The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days
What is the work rate of 1 worker?Work rate is the rate at which a specified work is completed.
The number of days it will take 10 workers to create 20 products = 40 days
Therefore;
The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days
Where 1 worker can create 20 products in 400 days, then;
The work rate for one worker indicates;
The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5
5 workers will take = 400 days ÷ 5 = 80 days
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Multiply the product
(m+3)(m-3)
Answer:
The answer to (m+3)(m-3) is m^2-9.
Step-by-step explanation:
We will use distributive law to solve this question.
m(m-3)+3(m-3)
= m^2-3m+3m-9
= m^2-9 (since, 3m-3m=0)
As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.
so, here a=m and b=3.
(m+3)(m-3)
=m^2-3^2
=m^2-9
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
The requreid, as per the given percentage condition Mia tips the movers $80.
To find the amount of the tip, we need to calculate 16% of the total cost of the services, which is $500.
16% of $500 = 0.16 x $500 = $80
Therefore, Mia tips the movers $80.
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Three expressions that are equivalent to 3/5a+10?
Cuantos subconjuntos tiene A={a, r, i, t, m, e, t, i, c, a}
The number of subsets that the set has are 128 subsets.
How to find the number of subsets?First, let's remove the duplicates from the set A. The distinct elements in set A are:
A = {a, r, i, t, m, e, c}
Now, we can find the number of subsets. For each element in the set, we have two choices: either it is included in the subset, or it is not. Therefore, there are 2^n subsets for a set with n distinct elements.
In our case, n = 7, so there are 2^7 = 128 subsets for the given set A.
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Mr. Greene created a data set that represents the daily high temperatures, in degrees Fahrenheit, in his city over a week. The values in the table describe the data set. Minimum 73 Mean 77.86 Mean Absolute Deviation 2.73 Median 79 Interquartile Range 6 Maximum 82 Mr. Greene wants to use a single number that summarizes the temperatures for each day. Which value should he use? A. interquartile range B. mean absolute deviation C. mean D. maximum
The correct option is C. mean, that is Mr. Greene should use the mean temperature, which is 77.86°F.
What is a mean value?In mathematics, the mean value is a measure of central tendency of a set of numbers. It is also known as the arithmetic mean and is found by adding all the numbers in a set and dividing the sum by the total number of values. The mean is commonly used to represent the typical or average value of a set of data. It is a useful tool in statistics and other branches of mathematics for analyzing data and making predictions. The mean value can be affected by outliers or extreme values in a set of data, which can skew the results. However, in many cases, the mean provides a reliable and useful measure of central tendency.
Mr. Greene should use the mean temperature, which is 77.86°F, to summarize the temperatures for each day. The mean is a good measure of central tendency when the data set is approximately symmetric and has no significant outliers, which appears to be the case here. Additionally, using the mean will provide a single number that is representative of the entire data set. The interquartile range and mean absolute deviation are measures of spread and do not provide a summary of the temperatures for each day, and the maximum temperature is just one value and may not be representative of the entire data set.
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1. Which set of ordered pairs DOES NOT represent a function?
a. (0, 1), (2,3), (3,4), (5,6)
b. (1, 1), (2, 2), (3,3), (4,4)
c. (1,4), (1, 5), (1,6), (1,8)
d. (0,7), (2, 4), (4,7), (5,7)
Answer:
C.
Step-by-step explanation:
because x value cannot be repeated in an ordered pair
Is the range a subset or a proper subset of the codomain?
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
What is a subset?A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
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The dot plot shows the height, in feet, of a group of trees being studied. How many trees are being studied? Enter the answer in the box.
Answer:
13
Step-by-step explanation:
By counting the amount of dots there is on the graph you would end up with 13 trees.
How many lines of symmetry does a rhombus have
Answer: 2
Step-by-step explanation:
Answer:
2 lines of symmetry.
Suppose a(x) takes integers as inputs (so x=-4 is in the domain, but x=1/2 isn't, for example) and returns 1 if x is odd and 0 otherwise. Is a(x) a function? Is it a one-to-one function? Why?
