he bought if he spent $38.
Answer:
[tex]38=4c+2m[/tex]
Step-by-step explanation:
I will use the letter c to represent bags of chips, and the letter m to represent pounds of meat.
The total cost of c bags of chips is 4 times c. The total cost of m pounds of meat is 2 times m. The total amount that he spends is $38. Therefore, this equation can be written.
[tex]38=4c+2m[/tex]
During a rainstorm, a pail collects 1 3 of an inch of water in 5 6 of a minute. At what rate is the pail collecting water?.
The rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
What is rate in mathematics?
A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).
The rate can be configured as.
Rate = [tex]\frac{1/3}{5/6}[/tex]
Rate = [tex]\frac{2}{5}[/tex]
Hence, the rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
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for a standard normal distribution, 95% of the datapoints are contained in the interval [ -x , x ]. what is the value of x?
Standard deviation - The value of x is 1.96.
What is standard normal distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].
The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.
Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.
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Select the correct answer from each drop-down menu.
For the diagram shown, complete a true statement.
A
B
G
DE is the ray with endpoint
D
E
GA and DF
intersect.
The DE is the ray with end point E and the ray GA and ray DF will not intersect
From the given diagram
Consider the ray DE,
The starting point of the ray DE = D
Then the end point of the ray DE = E
The D is the starting point and E is the end point of the ray DE
Therefore DE is the ray with end point E
Consider the ray GA and DF, those rays are not in contact and going opposite direction, therefore it will not intersect
The GA and DF will not intersect
Hence, the DE is the ray with end point E and the ray GA and ray DF will not intersect
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What’s the IQR for jacobs data set
The IQR for Jacob's data set is determined as: 2 seconds.
What is the Interquartile Range of a Data Set?To find the interquartile range (IQR) of a Data set, find the third quartile value and the first quartile value. Their difference is the Interquartile Range (IQR) of the data.
Interquartile Range (IQR) = third quartile - first quartile.
In the box plot given, we can deduce that:
Third quartile = 15.5
First quartile = 13.5
Interquartile Range (IQR) = 15.5 - 13.5
Interquartile Range (IQR) = 2 seconds
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Answer: 2 seconds
Step-by-step explanation:
Does anyone know the answer to the last part of this question ?? I already got the rest, I just need the last one.
PLEASE HELP !!
DONT ANSWER IF YOU DONT KNOW IT !! i will report you if you answer with anything else.
Only answer if you know!!
Answer: 62.5
Step-by-step explanation:
To break even, profit equals zero.
[tex]1.60n-100=0\\\\1.60n=100\\\\n=62.5[/tex]
When the product of 6 and the square of a number is increased by 5 times the number.
The square of a number is increased by 5 times the number [tex]6x^{2} +5x-4=0[/tex]
What is quadratic equation?
A quadratic equation is a second order equation written as a[tex]x^{2}[/tex] + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Product of 6 and the square of a number is increased by 5 times the number, he result is 4.
Consider x as the number,
The question can be written as:
[tex]6(x^{2} )+5(x)=4[/tex]
[tex]6(x^{2} )+5(x)-4=0[/tex]
Hence, the answer for the given question is [tex]6x^{2} +5x-4=0[/tex].
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Calculate the volume of the frustums (image attached), I would really appreciate some help!
Answer: USE the forumla
Step-by-step explanation:
Consider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H + h'. Its volume (V) can be calculated by using: V = πh/3 [ (R3 - r3) / r ] (OR) V = πH/3 (R2 + Rr + r2)
Put the numbers in order from smallest to largest.
= 3.24 x 10°
= 4.68 z 10
= 5.48 x 10°
6
= 8.34 z 10 2
1.2 z 107
27
Order for the given exponential numbers will be:
5.48 x [tex]10^{9}[/tex]
3.24 x 10^{9}
1.2 x 10^{7}
8.34 x 10^{-2}
4.68 x 10^{-6}
What are the exponential functions?
A mathematical function called an exponential function is employed frequently in everyday life. It is primarily used to compute investments, model populations, find exponential decay or exponential growth, and so forth. You will discover the formulas, guidelines, characteristics, graphs, derivatives, exponential series, and examples of exponential functions in this article. The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be greater than 0. The transcendental number e, or roughly 2.71828, is the most frequently used exponential function base.
With the highest power in exponential function,
function will be more greater if the numbers multiplied by exponential function are in same order of decimal number.
In given Que,
numbers multiplied are all of 2 decimal number.
So, we can directly compare the values x in e^{x}
i.e. 9 > 7 > -2 > -6
for same value of x: compare value of number multiplied.
Hence, we found out the correct answer.
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Part H is not showing including H too, can someone please help me
The scale factor k=5
corresponding parts are:
AL--> TD
TK---> AH
DK---> LH
angle A-----> angle T
angle D-----> angle L
angle H-----> angle K
What is scale factor?
The difference in scale between an original object's scale and that of a new, smaller representation is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.
The letter H lies on the line TK
Scale factor k
=( side length of new image)/ ( corresponding side length of new image)
=TD/AL=15/3=5
k=5
From the figure, corresponding parts are as below:
AL--> TD
TK---> AH
DK---> LH
angle A-----> angle T
angle D-----> angle L
angle H-----> angle K
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a grocer purchase 5 dozenegg at rs 12 each.10 eggs are broken and he sold remaining at rs 14 each (i)his total loss or profit find profit or loss percent.
