The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.
What is an isosceles right angled triangle?It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.
Given;
Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.
The addition of the internal angles of triangle is 180
So, let vertex angle be x
The other two sides will be x+10,
x+x+10+x+10=180
3x+20=180
x=160/3
x=53.3
Therefore, the vertex angle of the triangle will be 53.3degrees.
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Whitney prepared 16 kilograms of dough after working 4 hours. How much dough did
Whitney prepare if she worked for 5 hours? Assume the relationship is directly proportional.
Answer:
Step-by-step explanation:
time take for 1 dough = 16kg/4hours= 4kg/hour
Dough in 5 hours = 4 x 5 = 20
She prepared 20kilograms of dough in 5 hours
June has decided to take up quilting. She bought a sewing machine for $135. It costs her $11.75 in raw materials to make a quilt, and she can sell a quilt for $28.50.
Which of the following graphs best illustrates June’s situation?
Answer: The best graph to illustrate June's situation is a cost-volume-profit (CVP) graph, which shows the relationship between the revenue, cost, and volume of goods sold.
In June's case, her fixed costs (the cost of the sewing machine) are constant and do not change regardless of the number of quilts she makes and sells. Her variable costs (the raw materials) are directly proportional to the number of quilts she makes and sell. Her revenue is directly proportional to the number of quilts she sells.
The CVP graph will show a line representing fixed costs, a line representing variable costs, and a line representing revenue. The point at which the total costs (fixed costs + variable costs) equal the revenue represents the break-even point, at which June neither makes a profit nor incurs a loss. Beyond this point, June will make a profit, and before this point, she will incur a loss.
The CVP graph can be used to determine the break-even point and to make predictions about the future financial performance of a business, based on changes in volume, costs, or price.
Step-by-step explanation:
a farmer, cole, who is 6 feet tall, wants to determine the height of his barn. cole notices that his shadow is 14 feet long. the shadow cast by his barn is 70 feet long. how tall is the barn?
The barn with shadow height, 70 feet, having the the height which is equals to the 30 feet, that is barn is 30 feet tall.
The height of farmer Cole = 6 feet
The height of shadow of farmer Cole = 14 feet
The height of shadow of barn = 70 feet
Let the height of barn be ' x feet '. We have to determine the value of x. Now, we the above figure, AB and CD represents height of barn and Cole respectively. Similarly BE and CE represent the shadow height of barn and Cole respectively.
Let angle BAE made here be equals to θ. Also angle BAE = angle CDE = θ. Now, consider right angled triangle, CDE with sides. Using triganomertric functions, tanθ = height/base
=> tanθ = CE/CD = 14/6
simplify, tanθ = 7/3 --(1)
Also, consider right angled triangle ABE,
tanθ = height/base = BE/AB
=> tanθ = 70 / x
=> x tanθ = 70
from equation (1), x (7/3) = 70
=> 7x/3 = 70
=> 7x = 210
=> x = 210/7
=> x = 30
Hence, required value of x is 30 feet.
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From the set {7, 9, 36}, use substitution to determine which value of x makes the inequality true. 2x < 18
The only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.
We can use substitution to find which value of x makes the inequality 2x < 18 true by trying each value in the set {7, 9, 36} one by one.
Let's start with x = 7:
2x = 2(7) = 14
14 < 18 is true, so x = 7 satisfies the inequality.
Next, let's try x = 9:
2x = 2(9) = 18
18 < 18 is not true, so x = 9 does not satisfy the inequality.
Finally, let's try x = 36:
2x = 2(36) = 72
72 < 18 is not true, so x = 36 does not satisfy the inequality.
Therefore, the only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.
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You must show all work and explain your strategy (with the reason for each step) to receive full credit!
Using the diagram in the problem angle TQU is solved to be
53.14 degreesHow to find angle TQU
The angle at U is 90 degrees, Using the concept of adjacent angles the three angles at U is solved
Using the trigonometry relations of right triangle we solve for angle PQT'
tan (angle PQT) = 1 / 3
angle PQT = arc tan (1 / 3)
angle PQT = 18.43
angle PQT = angle UQS and
angle PQT + angle UQS + angle TQU = 90 degrees adjacent angles
2 * 18.43 * angle TQU = 90
angle TQU = 90 - 2 * 18.43
angle TQU = 53.14 degrees
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Line f has a slope of 8 Line g is parallel to line f. What is the slope of line g?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
if it's parallel isn't the slope the same?
g even rolls suppose you roll a fair six-sided die until you get a 6. what is the expected number of rolls given that all the numbers you see are even?
The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.
The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.
The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.
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help! what do i do hbvgvgvg
I need help solving this assignment. 1
6
g+3=4–
1
3
g
The solution of the equation 16g + 3 = 4 - 13g is g = 1/29
An equation is a statement that two expressions are equal. In other words, it's a mathematical sentence that says that the value on the left side of the equation is equal to the value on the right side.
