The recursive definition of the arithmetic sequence -34, -21, -8 is:
f(1) = -34.f(n + 1) = f(n) + 13.What is an arithmetic sequence?It is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
An arithmetic sequence can also be defined recursively, as follows:
[tex]f(1) = a_1[/tex]f(n + 1) = f(n) + d.In this problem, the sequence is given as follows:
-34, -21, -8.
Hence the first term and the common ratio are given as follows:
First term: -34.Common ratio: 13, as each term is the previous term added to 13.Hence the recursive definition of the sequence is:
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joe and matthew plan to visit a bookstore. based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. a figure is shown with two tables, each with two rows. the top table has a top row that reads number of books joe will buy, 0, 1, 2, and a bottom row that reads probability, 0.50, 0.25, 0.25. the bottom table has a top row that reads number of books matthew will buy, 0, 1, 2, and a bottom row that reads probability, 0.25, 0.50, 0.25. assuming that joe and matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?
The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We are to find the probability where p(x) = 0 and p(y) = 0
This is where we would have
from the table, p(x) = 0 is 0.5
p(y) = 0 is 0.25
0.25 x 0.5 = 0.125
Hence the probability that no books would be bought is 0.125.
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which shape has a larger area: a rectangle that is 7 inches by 3/4 inch, or a square length 2 1/2 inches? Show your reasoning
The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.
What is area of plane shape?The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.
Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively
The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches
The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m
Therefore the square has larger area
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The mean temperature for the first 4 days in January was 3°C.
The mean temperature for the first 5 days in January was 1°C.
What was the temperature on the 5th day?
The temperature on the fifth day in January is -7°C.
What is mean?It should be noted that a mean simply means the average of a set of numbers that are given.
Since the mean temperature for the first 4 days in January was 3°C. The rural temperature will be:
= 4 × 3°C
= 12°C
The mean temperature for the first 5 days in January was 1°C. The total temperature will be:
= 5 × 1°C
= 5°C
The temperature of the fifth day will be the difference between the temperature. This will be:
= 5°C - 12°C
= -7°C
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What is the solution set of the inequality?
Answer:
the fourth one is the right one
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.
Check answer below in the image.
This stem-and-leaf plot shows the number of Australian road fatalities in April for the years 2009 to 2019. Find the range of the data. Stem Leaf 7 2 889 9 10 11 15 4 1 2 6 1 3 4 3 Key 13 0=130
If someone could please answer all 3 points (20 points)
The missing parts of the table for the function are 49, 1 and 49 respectively
How to complete the missing parts of the table?
An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ
Given: the exponential function y = (1/7)ˣ
In order to find the missing parts, we have to substitute the relevant values into the function. Thus:
For x = -2:
y = (1/7)ˣ
Substitute x = -2 into the function:
y = (1/7)⁻² = 49
For x = 0:
y = (1/7)ˣ
Substitute x = 0 into the function:
y = (1/7)⁰ = 1
For x = 2:
y = (1/7)ˣ
Substitute x = 2 into the function:
y = (1/7)² = 1/49
The missing part is 49
Therefore, the missing parts of the table are 49, 1 and 49 respectively
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What is the slope of the line that passes through the points (0, -10)(0,−10) and (-4, -11)(−4,−11)? Write your answer in simplest form.
The slope of the line that passes through the points is 1/ 4
What is slope?The gradient or slope of a line is a value or number describing both the direction and the steepness of a line.
The formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/ x₂ - x₁
Where;
y₁ is the first point on the y - axis y₂ is the second point on the y - axisx₁ is the first point on the x - axisx₂ is the second point on the x - axisNow, substitute the values, we have;
Slope, m = (-11 - ( -10)/ ( -4 - 0)
expand the brackets
Slope, m = - 11 + 10/ -4
Add the values
Slope, m = -1/ -4
Divide the values
Slope, m = 1/ 4
Hence, the value is 1/ 4
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Answer:
1/4
Step-by-step explanation:
14.9 - 15.1 EVALUATE PLEASE.