Answer:
Approximately 3% loss======================
Number of eggs purchased:
5*12 = 60Cost of eggs:
60*12 = 720Number of eggs sold:
60 - 10 = 50Money made:
50*14 = 700Profit or loss?
Cost (Rs 720) is greater than money made (Rs 700), so this is a lossPercent loss:
(720 - 700) / 720 × 100% = 20/720 × 100% =≈ 3%What is the equation of the line shown in this graph?
Answer:
Step-by-step explanation:
formula of a linear line - y=mx+c
so y=
m= gradient x =x coodinate c=y-intercept
c= -3
m = 0
which is y=-3
pls give me brainliest
pls:(
Answer:
y = - 3Step-by-step explanation:
Points given:
(- 2, - 3) and (3, - 3)This is a horizontal line with constant y - value of - 3.
So it equation is y = - 3.
-18t=-3(t+5) distributive property I only have 10 points.
Answer: t=1
Step-by-step explanation:
1. Distribute the -3
-18t=-3t-15
2. Move the -3t to the other side
-15t=-15
3. Divide by -15 to solve for t
t=1
the height and arm span of a sample of 50 teenagers identify the explanatory variable and the response variable for this relationship, if possible. either variable, height or arm span, could be the explanatory variable, because each could be used to predict or explain the other. the explanatory variable, arm span of teenagers, helps explain the response variable, height of teenagers. the explanatory variable, height of teenagers, helps explain the response variable, armspan of teenagers. the explanatory variable, teenagers, helps explain the response variable, armspan of teenagers. the explanatory variable, teenagers, helps explain the response variable, height of teenagers.
For the height and arm span of a sample of 50 teenagers explanatory variable and the response variable for this relationship is the explanatory variable, height of teenagers, helps explain the response variable, arm span of teenagers. (Option C)
An explanatory variable refers to the variable that can be manipulated in experiment by the researcher and is the independent variable whereas a response variable refers to the variable that is modified as a result and is the dependent variable. In the given case, the height is the explanatory variable while the arm span is the response variable as a teenager's arms spread is influenced by their height.
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What is Desmos in math?
Answer:
Desmos is a free graphing and teaching tool for math available on the web as well as on iOS and Android. In addition to plotting equations, classroom activities are available to help students learn about a variety of math concepts.
A definition of Desmos has been given below
What is Desmos?
Desmos can be applied in a variety of contexts. Students can avoid spending $100 on a graphing calculator by using it for free. It can be used by teachers to create stunning images for tests and presentations. But Desmos really shines in the classroom exercises. Teachers can use Desmos to assist students in making the connection between mathematical concepts and actual, concrete shapes and images. It's simple to begin an activity with your students: Just instruct the children to enter the website's activity code. Try the student preview of an activity before assigning it. In the teacher moves section at the bottom of each activity, you can find specific ways to guide your children while they work. The teacher dashboard allows for the tracking of progress.
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can you substitute y=2x+4 y=2
Answer: x = -1
Step-by-step explanation:
Since, you know y = 2, substitute that y-value into the other function:
[tex]2=2x+4\\\\2x=2-4=-2\\\\x=\frac{-2}{2} =-1[/tex]
The scale factor of a model of a hot air balloon to the actual hot air balloon is 1 to 5. The volume of the actual balloon is 5000m³.
What is the volume of the model?
The volume of the model of the air balloon is 1000m³.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.So, the volume of the model:
The ratio of the volume of, the model: actual balloon = 1:5The volume of an actual air balloon is 5000m³.So, calculate the volume of the model as follows:
1/x = 5/50005000 = 5x5x = 5000x = 1000m³Therefore, the volume of the model of the air balloon is 1000m³.
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2. An auto repair shop charges $50 plus $25 per hour. Using C for cost and h for hours, write an
equation to model the problem. Then, use your equation to find the cost for an 8-hour repair job
at the shop.
Answer:
Step-by-step explanation:
The equation would be y=25x+ 50 which is linear. Radical expressions have a number under the radical sign which this equation doesn't. Rational expressions have fractions containing polynomials in the numerator and denominator and exponential equations have 'x' as the exponent in a function.
The trim loss percent for rutabagas is 19%. If you purchase rutabaga for $0.79 per pound, how much would 3 pounds 9 ounces cost?
3 pounds 9 ounces of rutabagas would cost $2.28
How to determine the cost of rutabagasThe question is a percentage problem
The trim loss percent for rutabagas is 19%
= 19 percent
= 19 / 100
= 0.19
trim loss factor = 1 - 0.19 = 0.81
selling price of rutabagas = $0.79 * 0.81 = 0.6399
converting all the unit in pounds
3 pounds 9 ounces: if 1 pound is 16 ounces then 9 ounces will be
3 pounds 9 ounces: 9/16 ounces = 0.5625
therefore we have 3.5625 pounds of rutabagas
3.5625 pounds of rutabagas will cost
= 3.5625 * 0.6399
= $2.28
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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
18, 14, 10, .
Answer: The sequence has a common difference between consecutive terms
14 - 18 = 10 - 14 = - 4
This indicates it is an arithmetic sequence with a common difference - 4
Step-by-step explanation:
How many millimeters(mm)are there in 3.5 meters(m)
Answer:
3,500 Millimeters
Step-by-step explanation:
1 Meter = 1,000 Millimeters so,
3.5 meters = 3,500 Millimeters