In your problem, you have the equation:
16g + 3 = 4 - 13g
To solve this equation, the goal is to isolate the variable "g" on one side of the equation, so we can find its value. To do that, we need to use some algebraic techniques.
First, we can simplify the equation by combining like terms. We can add 13g to both sides of the equation to get:
16g + 13g + 3 = 4
Now we can combine the like terms on the left side of the equation:
29g + 3 = 4
Next, we want to isolate the variable "g" on one side of the equation. To do that, we can subtract 3 from both sides of the equation:
29g = 1
Finally, we can solve for "g" by dividing both sides of the equation by 29:
g = 1/29
So the solution to the equation is g = 1/29.
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Complete Question:
I need help solving this assignment.
Solve the equations 16g+3=4–13g
PROMPT: A spherical toy of diameter 75 cm must have a triangular sticker of height 12 cm and base of 10 cm. What is the surface area not covered by the sticker?
CLAIM:
EVIDENCE:
REASONING:
The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:
A = 4π(37.5)²
A = 4π(1406.25)
A ≈ 17593.29 cm²
The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:
A = 1/2 (10)(12)
A = 60 cm²
The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:
A_not_covered = A - A_sticker
A_not_covered ≈ 17593.29 - 60
A_not_covered ≈ 17533.29 cm²
Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.
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Britney invested $500 in stocks. After one year, the value of her stocks has increased to
$530. Britney wants to use the growth from the first year to estimate future growth.
Write an exponential equation in the form y = a(b)* that can model the estimated value of
Britney's stocks, y, after x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation in the form y= a[tex](b)^x[/tex] that can model is y= 500[tex](1.06)^x[/tex].
What is Exponential Function?In mathematics, an exponential function is a relationship of the type
y = [tex]a^x[/tex], where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
Given:
Britney invested $500 in stocks.
After one year, the value of her stocks has increased to $530.
We know the Exponential Function y= a[tex](b)^x[/tex]
As, a= 500, y= 530, x= 1
So, y= a[tex](b)^x[/tex]
530 = 500 [tex](b)^1[/tex]
530 / 500 = b
b= 1.06
So, the exponential equation is y= 500[tex](1.06)^x[/tex]
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f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer:
The values of x for which f(x) = g(x) are:
x = -1x = 3Step-by-step explanation:
To find all the values of x for which f(x) = g(x), equate the given functions:
[tex]\implies f(x)=g(x)[/tex]
[tex]\implies -x^2+5=-2x+2[/tex]
Rearrange the equation so that it is in the quadratic form ax²+bx+c=0:
[tex]\implies -x^2+5+2x-2=0[/tex]
[tex]\implies -x^2+2x+3=0[/tex]
Divide both sides by -1:
[tex]\implies x^2-2x-3=0[/tex]
Factor the quadratic equation:
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
To solve for x, apply the zero-product property:
[tex](x+1)=0 \implies x=-1[/tex]
[tex](x-3)=0 \implies x=3[/tex]
Therefore, the values of x for which f(x) = g(x) are:
x = -1x = 3We can check the solutions by substituting each found value of x into the functions.
[tex]f(-1)=-(-1)^2+5=4[/tex]
[tex]g(-1)=-2(-1)+2=4[/tex]
[tex]f(3)=-(3)^2+5=-4[/tex]
[tex]g(3)=-2(3)+2=-4[/tex]
As f(-1) = g(-1) and f(3) = g(3), this proves that the values of x for which f(x) = g(x) are x = -1 or x = 3.
Equate Both equatios and find x
f(x)=g(x)-x²+5=-2x+2x²-5=2x-2x²-2x-3=0(x+1)(x-3)=0The points are -1,3
Solve for x. Round to the nearest tenth,if necessary.
The value of x is approximately 0.8 cm when rounded to the nearest tenth.
Describe Triangle?A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.
The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:
sin(IHJ) = IJ/IH
Taking the sine of both sides and substituting the given values, we get:
sin(23°) = x/2
Multiplying both sides by 2, we have:
x = 2*sin(23°)
Using a calculator, we get:
x ≈ 0.83
Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.
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Given:-1/2x>6.
Choose the solution set.
xix R, x>-12
xix
R, x>-3]
xIxER,x<-3)
R, x<-12
Solution of given inequality is x < -12.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
Given inequality
- (1/2)x > 6
Multiplying with 2 on both sides
- (2/2)x > 6×2
- x > 12
Multiplying with -1 on both sides
x < -12
Hence, x < -12 is the solution of given inequality.
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Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 5.
With dilation at center (0,0) and a scale factor of 5, the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).
What exactly is dilation?
Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:
RotationTranslationReflectionDilation or ResizingDilation Properties
Some characteristics of forms that stay constant during dilation changes are:
The figure's angles are all the same.The midpoints of the figure's sides stay the same as the midpoint of the dilated form.The figure's parallel and perpendicular lines stay the same as the dilated figure's parallel and perpendicular lines.The visuals stay unchanged.Now,
As we can see from properties that the image does not change in dilation it stays same and angles are also same.
So, we can see coordinates from the given graph
hence,
the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).
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Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor?
The sum of two numbers is 14. The difference of twice the first and the second is -5. What are the two numbers?
The two numbers are 3 and 11 respectively
How to determine the numbersFrom the information given, we have that
The first number is x
The second number is y
Also,
2x - y = -5
x + y = 14
Make 'x' the subject from equation 2
x = 14 - y
Make 'x' the subject
2(14-y) - y = -5
28 - 2y - y= -5
collect like terms
-3y = -33
y = 11
Substitute the values
x = 3
Hence, the values are 3 and 11
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30 percent of what number is 15
Step-by-step explanation:
50
because 50*(30/100)=1500/100
then it gives 15
so the 30 percent of a number is 15 that number is 50.
The requried, 30 percent of 50 is 15, as of the given condition.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
We can use algebra to solve the problem.
Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:
30% of x is 15:
0.3x = 15
To solve for x, we can divide both sides of the equation by 0.3:
x = 15 ÷ 0.3
x = 50
Therefore, 30 percent of 50 is 15.
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PLEASE SHOW UR WORK ANSWER QUICK
The profit that they will make if they have 24 dogs for adoption is given as follows:
$160.
How to obtain the profit?The profit is obtained with the subtraction of the revenue by the costs.
The revenue and the costs for this problem are obtained as follows:
Revenue: $45 for each of the 24 dogs adopted.Costs: $920 on supplies.Hence the profit made is obtained as follows:
Profit = 45 x 24 - 920
Profit = $160.
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Which expression is equivalent to
O
13
√√2
√√√/2
8-3√11 is the expression which is equivalent to √11+√64-2√44.
What is Expression?The combination of variables, numbers and operators is called as expression.
The given expression is √11+√64-2√44
Square root of 11 plus square root of sixty four minus two square root of forty four.
Let us find the equivalent expression of √11+√64-2√44
The expressions in which the expressions look different but have save same value are Equivalent
√11+√64-2√44
√11+8-2√4×11
√11+8-4√11
Combine like terms
8-3√11
Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.
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Which expression is equivalent to √11+√64-2√44
A. 8-4√44
B. 5√3-4√11
C. 8-3√11
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the total cost, C, after h hours of babysitting. How much money will she make if she baby-sits 5 hours?
The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us suppose the number of hours = x.
The cost of additional hour is $5.
The cost of x hours is 5x.
Given that, Nicole charges a flat fee of $3, plus $5 per hour.
C = 3 + 5x
If she baby sits for 5 hours, that is x = 5, then:
C = 3 + 5(5)
C = 3 + 25
C = $28
Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.
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an analyst has a sample of 28 observations of the weekly return of an index portfolio that includes 50 stocks. the weekly returns are approximately normally distributed, and the sample mean and sample variance are 1.2% and 0.00175. a 90% confidence interval for a weekly return is closest to:
We are 90% confident that the true weekly return of the index portfolio is between 1.186% and 1.214%.
One important concept in statistics is a confidence interval, which is a range of values that is likely to contain the true value of a parameter, such as a population mean or proportion.
The analyst has a sample of 28 observations of the weekly return, which is assumed to be normally distributed. The sample mean is 1.2% and the sample variance is 0.00175. With this information, we can calculate the standard error of the mean, which measures the variability of the sample mean from one sample to another. The formula for the standard error is:
standard error = sample standard deviation / square root of sample size
In this case, the sample standard deviation is the square root of the sample variance, which is approximately 0.0418%. The square root of the sample size is 5.2915. Therefore, the standard error of the mean is:
standard error = 0.0418 / 5.2915 = 0.0079%
To construct a 90% confidence interval for the weekly return, we need to use the t-distribution, which is a probability distribution that takes into account the sample size and the level of confidence. The t-distribution has more variability than the normal distribution, which results in wider confidence intervals for smaller sample sizes.
The formula for a t-confidence interval is:
sample mean ± t-value x standard error
The t-value depends on the sample size and the level of confidence. For a sample size of 28 and a 90% confidence level, the t-value is 1.699. Therefore, the confidence interval is:
1.2 ± 1.699 x 0.0079 = [1.186%, 1.214%]
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PLSSS HELP ASAP PSLPLSPSL
find each value
The value of x is 7, therefore AC = 23 and BD = 23, which means diagonals AC = BD.
What is linear equations in two variables?
A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation in two variables is a straight line in the Cartesian coordinate system.
