The probability of k "heads" is given by:P (k) = C(25, k) (0.5)^(k) (0.5)^(25-k)where C(25, k) = 25!/[k!(25-k)!].The result of a coin being tossed 25 times shows 9 "heads" and 16 "tails."
The probability of having 9 "heads" in 25 coin tosses is given by:P(9) = C(25, 9) (0.5)^(9) (0.5)^(25-9) = 0.097.While the probability of having 16 "tails" in 25 coin tosses is given by:P(16) = C(25, 16) (0.5)^(16) (0.5)^(25-16) = 0.098.Both the probabilities, P(9) and P(16), are nearly the same.
This means that the occurrence of 9 "heads" and 16 "tails" is equally likely. Therefore, it is not at all surprising to get 9 "heads" and 16 "tails" in 25 coin tosses, even if the coin is unbiased.
To know more about surprising visit:
brainly.com/question/28731288
#SPJ11
Garrett found the slope of the values in the table: A 2-column table with 3 rows. Column 1 is labeled Years: x with entries 4, 8, 12. Column 2 is labeled Hourly rate: y with entries 12. 00, 13. 00, 14. 0. 1. Slope = StartFraction 12 minus 8 Over 14. 00 minus 13. 00 EndFraction. 2. Slope = StartFraction 4 Over 1. 00 EndFraction. 3. Slope = 4. Is Garrett’s slope correct? If not, identify his error? Yes. Garrett found the slope correctly. No. He should have put the x values in the denominator and the y values in the numerator. No. He should have gotten a negative answer for slope because the values are decreasing. No. He should have gotten the answer StartFraction 1 Over 25 EndFraction.
No, Garrett's slope is not correct. He should have put the x values in the denominator and the y values in the numerator.
Garrett made an error in calculating the slope. The slope represents the change in the dependent variable (y) per unit change in the independent variable (x). In this case, the independent variable is "Years" (x) and the dependent variable is "Hourly rate" (y).
To calculate the slope correctly, we need to divide the change in y by the change in x. Garrett incorrectly subtracted the x values from each other and the y values from each other, resulting in an incorrect calculation.
The correct calculation would be:
Slope = (13.00 - 12.00) / (8 - 4)
= 1.00 / 4
= 0.25
Therefore, the correct slope is 0.25 or StartFraction 1 Over 4 EndFraction.
Garrett's error was that he should have put the x values (4, 8, 12) in the denominator and the y values (12.00, 13.00, 14.00) in the numerator to calculate the slope correctly.
To learn more about independent variable visit:
brainly.com/question/29301912
#SPJ11
Two siblings have savings accounts for the money that they are earning. The older sister started her account with $50, while her younger brother started his account with $80. She is adding $7 per week, while her brother saves an additional $5 per week.
To calculate their savings after a certain number of weeks, we can use the given information to determine the total savings for each sibling. Total savings of the younger brother = $80 + $5n. Total savings of the older sister = $50 + $7n.
The older sister started her savings account with $50 and is adding $7 per week. The younger brother started his savings account with $80 and is adding $5 per week.
For the older sister, her initial savings is $50, and she adds $7 per week. After n weeks, her total savings can be calculated using the equation:
Total savings of the older sister = $50 + $7n.
For the younger brother, his initial savings is $80, and he adds $5 per week. After n weeks, his total savings can be calculated using the equation:
Total savings of the younger brother = $80 + $5n.
By substituting the value of n, we can determine the total savings for each sibling after a specific number of weeks.
To learn more about equation click here: brainly.com/question/28243079
#SPJ11
There were 73 yellow tic tacs in a container of 250 tic tacs. What percent of tic tacs were yellow?
Approximately 29.2% of the tic tacs in the container are yellow. To interpret this percentage, we can say that for every 100 tic tacs in the container, around 29 of them are yellow.
To find the percentage of yellow tic tacs in the container, we can use the formula:
Percentage = (Number of Yellow Tic Tacs / Total Number of Tic Tacs) x 100
In this case, the number of yellow tic tacs is given as 73, and the total number of tic tacs is 250. Substituting these values into the formula, we get:
Percentage = (73 / 250) x 100
To simplify the calculation, we can divide both the numerator and denominator by 5:
Percentage = (73 / 5) / (250 / 5) x 100
= 14.6 / 50 x 100
= 0.292 x 100
= 29.2
Therefore, the percentage of yellow tic tacs in the container is 29.2%.