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function.
Describe function.A mathematical item called a function accepts an input and creates an output. It looks like an apparatus with an input and an output. A formula or a graph can both be used to express a function. For instance, the function f(x) = x² returns the square of an input x as output.
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function. A(x) is not one-to-one, for instance, because a(1) and a(3) are both equal to 1.
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In the 1992 Winter Olympic trials, John Jennings pushed the USA bobsled with a force of 110 N at an angle of 42with the horizontal. Find the horizontal and vertical components of the force
Round to the nearest hundredth!!!!!!
The horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
How to determine the horizontal and vertical components of the forceThe force can be broken down into its horizontal and vertical components using trigonometry.
Horizontal component:
cos(42) = adjacent/hypotenuse
adjacent = cos(42) * 110 N
adjacent ≈ 80.34 N
Vertical component:
sin(42) = opposite/hypotenuse
opposite = sin(42) * 110 N
opposite ≈ 74.62 N
Therefore, the horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
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Find the number of different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together (i.e. maximum two Es next to each other).
The eight letters in the word DECEIVED may be arranged in 4200 distinct ways, with two Ds grouped together and three Es not all together.
The following approach may be used to determine how many different ways there are for the eight letters in the word DECEIVED to be arranged such that two Ds are together and three Es are not altogether:
Treat the two Ds as a single object, which we can call DD. Now we have 7 objects to arrange: DD, E, E, C, V, I, and E.First, we count the total number of arrangements of these 7 objects, without considering any restrictions. This is simply the number of permutations of 7 objects, which is 7! = 5040.Next, we count the number of arrangements in which the three Es are all together. We can treat the three Es as a single object, which we can call EEE. Now we have 6 objects to arrange: DD, EEE, C, V, I, and an extra E. The number of arrangements of these objects is 6!, since we can treat the EEE as a single object.However, we have overcounted the arrangements in which the two Es are together with the EEE object. To correct for this, we can treat the two Es as a single object, which we can call EE. Now we have 5 objects to arrange: DD, EEE, EE, C, V, and I. The number of arrangements of these objects is 5!, since we can treat the EEE and EE as single objects.Therefore, the number of arrangements in which the three Es are not all together is the difference between the total number of arrangements and the number of arrangements in which the three Es are all together, minus the number of arrangements in which the two Es are together with the EEE object:7! - 6! - 5! = 5040 - 720 - 120 = 4200
Therefore, there are 4200 different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together.
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The radius of the wheel is 1.2 feet. What is the distance traveled when the wheel turns 20 time?
The distance traveled by the wheel when it turns 20 times is 150.7964 feet.
What is circumference?
The circumference of a wheel can be calculated as:
Circumference = 2 x π x radius
where π (pi) is a mathematical constant approximately equal to 3.14159.
The distance traveled by a wheel when it turns is equal to the circumference of the wheel multiplied by the number of times it turns.
Given that the radius of the wheel is 1.2 feet, the circumference of the wheel is:
Circumference = 2 x π x radius
Circumference = 2 x 3.14159 x 1.2
Circumference = 7.53982 feet (rounded to 5 decimal places)
Therefore, each time the wheel turns, it travels a distance of 7.53982 feet. To find the distance traveled when the wheel turns 20 times, we can multiply the distance traveled each time by the number of times the wheel turns:
Distance traveled = Circumference x Number of turns
Distance traveled = 7.53982 feet x 20
Distance traveled = 150.7964 feet (rounded to 4 decimal places)
Therefore, the distance traveled by the wheel when it turns 20 times is 150.7964 feet.
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4. Your teacher decides to determine groups in your class by pulling names
out of a hat and not replacing them. What type of event is this?
O independent event
dependent event
Answer:
dependent
Step-by-step explanation:
its dependent because the names getting pulled depends on the names pulled first
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 27 N acts on a certain object, the acceleration of the object is 9 m/s². If the force is changed to 24 N, what will the object's acceleration be?
