Answer:
10
Step-by-step explanation:
no explanation just math-way
Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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Help me solve this please
Answer:
Step-by-step explanation:
The four options just swap the order, and you should choose them all
A basket of the fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, draw the 2nd piece of fruit from the basket, keep that, and then draw a third piece of fruit from the same basket. What is the probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded?
A. 5/144
B. 5/108
C. 1/28
D. 1/22
The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.
What is the probability:The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The outcome of an event may be known to us or unknown to us. When this happens, we indicate that there is a probability that the event will happen or not.
It is also defined as the ratio of the number of favorable outcomes to the total number of outcomes.
The formula for the probability of an event is given by
P(E) = No of favorable outcomes/ Total No of outcomes ]
Here we have
A basket of fruit contains 4 bananas, 3 apples, and 5 oranges.
Total number of fruits = 4 + 3 + 5 = 12
By the given formula,
Probability of selecting 1 banana = 4/12 = 1/3
Probability of selecting 1 apple = 3/12 = 1/4
Probability of selecting 1 orange = 5/12
The order of the fruits that is given is 1 banana, then 1 apple, then 1 orange
Let's assume that,
We taken 1 banana
=> The probability of selecting one banana = 1/3
After taking one banana, remaining fruits = 12 - 1 = 11
Now we have drawn 1 apple
=> The probability of selecting one apple in 11 fruits = 3/11
After taking one apple remaining fruits = 11 - 1 = 10
=> The probability of selecting one orange from 10 fruits = 5/10 = 1/2
From the above calculations,
The probability of selecting in given order = (1/3)(3/11)(1/2) = 3/66 = 1/22
Therefore,
The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 six tenths
Player 2 five ninths
Player 3 four sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
The likelihood event:
Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).
The correct option is A.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Given:
Three softball players discussed their batting averages after a game.
Probability:
Player 1 = six tenths = 6/10
Player 2 = five ninths = 5/9
Player 3 = four sevenths = 4/7
To find better batting averages:
LCM of 10, 9 and 7.
10 = 2 x 5. 9 = 3 x 3, 7 = 7
So, the LCM (10, 9, 7) = 630
Now we have the number of chances are equal for each of the three players.
So, the P(Player 1) = 6/10 = 378/630
P(Player 2)= 5/9 = 350/630
P(Player 3)= 4/7 = 360/630
The Player 1 has better batting average than Player 2 and Player 3.
Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).
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Is angle 1 vertically opposite to angle 4?
Yes, angle 1 is vertically opposite to angle 4 because they are formed due to the intersection of straight lines.
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.
For example, if two lines intersect and make an angle, say X=55°, then its opposite angle is also equal to 55°. And the adjacent angle to angle X will be equal to 180 – 55 = 125°
In the given figure, ∠AOC and ∠BOD form a pair of vertically opposite angles and similarly ∠AOD and ∠BOC form such a pair. Therefore,
∠AOC = ∠BOD
∠AOD = ∠BOC
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quadratic expression x² +6x +5
Answer:
if its for factor, we have (x+1)(x+5), if its for formula, its x=-1, -5
Step-by-step explanation:
The perimeter of triangle ABC is 26 units. The altitudes of triangle ABC are in the ratio 2: 3: 4. Compute the area of triangle ABC.
please help me w step by step explanation and work tysm !
Answer:
59
Step-by-step explanation:
How do you simplify 3 Way ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 225: 125: 25
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
225/5: 125/5: 25/5
45: 25: 5
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 9: 5: 5.
45/5: 25/5: 5/5
9: 5: 1
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What is the value of log2 base 2?
the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one
How do you find the value of log base 2?
Properties of Log Base 2
Multiply two numbers with base 2, then add the exponents. Divide two numbers with the base 2, subtract the exponents. Power Rule: Raise an exponential expression to power and multiply the exponents.
Use the change-of-base formula:
since we know that natural log and log with base 10 are different
So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:
Hence , the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one
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3(-n + 4) + 5n = 2n A) n = 3 B) no solution C) infinitely many solutions
Part 1: Use inverse operations and rules of equation solving to determine the correct answer to Mrs. Jones's quiz question number 14. Include all of your work in your final answer. Part 2: Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer.
(A) There is only one solution to the given system.
(B) There is no solution to the given system
(C) There are infinite solutions to the system.
What is solution of the system?
A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
Given:
3(- n + 4) + 5n = 2n ← distribute and simplify left side
- 3n + 12 + 5n = 2n
2n + 12 = 2n ( subtract 12 from both sides )
2n = 2n - 12 ( subtract 2n from both sides )
0 = - 12 ← not possible
This indicates the equation has no solution
Comparing the types of solutions
A n = 3
Indicates that there is only one unique solution to the equation.