It's important to note that when dealing with percentages, it's common practice to round to a certain number of decimal places or use significant figures. In this case, the percentage was rounded to one decimal place. Depending on the context or specific instructions, the rounding may vary.
Learn more about percentage at: brainly.com/question/28998211
#SPJ11
Tess and Dan have $24. 00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24. 50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24. 50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work. HELP QUICK!!!
Tess is correct in her calculations, and they have enough money to purchase the book. The discounted price for the book is $20.83 after applying the 15% discount. Adding 10% sales tax to this amount gives a final purchase amount of $22.91. Since both Tess and Dan have $24.00 each, they have enough money to buy the book.
1. Tess correctly applies the 15% discount to the original price of $24.50, which gives a discounted price of $20.83. Then, she adds 10% of this discounted selling price back to find the final purchase amount. Calculating 10% of $20.83 gives $2.08, which when added to $20.83, results in a purchase amount of $22.91.
2. Dan's approach involves calculating 85% of the original price, which gives $20.83 (same as the discounted price Tess found). Then, he computes 110% of this reduced price to account for the 10% sales tax. Calculating 110% of $20.83 gives $22.91, which matches the final purchase amount calculated by Tess.
3. Since both Tess and Dan have $24.00 each to spend, and the purchase amount is $22.91, they have enough money to buy the book.
Learn more about selling price here: brainly.com/question/29065536
#SPJ11
Sansa was explaining the meaning and usefulness of the statement tan 40° ≈ 0. 84. Which
true statements below could be part of that explanation? Select all that apply.
o All right triangles with an acute angle of 40° are similar to each other.
o The sum of the squares of the legs of right triangles with a 40° angle equal 40".
o Knowing that tan 40° ≈ 0. 84 is enough information to calculate the sides of any 40°-
50°-90° triangle.
o If you know tan 40° ≈ 0. 84 and the length of the leg opposite to the 40° angle, then
you can calculate the length of the other leg.
o The ratio of the opposite side to the hypotenuse in any right triangle with an angle of
40° is always approximately 0. 84
The true statements that could be part of the explanation of the statement "tan 40° ≈ 0.84" are: All right triangles with an acute angle of 40° are similar to each other. If you know tan 40° ≈ 0.84 and the length of the leg opposite to the 40° angle, then you can calculate the length of the other leg. The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84
In a right triangle, the tangent of an acute angle is defined as the ratio of the opposite side and the adjacent side of that angle. Mathematically, for an acute angle A, tan(A) = opposite/adjacent. In the current case, we are discussing tan 40°. So, if the angle A in a right triangle is 40°, and if the opposite side to that angle is x and the adjacent side is y, then tan 40° = x/y .If we know the value of tan 40°, then we can calculate the value of x/y or y/x .In the following true statements, we will discuss how we can use tan 40° to make some conclusions: The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84This statement is true. This is based on the definition of tangent. tan 40° = opposite/adjacent. In a right triangle with an angle of 40°, the hypotenuse is neither the opposite side nor the adjacent side. But, we can write the above equation as opposite/hypotenuse = tan 40°/1. So, the ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84.
Learn more about right triangles here:
https://brainly.com/question/23924136
#SPJ11
For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2.
The profit equation for the company, subtract the cost equation from the revenue equation, which is 40x - 0.5x^2 - 300.
The cost equation for producing x items is given as 60x + 300. This means that the cost per item is $60 and there is a fixed cost of $300. The revenue equation for selling x items is given as 100x - 0.5x^2. This equation represents the revenue generated from selling the items, taking into account the price per item and the quantity sold. To calculate the profit, we subtract the cost equation from the revenue equation. Thus, the profit equation becomes 100x - 0.5x^2 - (60x + 300) = 40x - 0.5x^2 - 300. This equation represents the profit earned by the company for producing and selling x items, considering both the costs and the revenue generated.
To learn more about equation click here
brainly.com/question/29657983
#SPJ11
Daveed says that a system of two linear equations must have at least one solution as long as the lines have different intercepts. For example, the equations y=2x+3 and y=3x-2. Select the pair of linear equations that can be used to disprove Daveed’s claim
The pair of linear equations that can be used to disprove Daveed's claim is y = 2x + 3 and y = 2x + 5.
