The first 5 terms of a sequence are shown are called arithematic sequence.
What is arithmetical sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is.
A collection of numbers that follow a pattern is called a sequence.
As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulas for arithmetic sequences.
The equation to determine the nth term in an arithmetic sequence
The formula for calculating the sum of an arithmetic sequence's first n terms
The arithmetic sequence formula can be used to discover any term in the arithmetic sequence.
AP = –3, –2.5, –2, –1.5, –1,
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Assume that when adults with smartphones are randomlyselected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. Round to 4 decimals
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
what is probability?The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
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a. 1 /2 + 5 12 greater than 1 less than 1 b. 2 7/8 – 1 7/9 greater than 1 less than 1.
what is the total surface area of the triangular prism in square centimeters?
A 240 cm^2
B 368 cm^2
C 320 cm^2
D 344 cm^2
Answer:
D
Step-by-step explanation:
base area = (6 · 4)/2 = 24/2 = 12 cm²
half base length = 6 : 2 = 3 cm
leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm
perimeter = (5·2) + 6 = 10 + 6 = 16 cm
lateral area = 16 · 20 = 320 cm²
surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The true statements about the circle are
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. How to determine the true statements about the circle?From the question, we have the following parameters that can be used in our computation:
x² + y² - 2x - 8 = 0
Generally, To convert this equation to standard form, we need to complete the square.
First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:
x² - 2x + y² - 8 = 0
Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.
To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:
So, we have
x² - 2x + (1²) + y² - 8 = 0 + (1²)
Evaluate
(x - 1)² + y² - 8 = 1
Finally, we can rearrange the terms
So, we have
(x - 1)² + y² = 9
Express 9 as the square of 3
(x - 1)² + y² = 3²
So, the standard form of the equation is (x - 1)² + y² = 3²
The standard equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
When these equations are compared, we have
Center = (a, b) = (-1, 0)
Radius = r = 3
The point (-1, 0) lies on the x-axis
This means that the center is on the x-axis.
Also, it means that the radius of the circle is 3 units
This radius is the same for a circle that has the form x² + y² = 9
This is so because 9 can be expresses as the square or 3, and r = 3
Hence, the correct statements are (a), (b) and (e)
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Complete Question
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?
Select three options.
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Greg the doggo has a rectangular playpen that he and the other dogs can "chill" in. The playpen has an area of 32 square feet . The pen's length is 4 feet longer than its wide.
Include an equation to represent this situation.
The required equation for the width of the rectangular playpen is w² + 4w -32 = 0.
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
here,
let the length be l and width be w,
According to the question,
l = w + 4
Now,
Area of the pen = length × width
Area of the pen = (w + 4) × w
32 = w² + 4w
w² + 4w -32 = 0
Thus, w² + 4w -32 = 0 is the required equation that represents the rectangular playpen.
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What is the vertical asymptote of the function? x = –3 x = –2 x = 0 x = 3
Answer:4
Step-by-step explanation:i did the quiz
nj bought a car for $20,000. two years later, the car has depreciated to a value that is 81% of what he paid. which equation(s) represent the exponential relationship?
V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.
The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.
One equation that represents this relationship is:
V = 20,000 * 0.81^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.
Another equation that represents this relationship is:
V = 20,000 * (1 - 0.19)^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.
Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.
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Please please please help me I need it asap! Please!!
Point A, located at (-11, -7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C.
What are the coordinates of points B and C?
A: Point B: (-11, 7) Point C: (11, -7)
B: Point B: (11, -7) Point C: (11, 7)
C: Point B: (11, -7) Point C: (-11, 7)
D: Point B: (-11, 7) Point C: (11, 7)
Rewrite in simplest terms: -3(7f+3f+9) -4f
-3(7f + 3f + 9) - 4f
Distribute.
(−3)(7f) + (−3)(3f) + (−3)(9) + −4f
−21f + −9f + −27 + −4f
Combine like terms.
−21f + −9f + −27 + −4f
(−21f + −9f + −4f) + (−27)
−34f + −27
-34f + -27
. Stanley needs to get 12 gallons of gas. He finds a gas station that is advertising their price at $3.479/gallon.
A. What will the cost be if the gas station rounds the final cost of gas (to the nearest hundredth) after all calculations?
B. What will the cost be if the gas station rounds their price per gallon (to the nearest hundredth) and then calculates the total price?
C. Which option will save Stanley money?
In case A:
The amount to be paid = $41.75
In case B :
The amount to be paid = $41.76
So, the Case A is better option.
Finding the right answer using the round off to nearest hundredth.
How to change any value to it's nearest hundredth ?
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
Steps to find nearest hundredth of any value:
Step 1:
Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.
Step 2:
Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.
Step 3:
If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.
Step 4:
If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.
Case A :
The price for each gallon = $3.479
So, the total price for 12 gallon = $41.748
In case A total amount is rounded off
So, the price = $41.75
Case B :
The price for each gallon = $3.479
Rounding off the price for each gallon = $3.48
So, the total amount for 12 gallon = $41.76.