*Worth 100 points and will award brainliest for the first correct answer.*
Given:
[tex]\vec F_{1} =27 \ N[/tex]
[tex]\vec F_{2} =24 \ N[/tex]
[tex]\vec a_{1} = 9 \ m/s^2[/tex]
Find:
[tex]\vec a_{2} = ?? \ m/s^2[/tex]
We know that [tex]\vec F= m \vec a[/tex]. Use [tex]\vec F_{1}[/tex] and [tex]\vec a_{1}[/tex] to find mass, m.
[tex]\Longrightarrow \vec F_{1} = m \vec a_{1} \Longrightarrow 27= m(9) \Longrightarrow m= \frac{27}{9} \Longrightarrow m= \boxed{ 3 \ kg }[/tex]
We now know the mass of the moving object we can now find [tex]\vec a_{2}[/tex].
[tex]\Longrightarrow \vec F_{2} = m \vec a_{2} \Longrightarrow 24= (3) \vec a_{2} \Longrightarrow \vec a_{2}= \frac{24}{3} \Longrightarrow \vec a_{2}= \boxed{ 8 \ m/s^2 } \ \therefore \ Sol.[/tex]
Use the figure shown to the right to find the value of x.
x=.
The distance from the center are equal,
x = 6
How to find xThe value of x is solved using the relationship existing between chords and the bisectors.
It will be noted that the line from the center
are perpendicular to the chord and bisects the chord into equal halvesIn the figure, since the chords are equal and the line from the center are perpendicular bisectors then the line from the center are equal.
we can therefore say that x = 6
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Trigonometry help me please!
As per the question of trigonometry the another equation that describes the given graph is
y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.
In trigonometry what are the domain and range of the standard functions?The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental geometrical operations in trigonometry. These functions' domain and range are as follows:Sine Function (sin x): All real numbers are its domainRange: [-1, 1]The domain of the cosine function (cos x): all real numbersRange: [-1, 1]Domain: All real numbers, excluding x = (n + 1/2), where n is an integer. Tangent Function (tan x):the entire real number rangeDomain: All real numbers except for x = n, where n is an integer. Cotangent Function (cot x)the entire real number rangeDomain: All real numbers, excluding x = (n + 1/2), where n is an integer. Secant Function (sec x)Range: (-∞, -1] U [1, ∞)Domain: All real numbers except x = n, where n is an integer. What distinguishing characteristics can be found in the sine and cosine function graphs?The sine and cosine function graphs' main characteristics are:
The sine and cosine functions are both periodic, which means that their graphs repeat at regular intervals. The maximum distance between the function value and the horizontal axis is determined by the sine and cosine functions' amplitudes. Zeros: The positions where the sine and cosine functions intersect the horizontal axis are known as the zeros.The functions' maximum and minimum values occur at the period's endpoints. For charting and analyzing the behavior of the sine and cosine functions, it is crucial to comprehend these fundamental characteristics.a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.
[tex]cos((a+b)/2) = 2 cos(sin(a-b)) sin((a-b)/2)[/tex][tex]Sin((a+b)/2) = cos(a) - cos(b) sin((a-b)/2)[/tex]Using this identity, the given equation can be made simpler:[tex][(2 cos(5x) sin(-4x))/(-2 sin(5x) sin(-4x)] gives y.\\y = -cos(5x)[/tex]So, the equation [tex]y = -cos(5x)[/tex] can be used to describe the graph.b. We can simplify the following equation and compare it with [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.
We obtain this by applying the same trigonometric identity as before.
Y is equal to [tex][((sinx - sin9x)/(cosx - cos9x)][/tex]Y is equal to [tex][(2 cos5x sin(-4x))/(-2 sin5x sin(-4x)][/tex] (using the identities [tex]cos(a) - cos(b) and sin(a) - sin(b))[/tex][tex]y = -cos5x[/tex]As we can see, the following equation's shortened form is equal.To know more about trigonometric functions visit:
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a rectangular field has a perimeter of 400 yards the length of the field is 3 times the width what is the length of the field and what is the width of the field
The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.
what is perimeter ?A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.
given
Assume that the rectangular field has a width of "x" yards.