Daveed's claim states that a system of two linear equations must have at least one solution as long as the lines have different intercepts. However, the pair of linear equations y = 2x + 3 and y = 2x + 5 disproves this claim.
Both equations have the same slope of 2, indicating that the lines are parallel. In this case, the lines will never intersect, regardless of their different intercepts (3 and 5, respectively). Since the lines are parallel and will never cross, there is no common solution to the system of equations. This contradicts Daveed's claim that as long as the lines have different intercepts, there will always be a solution.
Therefore, the pair of linear equations y = 2x + 3 and y = 2x + 5 can be used to disprove Daveed's claim about the existence of at least one solution in a system of linear equations with different intercepts.
To learn more about linear equations
brainly.com/question/29001435
#SPJ11
Write the equation of the line that passes through the coordinates 30,9 and 25,5. Point Slope Form
The equation of the line that passes through the coordinates (30,9) and (25,5) in point-slope form is y - 9 = (5-9)/(25-30)(x - 30).
To find the equation of a line in point-slope form, we need to know the coordinates of a point on the line and the slope of the line.
Given the coordinates (30,9) and (25,5), we can find the slope of the line using the formula: slope (m) = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates (30,9) and (25,5), we substitute the values into the slope formula:
m = (5 - 9)/(25 - 30)
m = -4/-5
m = 4/5
Now that we have the slope (m), we can use the point-slope form of the equation: y - y1 = m(x - x1).
Substituting the values of (x1, y1) = (30,9) and m = 4/5 into the equation, we get:
y - 9 = (4/5)(x - 30)
Simplifying the equation gives us the final result:
y - 9 = (4/5)x - 24
y = (4/5)x - 24 + 9
y = (4/5)x - 15
Therefore, the equation of the line that passes through the coordinates (30,9) and (25,5) in point-slope form is y - 9 = (5-9)/(25-30)(x - 30).
To learn more about coordinates, click here: brainly.com/question/31293074
#SPJ11
If the balance at the end of eight years on a investment if $230 that has been invested at a rate of 3% is $285. 20, how much was the interest
To find the amount of interest earned, we can subtract the initial investment from the final balance.
The initial investment is $230, and the final balance is $285.20. Therefore, the interest earned is:
Interest = Final balance - Initial investment
= $285.20 - $230
= $55.20
So, the interest earned on the investment is $55.20. This represents the additional amount gained on top of the initial investment over the period of eight years, considering a 3% interest rate.
Learn more about interest rate here: brainly.com/question/30907196
#SPJ11
Suppose you invest 10,000 part at 6% annual interest and the rest at 9% annual interest. if you received 684$ in interest after one year how much did you invest at each rate
$7200 was invested at 6% and $2800 was invested at 9% to earn a total interest of $684 after one year. Let's denote the amount invested at 6% as x, and the amount invested at 9% as 10,000 - x.
We know that the total interest received after one year is $684.
Calculate the interest earned from each investment:
Interest from the amount invested at 6%: 0.06x
Interest from the amount invested at 9%: 0.09(10,000 - x)
Set up an equation using the given information:
0.06x + 0.09(10,000 - x) = 684
Solve the equation for x:
0.06x + 900 - 0.09x = 684
-0.03x = -216
x = 7200
Calculate the amount invested at 6% and at 9%:
Amount invested at 6%: x = $7200
Amount invested at 9%: 10,000 - x = $2800
Therefore, $7200 was invested at 6% and $2800 was invested at 9% to earn a total interest of $684 after one year.
To learn more about investment click here:
brainly.com/question/17252319
#SPJ11
Find the value of x and list the sides of ∆ABC in order from shortest to longest if the angles have the indicated measures. m∠A= (9x + 29), m∠B= (93 - 5x )°, and m∠C= (10x + 2)°
Therefore;`a < b < c`The sides of the triangle are listed in order from shortest to longest as follows:
`Side a < Side b < Side c`
Let's apply the angle sum property to ∆ABC such that;
`[tex]\angle A + \angle B + \angle C = 180[/tex]`We can now substitute the angle measures provided by the problem statement to get an equation in terms of x such that;`(9x+29)+(93-5x)+(10x+2)=180`Simplify and solve for x:`9x+29+93-5x+10x+2=180`Simplify like terms to get;`14x+124=180`Subtract 124 from both sides of the equation to get;`14x=56`Divide both sides of the equation by 14 to get:`x=4`Now that we know x, we can use it to determine the measures of the angles.