In a trapezium, the diagonals divide the trapezium into four triangles. The diagonals of a trapezium are also equal to the sum of the two parallel sides.
Let the two parallel sides of the trapezium be a and b. Then, we have:
8x - 33 = a + b ...(1)
37 - 2x = a + b ...(2)
We can solve for x by setting (1) and (2) equal to each other:
8x - 33 = 37 - 2x
10x = 70
x = 7
8(7) - 33 = 23
37 - 2(7) = 23
Therefore, the value of x is 7.
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The matrix 1 −1 ]5
0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter. (If an answer does not exist, enter DNE.)
The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.
The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).
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The complete question is
The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet.
If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor?
832.50
1,300.10
1,664.99
2,600.19
(Please only the right answer. Thanks!)
The cost to wax the floor will be $2,184.03.
What is the area of any geometrical shape?
The area of a geometrical shape is a measurement of the extent of a two-dimensional surface. It is the measure of the amount of space inside the shape, which can be expressed in square units, such as square inches, square feet, or square meters.
Rectangle: area = length x width
Trapezoid: area = ((base1 + base2) / 2) x height
To find the area of the floor, we need to split the shape into two parts: a trapezoid on top and a rectangle on bottom.
The area of the trapezoid is: (33 + 19) / 2 * 14 = 385 square feet
The area of the rectangle is: 33 * 28 = 924 square feet
The total area is: 385 + 924 = 1309 square feet
Multiplying by the cost per square foot, we get:
1309 * 1.67 = 2184.03
Hence, the cost to wax the floor will be $2,184.03.
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Rick is 11 3 4 years old. Lane is 1 3 8 years older than Rick and Jane is 1 1 5 years older than Lane. How old is Jane
The age of the jane is 565/48 years old.
Age problemProblems on ages is a common topic from which questions are asked in almost all Government exams in the quantitative aptitude section.
in this the ages has been found by solving the relationship between the ages given in the question.
the age of rick is = 11 3/4 years old
= 47/4 years old
the age of the lane is 1 3/8 years older than rick
so we add 1 3/8 in the age of rick to find out the age of lane,
so, the age of Lane is = 47/4 + 1 3/8
= 47/4 + 11/8
= (94 + 11)/8
= 105/8 years old .
the age of the jane is 1 1/5 years older than Lane
so we add 1 1/5 in the age of lane to find out the age of jane,
so, the age of jane is = 105/8 + 1 1/5
= 105/8 + 6/5
= (525 + 40)/48
= 565/48 years old .
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Kyle is at the end of a pier 30 feet above the ocean. His eye level is 6 feet above the pier.
He is using Binocular to watch a whale surface. If the angle of depression of the whale is
25°, how far is the whale from Kyle's binoculars?
Step-by-step explanation:
Let the distance between them be y
sin20° =
=> 0.342 = [ sin20° = 0.342]
=> y = 33/ 0.342
=> y = 96.5 ft
So, the distance between them is 96.5 ft
Find the measure of two complementary angles, ZA and ZB, if
mA=7x+4 and mZB=4x+9.
The measure of ∠A is 53.
The measure of ∠B is 37.
What is an expression?An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠A and ∠B are complementary.
This means,
∠A + ∠B = 90
Now,
∠A = 7x + 4
∠B = 4x + 9
7x + 4 + 4x + 9 = 90
11x + 13 = 90
11x = 90 - 13
11x = 77
x = 7
Now,
∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53
∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37
Thus,
∠A = 53
∠B = 37
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Groundhog Day predictions have a 39% accuracy. How baby times should we expect to be correct over the next 38 years? *PLEASE HELP*
It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
What is the expected value?The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.
Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.
To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),
39% * 38 = 14.82
So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
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Here are the first four terms of a sequence.
7
12
17
22
Write an expression for the nth term of this sequence
Answer:
[tex]\mbox{\large a_n = 2 + 5n}[/tex]
Step-by-step explanation:
The sequence is 7 12 17 22
This is an arithmetic sequence where any two successive terms is a constant known as the common difference
The difference between any two successive terms is 5
The common difference is 5
The nth term can be found by the expression
[tex]a_n = a_1 + d(n-1)[/tex]
where
[tex]a_n \textrm{ is the $n^{th}$ term}[/tex]
[tex]\mathrm{a_1\;is\;the\;first\;term}[/tex]
[tex]\mathrm{d\;is\;the\;common\;difference}\\[/tex]
In this sequence
[tex]a_1 = 7\\d = 5\\[/tex]
[tex]a_n = 7 + 5(n-1)\\\\a_n = 7 + 5n - 5\\\\a_n = 2 + 5n[/tex]
We can verify that this is correct is to determine the 5th term of the sequence which should be 22 + 5 = 27
Applying the expression for 5th term
[tex]a_5 = 2 + 5(5)\\= 2 + 25\\= 27[/tex]