Answer:
-0.2
Step-by-step explanation:
14.9-15.1= -0.2
To do equations like this in the beginning I used to switch the terms and then add a negative symbol in front of it
I would solve it like this
15.1-14.9
.2
And now since I switched the terms I change the sign to negative
-0.2
Hopes this helps please mark brainliest
I need help please
Answer:
it is d
Step-by-step explanation:
Answer: Down Below ↓
Step-by-step explanation: Here's an easy tip for measuring the angles of triangles. Every triangle has a sum (total) of 180 degrees. Take the two angles that are already shown, add them together, then subtract them from 180.
I cannot read the numbers on the paper, so I hope this answer somewhat helps.
Edit: Oh my lord, it's a coloring page too? I remember those, they suck. :')
Compare and Explain: Are they equivalent?
3 hours worked for $12; 9 hours worked for $36
Answer:
Yes they are equivalent.
Step-by-step explanation:
$12 divided by 3 is $4
$36 divided by 9 is also $4
Therefore they are equivalent.
Your welcome
Answer:
Yes!
Step-by-step explanation:
You divide 3 by 12 because that's how much they work for an hour. That means they make $36 for 9 hours.
12 ÷ 3 = 4
36 ÷ 9 = 4
They have the same answer which makes them equivalent.
it is known that 15% of the calculators shipped from a particular factory are defective. what is the probability that exactly four of ten chosen calculators are defective?
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, whereC5 3= 5!/3/2=4*5/2=10p is the probability that one randomly selected calculator is defective= 10%=0.1q is the probability that one randomly selected calculator is non-defective.q=1-p=1-0.1=0.9So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081learn more about probability click here:
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Can somebody help me on this please
Since it is labeled that this triangle has two equal sides, it is isosceles. Isosceles triangles' acute angles are always congruent, so we can infer that there are two angles with a measurement of 29 degrees. Knowing that all of the angles in a triangle add up to 180 degrees, we can set up this equation:
2*29 + 11x - 65 = 180
58 + 11x - 65 = 180
-7 + 11x = 180
11x = 187
x = 17
Knowing that "x = 17" we can find the measurement of the obtuse angle:
11*17 - 65
= 187 - 65
= 122
-7/6 - (-1/9) Evaluate.
- Simplest form.
-1/3 + 5/7 Add.
- Simplest form.
After evaluating those terms,
we get the answer as
1. -7/6 - (-1/9) =[tex]\frac{-19}{18}[/tex]
2. -1/3 + 5/7 = = [tex]\frac{8}{21}[/tex]
What are fractions?A fraction is a number that has a numerator as well as a denominator.
1 / 2 is an example of a fraction. The top part of the fraction is the numerator and the bottom part of the fraction is the denominator.
Fractions represent one value. Dividing the numerator by the denominator shows what decimal value fractions have. For example, 1/2 is equal to 1 ÷ 2 which equals 0.5.
in this we have to evaluate
1. -7/6 - (-1/9)
= [tex]\frac{-7}{6}[/tex] - ([tex]\frac{-1}{9}[/tex])
= [tex]\frac{-21+2}{18}[/tex]
=[tex]\frac{-19}{18}[/tex]
Hence , after solving we get the desired result as -19/18 .
2. -1/3 + 5/7
= [tex]\frac{-1}{3}[/tex] + [tex]\frac{5}{7}[/tex]
= [tex]\frac{-7 + 15}{21}[/tex]
= [tex]\frac{8}{21}[/tex]
Hence, after solving we get the desired result as 8/21 .
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Can yall help me on this?
x-intercept is (-250, 0) and y-intercept is (0, 100)
What is x-intercept and y-intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.
First, find x-intercept
For x-intercept it means y = 0
observe the graph and see the blue line cuts the x-axis when y = 0
We see, x = -250
so, the x-intercept is = (-250, 0)
Now, same thing do to find y-intercept
For y-intercept it means x = 0
observe the graph and see the blue line cuts the y-axis when x = 0
We see, y = 100
so, the y-intercept is = (0, 100)
Therefore, x-intercept is (-250, 0) and y-intercept is (0, 100).