Therefore;`m∠A = 9x + 29 = 9(4) + 29 = 65°``m∠B = 93 - 5x = 93 - 5(4) = 73°``m∠C = 10x + 2 = 10(4) + 2 = 42°`
We are now going to list the sides of the triangle in order from shortest to longest using the information provided in the problem statement. Here's how to do it:
From angle A, we know that the side opposite it, which is side a, is the shortest side of the triangle.
Therefore;`a < b < c
`From angle B, we know that the side opposite it, which is side b, is longer than side a. We can now rewrite our inequality to show the relationship between sides a, b, and c such that;`a < b < c`We can then use the information provided by angle C to figure out which side is the longest. Since angle C is the largest angle of the triangle, we can assume that side c is the longest side.
To know more about angle:
https://brainly.com/question/31818999
#SPJ11
29-30. Mr. Santos plans to construct a circular dinner table with a square centerpiece in the center. The radius of thetable should be the same measure as the side of the square centerpiece. Write an expression for the remaining area ofthe table not covered by the centerpiece in terms of the side of the square. Write your answer in factored form. (3pts)Answer:
The expression for the remaining area of the circular dinner table not covered by the square centerpiece, in terms of the side of the square, can be written as (πr²) - (side²), where r represents the radius of the circular table.
To find the remaining area of the table not covered by the square centerpiece, we need to subtract the area of the square from the area of the circle. The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the radius of the circular table is the same measure as the side of the square centerpiece, we can write the expression for the area of the circle as A = π(side²). The area of the square centerpiece is given by the formula A = side². Therefore, the expression for the remaining area of the table not covered by the centerpiece is (πr²) - (side²), which can also be written as π(side²) - (side²), and factored as (π - 1)(side²).
To know more about radius here: brainly.com/question/13449316
#SPJ11
The head of the quality control department at a printing company would like to carry out an experiment to determine which of three different glues results in the greatest binding strength. Although they are not of interest in the current investigation, other factors thought to affect binding strength are the number of pages in the book and whether the book is being bound as a paperback or a hardback.
a. What is the response variable in this experiment?
b. What explanatory variable will determine the experimental conditions?
c. What two extraneous variables are mentioned in the problem description? Are there other extraneous variables that should be considered?
A) The response variable in this experiment is the binding strength. It is the variable that is being measured or observed to assess the impact of different glues.
B) The explanatory variable that will determine the experimental conditions is the type of glue. The three different glues being tested will be the different levels or treatments of this variable.
C) The two extraneous variables mentioned in the problem description are the number of pages in the book and whether the book is being bound as a paperback or a hardback. These variables are mentioned as factors that are not of interest in the current investigation but could potentially affect the binding strength.
Other extraneous variables that should be considered would depend on the specific circumstances and factors that might influence binding strength.
More on variables can be found here: https://brainly.com/question/15078630
#SPJ4
Now write as 100,000*1/100,000 multiplying 10 to a power by 10 to a power.
Any number raised to the power of zero is equal to 1. Therefore, the expression simplifies to 100,000 * 1/100,000 equals 1.
To simplify the expression 100,000 * 1/100,000 using the property of multiplying numbers with the same base raised to different exponents, we can rewrite it as:
(10^5) * (10^(-5))
When multiplying two numbers with the same base, we can add their exponents. Therefore, the expression becomes:
10^(5 + (-5))
The exponent 5 + (-5) simplifies to zero:
10^0
Any number raised to the power of zero is equal to 1. Therefore, the expression simplifies to:
1
Hence, 100,000 * 1/100,000 equals 1.
Learn more about expression here
https://brainly.com/question/1859113
#SPJ11
The value of a painting when purchased was represented by V. If over a three year period the painting increased in value by 33%, which expression represents the current value of the painting?
The painting has increased in value by 33% over a three-year period. To determine the current value of the painting, an expression can be utilized. The following expression represents the current value of the painting: V + 0.33V = (1 + 0.33)V = 1.33VWhere V represents the initial value of the painting.