The problem states that the field's length is three times its breadth, or three times yards.
The lengths of all the sides make up the rectangle's perimeter, therefore we can write:
[tex]Perimeter = 2 (length + width).[/tex]
In place of the values we hold:
[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]
The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.
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Find sin(B).
1. a/b
2. a/c
3. b/a
4. b/c
5. c/a
6. c/b
Answer:
4. b/c
Step-by-step explanation:
In a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle), the sine of the angle opposite side b (angle B) is given by:
Sin theta : Opposite/hypotenuse
sin(B) = b/c
Therefore, the answer is 4. b/c
Use the properties of logarithms to write the logarithm in terms of
log5(2) and log5(7).
The logarithm is
log5(98)
By using the properties of logarithms, The logarithm "log₅(98)" can be written as log₅(2) + log₅(7) + log₅(7).
We use the "product' and "quotient" logarithmic identities to write log₅(98) in terms of log₅(2) and log₅(7):
⇒ logₐ(b × c) = logₐ(b) + logₐ(c) ....(product rule)
⇒ logₐ(b/c) = logₐ(b) - logₐ(c) ...(quotient rule)
First, we write the number "98" as the product of 2 and 7, which is :
⇒ log₅(98) = log₅(2 × 7 × 7),
Using the product rule, we can split this into three logarithms;
⇒ log₅(2 × 7 × 7) = log₅(2) + log₅(7) + log₅(7),
So, we have,
⇒ log₅(98) = log₅(2) + log₅(7) + log₅(7),
Therefore, log₅(98) is equal to log₅(2) + log₅(7) + log₅(7).
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The given question is incomplete, the complete question is
Use the properties of logarithms to write the logarithm in terms of log₅(2) and log₅(7).
The logarithm is log₅(98).
Marta tiene un terreno de forma triangular cuya área es menor a 40 m¨2. La altura de su terreno triangular mide 2 metros más que su base.
Para esta situación, ¿Cuál de las siguientes afirmaciones es correcta? Escoge 1 respuesta:
a) La altura del terreno puede medir entre 2 metros y 10 metros.
b) El menor valor que puede tomar la base del terreno triangular es 2 metros.
c) La base del terreno triangular se encuentra entre 3 metros y 8 metros.
d) El mayor valor entero que puede tomar la altura del terreno es 8 metros.
The correct statement is option a) The height of the terrain can measure between 2 meters and 10 meters.
How to determine triangular terrain?Let the base of the triangular piece of land be x meters. Then, the height of the triangular plot is (x+2) meters.
The area of a triangle is given by the formula: A = (1/2)bh, where b is the base and h is the height.
Substituting the given values:
A = (1/2)x(x+2)
Simplifying:
A = (1/2)(x² + 2x)
Since the area is less than 40 m², write:
(1/2)(x² + 2x) < 40
Multiplying both sides by 2:
x² + 2x < 80
Rearranging and factorizing:
x² + 2x - 80 < 0
(x+10)(x-8) < 0
The roots of the quadratic equation are -10 and 8. Since the coefficient of x² is positive, the parabola opens upwards and is negative in between the roots. Therefore, the inequality is true when -10 < x < 8.
However, x cannot be negative, so the base of the triangular terrain is between 0 and 8 meters.
Substituting the values in the expression for the height, the height is between 2 and 10 meters.
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Please help solving this
Quite urgent, thanks :)
The measure of arc angle QT is determined as 142 ⁰.
The measure of m∠STR is determined as 23⁰.
What is the measure of arc angle QT?The measure of angle subtended by the arc QT is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠QST = ¹/₂( arc QT )
arc QT = 2 (m∠QST)
arc QT = 2 x 71⁰
arc QT = 142⁰
m∠STR = ¹/₂( arc SR )
m∠STR = ¹/₂ x 46⁰
m∠STR = 23⁰
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can you answer these two questions
The confidence interval can be expressed as a trilinear inequality: 82.9% < p < 95.7%.