So, the case A is better option.
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evaluate 4.56×36÷0.12
Answer:
1,368
Step-by-step explanation:
4.56x36=164.16
164.16/0.12=1368
Answer:
1368
Step-by-step explanation:
1368
write an equation for the line for each graph
The equation of each of the lines are:
1. y = 1/3x - 1
2. y = 3x + 1
3. y = 2/3x - 1
4. y = 3x
5. y = -2/3x - 1
6. y = 1/3x - 1
7. y = -3x + 2
How to Write the Equation of a Line?To write the equation of a line, find the following:
Slope (m) = rise/runy-intercept (b) = the point where the line intersects the y-axis.1. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
2. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 1.
To write the equation, substitute m = 3 and b = 1 into y = mx + b:
y = 3x + 1
3. Slope (m) = rise/run = 2/3
y-intercept (b) = -1.
To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:
y = 2/3x - 1
4. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 0.
To write the equation, substitute m = 3 and b = 0 into y = mx + b:
y = 3x
5. Slope (m) = rise/run = -2/3
y-intercept (b) = -1.
To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:
y = -2/3x - 1
6. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
7. Slope (m) = rise/run = -3/1 = -3.
y-intercept (b) = 2.
To write the equation, substitute m = -3 and b = 2 into y = mx + b:
y = -3x + 2
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HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:7.48521878104
Giovanni works as a tour guide during the summer. He earns $45 a day and $14 for each tour that he leads. Which function is used to find the total amount of money Giovanni will earn each day
The function that is used to find the total amount of money Giovanni will earn each day is; A = 14 + 45d
How to solve algebra word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are told that;
Giovanni works as a tour guide during the summer.
Amount he earns daily = $45
Amount earned for each tour = $14
Now, if the number of days he spends as a tour guide is d, then we can say that the total amount of money Giovanni will earn each day is expressed as;
A = 14 + 45d
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if 87.5 percent of a sample of pure 131i decays in 24 days, what is the half-life of 131i?
If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.
In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days
We need to find the the half-life of 131i
We know that the rate constant expression is given as :
k = (2.303/t)*(log (a / a-x))
where, t = 24 days
a = 100
a -x = 100 - 87.5
= 12.5 g
From the rate constant expression,
k = (2.303 / 24) * (log(100/12.5))
k = 0.0866
Now, the half life is given as :
k = 0.693 / t(1/2)
t1/2 = 0.693 / 0.0866
t1/2 = 8 days.
Therefore, the half-life of 131 i is 8 days.
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A photo is being resized to sell at a gallery. The original photo is 4 inches by 6 inches. Using the dimensions of 3 yds by 4.5 yds, find the scale factor.
The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.
What is the scale factor?The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
Given:
The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,
Calculate the scale factor as shown below,
Scale factor = Original dimension / new dimension
Scale factor = (4 × 6) / (3 × 4.5)
Scale factor = 1.8
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I NEED ANSWERS ASAP please guys this is due tomorrow and I have no idea what to do! Help!!
You could pick the question you want to answer..
The total time taken is 24 hours.
What is total time?
Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A automobile that has been totalled in an accident is irreparably damaged. Total Time is the result of multiplying the number of minutes in a day by the number of days in a given calendar month.
An inlet pipe takes 8 hours to fill a tank. An outlet pipe takes 12 hours to empty.
[tex]$\Rightarrow$[/tex] Time is taken to fill in 1 hour =1 / 8
[tex]$\Rightarrow$[/tex] Time taken to empty in 1 hour =-1 / 12
[tex]$\Rightarrow$[/tex] If both pipes are opened simultaneously tank be filled in 1 hour =1 / 8-1 / 12 =1 / 24 hours
[tex]$\therefore$[/tex] The total time taken is 24 hours.
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a biologist records the average weight of the brain and body for a number of mammal species the biologist uses the inequality [tex]60\leq 0.5x+2.5\leq 250[/tex] to determine the weight of the mammals whose brain weighs between 60 pounds(lb) and 250 lb. solve the inequality
The inequality is [tex]115\leq x\leq 495[/tex]
What is inequality?
A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
Given [tex]60\leq 0.5x+2.5\leq 250[/tex]
splitting the equation:
[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]
[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]
also
[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]
therefore the equation is
[tex]115\leq x\leq 495[/tex]
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-2y + 3 =21 solve linear equations
Answer:
y= -9
Step-by-step explanation:
Subtract 3 from both sides
-2y + 3-3= 21-3
-2y=18
Divide both sides by the same factor
-2y/-2 = 18/-2
y= -9
Answer: y = -9
Step-by-step explanation:
-2y+3=21
-2y=21-3
-2y=18
Divide that by -2:
y=-9
A car dealership pays $8350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this deallership
The retail price of the car is $ 9802.9.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.A car dealership pays $8350 for a car.
They mark up the price by 17.4%
8350 * 17.4% = 1452.9
retail price = 8350 + 1452.9 = $ 9802.9
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In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
Answer:
c = 14
Step-by-step explanation:
Please help. Solve the system of equations.