An expression can be utilized to represent the current value of a painting that has increased in value by 33% over a three-year period. The initial value of the painting is represented by the letter V, which is included in the expression. The 33% increase is represented by 0.33 V. To determine the current value of the painting, the expression must be evaluated. The expression V + 0.33V can be simplified by combining the two terms. This results in (1 + 0.33) V. The value of 1 represents the initial value of the painting, and 0.33 represents the 33% increase in value. To determine the current value of the painting, this expression can be multiplied. Multiplying 1.33 by the initial value of the painting, which is represented by V, yields the following expression: 1.33VThis expression represents the current value of the painting, which has increased in value by 33% over a three-year period. The value of the painting is now 1.33 times its initial value. Therefore, the painting has increased in value by 33%.
The current value of the painting can be determined by using an expression. This expression includes the initial value of the painting and the 33% increase in value that has occurred over a three-year period. The expression can be simplified and multiplied to determine the current value of the painting, which is represented by 1.33 V.
To know more about current value visit:
brainly.com/question/19259550
#SPJ11
Write the equation in slope-interceprbform that corresponds with this table x= -1,0,1,2,3,4 | Y= 6,8,10,12,14,16
The linear function that corresponds with the table is given as follows:
y = 2x + 8.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.When x increases by 1, y increases by 2, hence the slope m is given as follows:
m = 2.
When x = 0, y = 8, hence the intercept b is given as follows:
b = 8.
Hence the function is:
y = 2x + 8.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
PROFIT The monthly profit of a skateboard
company is 120x – 2,240, where x represents
the number of units sold. Find the monthly
profit if the company sells 42 skateboards.
The monthly profit of the skateboard company, based on the given equation, is determined by the number of units sold. The monthly profit of the skateboard company when it sells 42 skateboards is $2,800.
According to the given equation, the monthly profit of the skateboard company is represented by 120x - 2,240, where x represents the number of units sold. To find the monthly profit when the company sells 42 skateboards, we substitute the value of x with 42 in the equation.
Substituting x = 42 into the equation, we get:
Profit = 120(42) - 2,240
= 5,040 - 2,240
= 2,800
Therefore, the monthly profit of the skateboard company when it sells 42 skateboards is $2,800. This means that for each unit sold, the company earns a profit of $120, and when 42 skateboards are sold, the total profit amounts to $2,800. It's important to note that the equation assumes a linear relationship between the number of units sold and the profit.
Learn more about linear here:
https://brainly.com/question/31510530
#SPJ11
As 55 people left a fruit market they were asked if they had bought apples or bananas and clementines. the results were as follows. 29 bought apples, 34 bought bananas. 15 bought apples and bananas, 16 bought appels and clementines, 17 bought bananas and clementines, 3 bought none of these fruit.Venn diagramcalculate the value of x
To calculate the value of x in the Venn diagram, we need to consider the number of people who bought only apples, only bananas, only clementines, and combinations of these fruits.
Given the information provided, we know that 29 people bought apples, 34 people bought bananas, and 3 people bought none of these fruits. Let's denote the number of people who bought only apples as A, only bananas as B, only clementines as C, and the number of people who bought both apples and bananas as AB.
We can construct the following equations based on the information given:
A + AB + 16 = 29 (equation 1)
B + AB + 15 = 34 (equation 2)
C + AB + 17 = x (equation 3)
A + B + C + AB + 3 = 55 (equation 4)
Simplifying equations 1 and 2, we get:
A + AB = 13 (equation 5)
B + AB = 19 (equation 6)
From equations 5 and 6, we can subtract AB from both sides to find:
A = 13 - AB (equation 7)
B = 19 - AB (equation 8)
Substituting equations 7 and 8 into equation 4, we have:
(13 - AB) + (19 - AB) + C + AB + 3 = 55
Simplifying this equation, we get:
35 - AB + C = 55
Rearranging, we find:
C = 55 - 35 + AB
C = 20 + AB (equation 9)
Finally, substituting equations 7, 8, and 9 into equation 3, we have:
20 + AB + AB + 17 = x
Simplifying, we get:
2AB + 37 = x
Therefore, the value of x is 2AB + 37.
Learn more about Venn diagram here: brainly.com/question/20795347
#SPJ11
if the total surface area of cube is 216cm 2 then find its volume
To find the volume of a cube given its total surface area, we can use the formula for the surface area of a cube and then solve for the volume. The formula for the surface area of a cube is 6s^2, where s represents the length of the side of the cube.
By equating this formula to the given surface area value of 216 cm^2, we can solve for the side length. Once we have the side length, we can then calculate the volume using the formula V = s^3.