The confidence interval in interval form is (0.1864, 0.3026).
How to calculate confidence interval?The given confidence interval, 89.3% ± 6.4%, means that we are 89.3% confident that the true value of the population parameter lies within a range of 6.4% above and below the sample estimate.
To express this in the form of a trilinear inequality, first find the upper and lower bounds of the interval.
Upper bound = 89.3% + 6.4% = 95.7%
Lower bound = 89.3% - 6.4% = 82.9%
Therefore, the confidence interval 89.3% ± 6.4% can be expressed in the form of a trilinear inequality as:
82.9% < p < 95.7%
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A quadratic equation with opposite solutions can be found by multiplying ______
The equation will have ________.
A quadratic equation with opposite solutions can be found by multiplying a variable by its negative value. Specifically, if we start with a quadratic equation of the form:
ax^2 + bx + c = 0
We can find an equation with opposite solutions by multiplying either a or c by -1. For example, if we multiply c by -1, we get:
ax^2 + bx - c = 0
This equation will have opposite solutions if the discriminant, b^2 - 4ac, is negative. This is because the solutions of a quadratic equation are given by the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Thus, if the discriminant is negative, then the square root term will be imaginary, which means that the solutions will be complex conjugates of each other.
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what is the value of sec^-1(1.4)
The calculated value of sec^-1(1.4) is 44.41 degrees
What is the value of sec^-1(1.4)The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.
In other words, if secθ = x, then sec^-1(x) = θ.
To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.
However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.
Uisng a graphint tool, we have
sec^-1(1.4) = 44.41
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the libarian tracked how many books she checked out on selected days in January and Feburary .She displayed her information in the two dot plots shown. Find the median, mode and range for both dot plots.
The median, mode and range for both dot plots are:
Median = 7.5 and 5Mode = 7 and 8 & 4 and 5Range = 3 and 7Finding the median, mode and range for both dot plots.The median
This is the middle value
From the dot plots, we have the middle values to be
Group A = (7 + 8)/2 = 7.5
Group B = 5
So, we have
Median Group A = 7.5
Median Group B = 5
The mode
This is the number of books with the highest dots
From the dot plots, we have the modal values to be
Mode Group A = 7 and 8
Mode Group B = 4 and 5
The range
This is the difference between the smallest and highest number of books with the highest dots
From the dot plots, we have the range to be
Group A = 9 - 6 = 3
Group B = 10 - 3 = 7
So, we have
Range Group A = 3
Range Group B = 7
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Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
a. What was the book value of the equipment at December 31 the end of the fifth year?
b. Assume that the equipment was sold on April 1 of the sixth year for $105,800.
1. Journalize the entry to record depreciation for the three months until the sale date.
2. Journalize the entry to record the sale of the equipment.
The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
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Write a formula for the nth term of each sequence. first term 7 and common difference 15
As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.
what is sequence ?An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.
given
Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:
[tex]a = a1 + (n - 1) * d[/tex]
In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:
[tex]a = 7 + (n - 1) * 15[/tex]
As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.
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a) Calculate the scale factor from shape A to shape B. b) Find the value of t. Give each answer as an integer or as a fraction in its simplest form.
Answer:
a) The scale factor is [tex]\frac{4}{5}[/tex]
b) [tex]t=5\frac{3}{5}[/tex]
Step-by-step explanation:
The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.
In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.
Let's start by calling our "certain value" k.
[tex]5k=4=\\k=\frac{4}{5}[/tex]
Let's check 15 to make sure k is 4/5, like so:
[tex]15(\frac{4}{5})=\\\frac{60}{5} =\\12[/tex]
Since 15 times 4/5 is twelve, our initial answer was correct.
So, the scale factor, or k, is 4/5.
Following this logic, we know that 7 multiplied by the scale factor is equal to t.
Let's set up an equation and solve for t:
[tex]7(\frac{4}{5} )=t=\\\frac{28}{5} =t=\\5\frac{3}{5} =t[/tex]
So, [tex]t=5\frac{3}{5}[/tex]