B no solutions
This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is
0 = 12
C infinite solutions
This is indicated when you solve the equation and obtain
4 = 4 or - 3 = - 3
Hence,
(A) There is only one solution to the given system.
(B) There is no solution to the given system
(C) There are infinite solutions to the system.
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Marco's mom gave him d dollars for his allowance one week. He also earned $ 14.55 dollar sign, 14, point, 5 for his newspaper route that week.
The total amount of money that Marco has that week would be = $ d + 14.55.
What is an allowance income?An allowance income is defined as the amount of money an individual earns that can be used to solve their personal needs.
Marco received double payment, an allowance from the mother and from newspaper route.
The total amount of money received from his mother for allowance for that same week = $ d
The amount of money he earned from his newspaper = $14.55
Therefore the total amount of money Marco has that week =$ d + 14.55
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Complete question:
Marco's mom gave him d dollars for his allowance one week. He also earned \$14.55$14.55dollar sign, 14, point, 55 for his newspaper route that week.
How much money does Marco have?
Write your answer as an expression.
An experiment was conducted to see the effect altitude had on the boiling point of on Effect of Altitude on Boiling Point of Water Boiling Point (°F) 210- 200- 190+ 180- 170- 160- + 0 5,000 10,000 15,000 20,000 25,000 Altitude above Sea Level (ft) Which statement best explains the relationship between altitude and the boilin OA. There is a strong negative correlation between altitude and water's boiling point.
The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.
How to interpret the correlation relationship?In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.
Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.
Now, we want to determine whether it is a strong or weak correlation.
The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.
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Answer: A is correct
Step-by-step explanation:
took the test
Worksheet fun balancing equations
A sequence is represented by the explicit formula
The 40th term of the sequence aₙ = - 24 - 3n is - 144.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, A sequence is represented by the explicit formula aₙ = - 24 - 3n.
We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.
Therefore, To find a₄₀, we'll simply replace n with 40.
So, a₄₀ = - 24 - 3(40).
a₄₀ = - 24 - 120.
a₄₀ = - 144.
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URGENT!!!! 25 POINTS!!!
What is the linear function expressed by the following table?
The linear function expressed by the table is y = -1x + 4.
What is a linear function?
A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.
To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b
where m is the slope and b is the y-intercept
In order to find the slope 'm' we use the following formula:
m = (change in y)/(change in x) = (y2 - y1) / (x2 - x1)
Here,
m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1
The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.
To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation
y = mx + b
So now we know that m = -1,
plugging the first point (x,y) = (-2,2) in the equation
2 = -2 - b
b = 4
So the equation of the line is y = -1x + 4
Hence, the linear function expressed by the table is y = -1x + 4.
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ASAP 100 POINTS PLUS BRAINLIEST
A local rent-to-own business has a television set advertised with a purchase price of $1,095. 0. Calculate the APR if the finance terms are $29. 99 per week for 73 weeks. Round the final answer to the nearest tenth. (4 points)
73. 4%
71. 4%
81. 2%
Based on the provided information, the APR is 71.4%.
Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by
APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100
The finance terms in the given case is $29.99 per week for 73week. Hence,
Total amount paid = 29.99*73 = $2,189.27
Loan principal = $1,095
Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27
Fees = 0 (as it not mentioned in the question)
Number of days in loan terms = 73*7 = 511 days
Substituting the values in the formula,
APR = ((1094.27/1095)/511) * 365 * 100
APR = 71.4%
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Which equation has 3 as a solution set *?
The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.
Check the solution of equation 3x - 9 = 0
3x - 9 = 0
3x = 9
x = 3
Check the solution of equation 4x - 3 = 0
4x - 3 = 0
4x = 3
x = 3/4
Check the solution of equation 5x - 10 = 0
5x - 10 = 0
5x = 10
x = 10/5
x = 2
Check the solution of equation 7x - 49 = 0
7x - 49 = 0
7x = 49
x = 49/7
x = 7
Thus, only 3x - 9 = 0 satisfy the solution x = 3.
Hence, the correct option is A.
--The given question is incomplete, the complete question is
''Which equation has 3 as a solution set?
A. 3x - 9 = 0
B. 4x - 3 = 0
C. 5x - 10 = 0
D. 7x - 49 = 0''--
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which system of inequalities is represented on this graph? NEED THIS ASAP picture below
Find the value of StartFraction P (t) Over A EndFraction for this problem. StartFraction P (t) Over A EndFraction
The value of StartFraction P (t) Over A EndFraction for this problem will be 20
Take the value of x that they provide you and plug it into the problem for these kinds of difficulties.
The fraction's numerator is the highest number. It stands in for the entire thing that must be divided.
A fraction's denominator is the value at the bottom. It shows how many equally sized pieces are divided up in the object.
adding 3 to the formula:
6/(3) + 2(3)^2 —> use PEMDAS. Apply the 32 exponents first, followed by left-to-right multiplication and division, and finally addition.