Let's assume that the side length of the cube is represented by "s". The formula for the surface area of a cube is 6s^2. Given that the total surface area is 216 cm^2, we can set up the equation 6s^2 = 216. Solving this equation for "s", we find s^2 = 36. Taking the square root of both sides, we get s = 6. Now that we know the side length of the cube is 6 cm, we can calculate the volume using the formula V = s^3. Plugging in the value of s, we find V = 6^3 = 216 cm^3. Therefore, the volume of the cube is 216 cm^3.
To learn more about surface area; -brainly.com/question/2835293
#SPJ11
Which of the following is a property of inferential statistics but not of descriptive statistics? Select all that apply.the collection of datathe number of variables studiedthe use of a graph to visualize the datathe use of a statistical test to determine the likelihood of a relationship between two or more characteristics of the group under studythe purpose of the study is often to find a possible cause-and-effect relationship
The correct options are: The use of a statistical test to determine the likelihood of a relationship between two or more characteristics of the group under study. The purpose of the study is often to find a possible cause-and-effect relationship.
The properties of inferential statistics that are not typically associated with descriptive statistics are:
The use of a statistical test to determine the likelihood of a relationship between two or more characteristics of the group under study: Inferential statistics involves making inferences or drawing conclusions about a population based on a sample. Statistical tests are used to analyze the sample data and determine the likelihood of certain relationships or patterns occurring in the larger population. Descriptive statistics, on the other hand, focuses on summarizing and describing the observed data without making any generalizations to the larger population.
The purpose of the study is often to find a possible cause-and-effect relationship: Inferential statistics is commonly used in research studies that aim to establish causal relationships between variables. The statistical analysis helps researchers assess the significance of the relationship between variables and determine if there is evidence to support a cause-and-effect relationship. Descriptive statistics, on the other hand, primarily focuses on summarizing and describing data without making causal claims.
To summarize, inferential statistics involves using statistical tests to draw conclusions about a population and to determine the likelihood of relationships between variables. It is often used to investigate cause-and-effect relationships in research studies. Descriptive statistics, in contrast, is concerned with summarizing and describing data without making inferences to the larger population or establishing causal relationships.
Learn more about statistical test here:
https://brainly.com/question/15110538
#SPJ11
⎩⎪⎪⎨⎪⎪⎧f(1)=−62f(n)=f(n−1)+5Find an explicit formula for f(n)f(n)f, left parenthesis, n, right parenthesis.
The recursive formula states that f(n) is equal to f(n-1) plus 5.So, the explicit formula for f(n) is f(n) = -62 + 5(n-1).
To find the explicit formula, we need to analyze the given recursive formula for f(n). We are given that f(1) = -62, indicating the initial value of the sequence. The recursive formula states that f(n) is equal to f(n-1) plus 5.
Based on this information, we can derive the explicit formula as follows:
- For the first term, f(1), we already know the value is -62.
- For the second term, f(2), we can substitute n = 2 into the recursive formula: f(2) = f(2-1) + 5 = f(1) + 5 = -62 + 5 = -57.
- For the third term, f(3), we can substitute n = 3 into the recursive formula: f(3) = f(3-1) + 5 = f(2) + 5 = -57 + 5 = -52.
- We continue this process for each subsequent term, adding 5 to the previous term.
In general, for any value of n, the explicit formula for f(n) is given by f(n) = -62 + 5(n-1). This formula allows us to directly calculate the value of any term in the sequence without relying on the previous terms.
Learn more about explicit here:
https://brainly.com/question/25094536
#SPJ11
A store marks down the price of a necklace from $389. 85 to $314. 15. By what percent did the price decrease? Round to two decimal places. A. 13. 21% b. 15. 75% c. 19. 42% d. 24. 10%.
we find that the price decreased by 19.42%. Therefore, the answer is C. 19.42%.
To determine the percentage decrease in price, we can use the formula:Percentage decrease = ((Initial price - Final price) / Initial price) * 100.In this case, the initial price is $389.85, and the final price is $314.15. Plugging these values into the formula, we can calculate the percentage decrease:
Percentage decrease = ((389.85 - 314.15) / 389.85) * 100
Calculating the expression inside the parentheses, we have:
Percentage decrease = (75.70 / 389.85) * 100
Dividing the numerator by the denominator, we get:
Percentage decrease = 0.1942 * 100
Learn more about price here:
https://brainly.com/question/19091385
#SPJ11
If 1 U.S. dollar costs 1.1010 euros, then 1 euro must cost _____ U.S. dollars.A) 0.8080B) 0.85C) 0.87D) 00.90E) 00.91
If 1 U.S. dollar costs 1.1010 euros, then 1 euro must cost approximately 0.9082 U.S. dollars. None of the provided answer choices (A, B, C, D, E) exactly matches this value. However, option D, which states 00.90, is the closest approximation to the correct value.