Y=2x
Y=x^2-8
The solution of the system of equation is as follows;
when x = -2 , y = -4
when x = 4, y = 8
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let solve the system of equation by substitution method.
Therefore,
y = 2x
y = x² - 8
Using substitution,
2x = x² - 8
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) - 4(x + 2) = 0
(x - 4)(x + 2) = 0
x = -2 or 4
Hence,
when x = -2
y = 2(-2) = -4
when x = 4
y = 2(4) = 8
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19. Find the surface area of the cylinder. Give your answer to two decimal places.
Answer:
1155.52cm²
Step-by-step explanation:
A cylinder's volume is π r² h, and its surface area is 2π r h + 2πr²
radius(r) = 8cm
π = 3.14
height(h) = 15
2πrh + 2πr²
=2πr(h + r)
= 2 × 3.14 × 8 ( 15 + 8)
= 50.24(23)
= 1155.52cm²
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9. If the perimeter of the square above is 24, what is the area of the circle? Leave your answer
in terms of pi.
The area of the circle would be 36π.
What is the area of a circle?
If the circle has a radius then the area of the circle can be computed by using the formula
area = π * radius²
The perimeter of the square = 24
4 * side = 24
Side of a square = 24/4 = 6
Side of a square = radius of the circle
Substituting the radius of 6 into this formula gives:
area = π * 6²
Which simplifies to:
area = π * 36
Hence, the area of the circle would be 36π.
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Hillary makes two transactions while at the mall: • She returns an item to get $15 back at one store. • She buys an item for $15 at another store. Which is a correct description of the two quantities that represent these transactions? A The quantities have the same magnitude, but different signs. B The quantities have the same sign, but different magnitudes. C The quantities have different magnitudes and different signs. D The quantities have both the same magnitude and the same sign.
Answer:
the correct answer to this question would be D
one characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is:
A characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is timeliness of information.
Information's timeliness is a crucial aspect of data quality since incomplete or outdated information can influence people's actions. That consequently costs businesses time, money, and reputational harm.
The term "completeness" describes how thorough the information is. Consider if all the information you require is there when evaluating data completeness; for example, you might just require a customer's first and last name, but their middle initial might be optional.
Reliability in the context of data quality traits refers to the absence of contradiction between one piece of information and another piece of information from a different source or system.
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The sum of two numbers is 57 and the difference is 3. What are the numbers?
Answer:
The 2 numbers are 27 and 30
Step-by-step explanation:
Let call them x and y where x is the larger number and y is the smaller number :
x + y = 57 (obtained from the first line of the question)
x - y = 3 (obtained from the second line of the question)
Now we are going to use the rules of simultaneous equations to find x and y :
I will use elimination method :
Add the 2 equations to eliminate the y :
2x = 60
x = 30
Substitute x into equation 1 :
(30) + y = 57
Subtract 30 from both sides :
y = 57 - 30
y = 27
So
x = 30 and y = 27
As you can see the difference is also 3
The 2 numbers are 27 and 30
Hope this helped and have a good day
Which set of coordinates models the image of the triangle after a translation along <2, −9>?
A) M’(−5, 16), N’(−2, 13), P’(0, 15)
B) M’(−1, −2), N’(2, −5), P’(4, −3)
C) M’(−5, −2), N’(−2, −5), P’(0, −3)
D) M’(−1, 16), N’(2, 13), P’(4, 15)
Answer:
b
Step-by-step explanation:
i know
The solution is Option B.
The translation of triangle MNP along T < 2 , -9 > is
M’(−1, −2), N’(2, −5), P’(4, −3)
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
The notation for translation is T(h, k) where T is the translation, h is the change in the x-axis, and k is the change in the y-axis
Given data ,
Let the translated triangle be represented as ΔM'N'P'
Now , the translation rule is T < 2 , -9 >
Let the coordinates of the triangle ΔMNP be
The coordinates of M = M ( -3 , 7 )
The coordinates of N = N ( 0 , 4 )
The coordinates of P = P ( 2 , 6 )
Now , applying the translation rule of T < 2 , -9 > for the triangle MNP , we get
The coordinates of M' = M' ( -3 + 2 , 7 - 9 )
The coordinates of M' = M' ( -1 , -2 )
The coordinates of N' = N' ( 0 + 2 , 4 - 9 )
The coordinates of N' = N' ( 2 , -5 )
The coordinates of P' = P' ( 2 + 2 , 6 - 9 )
The coordinates of P' = P' ( 4 , -3 )
Hence , the coordinates of triangle M'N'P' is M’(−1, −2), N’(2, −5), P’(4, −3)
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Bob lifts a 15N rock through a distance of 1.7m. How much work does Bob do
Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do
What is work done?An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.
The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.
Work done (W) = F × s
Where, F = force
s = displacement
Now putting the values, we get-
or, W = 15 N × 1.7 m
or, W = 25.5 N-m or Joule
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11.3 is 7% of what?
Answer: 157.14
Step-by-step explanation: SDHU IK