6/x + 2x^2,
when x = 3
=20
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The question the incomplete the full question:
What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?
Answer:
The second part is 0.8 and B. About 1,845 years.
Step-by-step explanation:
:)
Please help me!! Find the area of the circle:)
Answer:
2.46
Step-by-step explanation:
Answer:
[tex]A=283.528736986[/tex]
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A=\pi \times r^2[/tex]
Remember that the radius is half the diameter, we are given the diameter which is 19, which means we need to find the radius:
[tex]d=19[/tex]
[tex]19\times\frac{1}{2} =9.5[/tex]
[tex]r=9.5[/tex]
Substitute and solve:
[tex]A=\pi \times9.5^2[/tex]
[tex]9.5^2=9.5\times9.5=90.25[/tex]
[tex]\pi \times90.25=283.528736986[/tex]
[tex]A=283.528736986[/tex]
Since the question doesn't say to round the area is "283.528736986."
Hope this helps.
A new social media site is increasing its user base by approximately 5% per month. If the site currently has 27,870 users, what will be the approximate user base be 6 months from now?
Answer:
37,349
Step-by-step explanation:
month 1
27870 x .05 = 1394
27870 + 1394 = 29264
month 2
29264 x .05 = 1463
29264 + 1463 = 30727
month 3
30727 × .05 = 1536
30727 + 1536 = 32263
month 4
32263 x .05 = 1613
32263 + 1613 = 33876
month 5
33876 x .05 = 1694
33876 + 1694 = 35570
month 6
35570 x .05 = 1779
35570 + 1779 = 37349
Answer:
35,570
Step-by-step explanation:
solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.
1. 27870*1.05= 29,263.5
2. 29263.5*1.05=30726.675
3.repeat
4.repeat
5.repeat
6.repeat
if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)
1. 27870÷10= 2,787
2. 2787÷2= 1393.5
3. 27870+1393.5 = 29263.5
solution 2 -Fast but probably needs a calculator
1. 27870*1.05^(5)= 35570
1.05 = monthly increase
power of 5 = ^(5) = 6 months - 1 = 5
A six-foot long ladder is leaning against a wall. The bottom of the ladder is 3 feet away from the wall. How high up the wall is the ladder
The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.
How to find height ?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.
The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.
So, if we square the length of the ladder (6^2 = 36)
The length of the base (3^2 = 9),
and add them together, then take the square root of that, we get the height of the wall.
sqrt(36+9) = sqrt(45) = 3*sqrt(5)
so the ladder is 3√5 feet high up the wall.
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Can someone show me step by step what to do next please I’m confused?!!! Please anyone
Answer:
You need to combine like terms
How do you convert log to the base e to log to the base 10?
To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)log10(2)=log(x)log(2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.
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Express (0.0425 + 25) as a fraction
Answer:
54 is the correct answer
What kind of triangle has 65 65 50?
Isosceles Triangle has 50°, 65°, 65°
An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.
Properties of Isosceles Triangle:
The two equal sides of an isosceles triangle are known as ‘legs’, and the angle between them is called the vertex angle or apex angle.In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. The side opposite the vertex angle is called the base and the base angles are equal, and perpendicular to the apex angle bisecting the base and the apex angle.To know more about Isosceles Triangle:
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Find the value of y
Answer:
y = 4
Step-by-step explanation:
The triangles are congruent.
8y = 6y + 8
2y = 8
y = 4
What is the 3 variable?
A three-variable system is a system of equations or inequalities involving three variables.
The three variables could refer to any three related quantities, such as a person's age, height, and weight. In a three-variable system, the number of equations is equal to the number of variables, so three equations are needed to solve the system. Each equation in the system will involve all three variables and will be solved through a combination of algebraic manipulation, substitution, and elimination techniques. Once all three equations have been solved, the values of the variables can be found.
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CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
An achievement exam was given to a population of 1,000 students. However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table. TEST SCORE 42 57 67 72 77 87 97 z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25 percentile rank 10 25 30 45 50 75 95 Using the table information, the test score representing the 3rd decile is: a. 67 b. 77 c. 57 d. 72 e. 97
The test score representing the 3rd decile is 67. So the option a is correct.
In the given question, an achievement exam was given to a population of 1,000 students.
However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.
TEST SCORE 42 57 67 72 77 87 97
z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25
percentile rank 10 25 30 45 50 75 95
Using the table information, we have to find the test score representing the 3rd decile.
As we know that the 3rd decile is equal to the 30th percentile.
So that the 3rd decile have the percentile rank = 30
The test score equivalent to percentile rank 30 is 67.
So, the test score representing the 3rd decile is 67. So the option a is correct.
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