To determine the cost of 1 euro in U.S. dollars, we need to find the reciprocal of the given exchange rate, which means dividing 1 by 1.1010. Using a calculator, we get the result as approximately 0.9082. Therefore, 1 euro would cost approximately 0.9082 U.S. dollars. None of the provided answer choices (A, B, C, D, E) exactly matches this value. However, option D, which states 00.90, is the closest approximation to the correct value of 0.9082. It is important to note that the answer is an approximation due to the rounding of the decimal places.
Learn more about decimal here: https://brainly.com/question/30958821
#SPJ11
Each morning Eric makes 50 cinnamon bagels for his customers at barneys bagels because of a recent increase in popularity of cinnamon bagels he has increase the number he backs each morning 58% how many cinnamon bagels does Eric bake each day?
Eric bakes 79 cinnamon bagels each day at Barney's Bagels, resulting from a 58% increase in the number he previously made.
Originally, Eric made 50 cinnamon bagels each morning. However, due to the increased demand and popularity of cinnamon bagels, he decided to increase his production. The increase is given as 58%, which means he is now baking 58% more bagels than before.
To calculate the new number of cinnamon bagels, we need to find 58% of 50 and add it to the original quantity.
58% of 50 can be calculated by multiplying 50 by 0.58:
58% × 50 = (58/100) × 50 = 0.58 × 50 = 29.
Now, adding the increase to the original quantity:
50 + 29 = 79.
Therefore, Eric now bakes 79 cinnamon bagels each day at Barney's Bagels, reflecting a 58% increase from his previous production.
Learn more about number here:
https://brainly.com/question/3589540
#SPJ11
In a certain country, the true probability of a baby being a girl is 0. 479. Among the next eight randomly selected births in the country, what is the probability that at least one of them is a boy ?
The probability that at least one of the next eight randomly selected births in the country is a boy is approximately 0.978 or 97.8%.
To calculate the probability of at least one boy among the next eight randomly selected births in the country, we can use the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. In this case, the event of interest is that none of the eight births is a boy.
The probability of having a boy in a single birth is 1 minus the probability of having a girl, which is 1 - 0.479 = 0.521.The probability of none of the eight births being a boy is (0.521)^8, as these events are independent.
Therefore, the probability of at least one boy among the next eight births is 1 - (0.521)^8.
Calculating this, we have:
1 - (0.521)^8 = 1 - 0.021743 = 0.978257.
So, the probability that at least one of the next eight randomly selected births in the country is a boy is approximately 0.978 or 97.8%.
To learn more about probability click here brainly.com/question/32117953
#SPJ11
The mesosphere is the layer of Earth's atmosphere
between 50 kilometers and 85 kilometers above
Earth's surface. At a distance of 50 kilometers from
Earth's surface, the temperature in the mesosphere is
-5° Celsius, and at a distance of 80 kilometers from
Earth's surface, the temperature in the mesosphere is
- 80° Celsius. For every additional 10 kilometers
from Earth's surface, the temperature in the
mesosphere decreases by k Celsius, where k is a
constant. What is the value of k?
The value of k, representing the decrease in temperature in the mesosphere for every additional 10 kilometers from Earth's surface, is -7° Celsius.
To determine the value of k, we need to find the change in temperature per kilometer in the mesosphere. Given that the temperature at 50 kilometers is -5° Celsius and the temperature at 80 kilometers is -80° Celsius, we can calculate the temperature difference between these two points.
The temperature difference is -80° Celsius minus (-5° Celsius), which is -80 + 5 = -75° Celsius.
Since this temperature difference occurs over 30 kilometers (80 km - 50 km), we can find the temperature change per kilometer by dividing the temperature difference by the distance:
-75° Celsius / 30 kilometers = -2.5° Celsius per kilometer.
Therefore, the value of k, representing the decrease in temperature per additional 10 kilometers, is -2.5° Celsius / 3 = -7° Celsius.
Hence, the value of k is -7° Celsius.
To learn more about mesosphere: -brainly.com/question/15011302
#SPJ11
Which mixed number is equal to 4 7/5?9 2/54 7/55 2/97 4/5
The mixed-number that is equal to 4 7/5 is 4 7/5 itself. The correct option is B) 4 7/5, using conversion into improper-fraction & vice-versa.
To convert the mixed number 4 7/5 into an improper fraction,
we will multiply the denominator by the whole number and add the numerator. 4 × 5 + 7 = 27.
Thus, 4 7/5 as an improper fraction is 27/5.
Now, we have to convert the given mixed numbers into improper fractions one by one, and then
compare it to 27/5 , is the fraction equivalent to 4 7/5.
Let's do it:
Option A:9 2/5 = 47/5
Divide 47 by 5 and we get 9 with a remainder of 2.
Thus, 9 2/5 = 47/5 which is not equal to 27/5.
Option B:4 7/5 = 27/5
As we know 4 7/5 as an improper fraction is 27/5, and it matches our answer with the given mixed number.
Option C:5 2/9 = 47/9
Divide 47 by 9 and we get 5 with a remainder of 2.
Thus, 5 2/9 = 47/9 which is not equal to 27/5.
Option D:4/5 = 0.8
Clearly, 0.8 is not equal to 27/5.
So, the mixed number that is equal to 4 7/5 is 4 7/5 itself. The correct option is B) 4 7/5.
To know more about improper-fraction, visit:
https://brainly.com/question/21449807
#SPJ11
Evaluate the expression Z/8, or z 8 for each of the following values for Z:
20) Z = 10.2
21) Z = 92
22) Z = 16.016
23) Z = 2
The evaluation of the expression Z/8 are:
20) Z = 10.2, Z/8 = 11.5
21) Z = 92, Z/8 = 11.5
22) Z = 16.016, Z/8 = 2.002
23) Z = 2, Z/8 = 0.25
How to evaluate the expression Z/8?To evaluate the expression Z/8 for each of the following values for Z, substitute each value of Z into the expression. That is:
20) When Z = 10.2
Z/8 = 10.2/8 = 1.275
21) When Z = 92
Z/8= 92/ 8 = 11.5
22) When Z = 16.016
Z/8 = 16.016 / 8 = 2.002
23) When Z = 2
Z/8 = 2/8 = 0.25
Learn more about expressions on:
https://brainly.com/question/29500077
#SPJ1
If you construct a line perpendicular to line A, given by y=22, through S (1,5), not on line y=22, find the distance from S to line A
To find the distance from point to line,which is a horizontal line, we can calculate the vertical difference between the y-coordinate of S and the y-coordinate of any point on line A. The distance from S to line A is 17 units.
Since line A is a horizontal line given by y = 22, the y-coordinate of any point on this line remains constant at 22. To find the distance from S (1, 5) to line A, we need to calculate the vertical difference between the y-coordinate of S and the y-coordinate of any point on line A.
The y-coordinate of S is 5, and the y-coordinate of any point on line A is 22. Therefore, the vertical difference is |5 - 22| = 17 units.
Hence, the distance from point S (1, 5) to line A (y = 22) is 17 units.
To learn more about vertical difference click here : brainly.com/question/30105249
#SPJ11
Solve the problem using a system of equations. Use substitution or Elimination.1. 14x+17y=99
This simplifies to: 42x + 51y = 297. We now have a new equation in terms of y. To solve for y, we need another equation. If you have another equation, please provide it, and we can continue solving the system of equations.
To solve the system of equations represented by 14x + 17y = 99, we can use either substitution or elimination methods. In this case, let's use the elimination method.
To use the elimination method, we need to manipulate the equations to eliminate one variable. In this case, we can eliminate the variable x by multiplying the first equation by 17 and the second equation by 14, resulting in:
(17)(14x + 17y) = (17)(99)
(14)(14x + 17y) = (14)(99)
Simplifying these equations gives us:
238x + 289y = 1683
196x + 238y = 1386
Now, we can subtract the second equation from the first equation to eliminate x:
(238x + 289y) - (196x + 238y) = 1683 - 1386
This simplifies to: 42x + 51y = 297
Learn more about elimination methods:
https://brainly.com/question/13877817
#SPJ11