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How much money does he earn when he sells 35 wooden toys? Emilio builds and sells homemade wooden toys for $12 each. The festival he is attending charges $50 to set up his booth. How much money does he earn when sells 35 wooden toys?
After selling 35 wooden toys and after cutting the expense of setting up his booth, Emilio earns $370.
What is BODMAS?
BODMAS, often known as the order of operations, is a method for carrying out operations in an arithmetic expression. Math is all about logic and some established principles that facilitate our computations. BODMAS is one of those commonly used rules for consolidating expressions with multiple operators.
Solution Explained:
A/Q, The price of one toy is $12
The cost of setting up the shop is $50
Therefore, the amount Emilio earns after selling 35 toys is:
(12 X 35) - 50
= 420 - 50
= 370
Hence, Emilio earns $370
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At the gym on Saturday, Reese ran 5 miles in the treadmill and then the completed 1 mile in the elliptical machine and burned 725 calories. On Sunday she ran 3 miles on the treadmill and completed 1 mile in the elliptical, and burned 505 calories. Write and solve a linear system to find the number of calories Reese burns on the machine
Answer:The equations are 5t + e = 725 and 3t + e = 505
Step-by-step explanation:Subtract equation (2) from equation (1) and you arrive at;
2t = 220
Divide both sides of the equation by 2
t = 110
Having calculated the value of t, substitute for the value of t into equation (1)
5t + e = 725
5(110) + e = 725
550 + e = 725
Subtract 550 from both sides of the equation
e = 175
The above calculations shows that the calories burned on each gym equipment are;
Treadmill = 110 per hour
Elliptical = 175 per hour
7 yd.
24 yd.
What is the length of the hypotenuse?
yards
C=
Answer:
25
Step-by-step explanation:
the equation is a^2+b^2=c^2
7^2=49
24^2=576
49+576=625
the square root of 625 is 25
Enter the equation of the graph in vertex form?
The equation of the given graph is y = (x + 4)² -5.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The vertex form of a parabola is y = (x - h)² + k which is opened upward direction and vertex is (h, k).
From the graph, the vertex of the quadratic equation is (-4, -5)
Thus h = -4 and k = -5.
Putting h = -4 and k = -5 in y = (x - h)² + k
y = (x - (-4))² + (-5)
y = (x + 4)² -5
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NEED HELP PLEASE AS FAST AS YOU CAN
Answer:
3.87
Step-by-step explanation:
b =
[tex] \sqrt{8 ^{2} -7 ^{2}} [/tex]
11. Using the equation: y + 2 = 3(x - 1).
a) Identify the slope and y-intercept.
b) Graph the equation.
c) Does the point (0,0) satisfy the equation?
Justify your answer.
For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.
Linear Function
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex].
m= the slope.
[tex](x_1,y_1)[/tex]= the coordinate of a point.
For the given example: m=1 and b=19.
The question gives: y + 2 = 3(x - 1). Therefore,
y + 2 = 3(x - 1)
y=3x-3-2
y=3x-5
Letter A - Identify the slope and y-interceptIf y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:
m= the slope. It can be calculated for Δy/Δx.
b= the constant term that represents the y-intercept
Thus, the slope is 3 and the y-intercept is -5.
Letter B - Graph the equation.For this, you should do a table with points
x y= 3x-5
-2 y=3*(-2)-5=-6-5= -11
-1 y=3*(-1)-5=-3-5= -8
0 y=3*(0)-5=0-5= -5
1 y=3*(1)-5=3-5= -2
2 y=3*(2)-5=6-5= 1
Draw a graph from these points, see the attached image.
Letter C - Does the point (0,0) satisfy the equation?The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.
y= 3x-5, for x=0
y=3*0-5
y=0-5
y=-5
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please help me
this is algebra
Answer:
The answer is 3.
Step-by-step explanation:
The highest coefficient is 3 (5x^3), the second one is 2 (4x), and the other two without coefficient are considered 1.
The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:
Z = (x - )/ ( / sqrt(n)
where,
x=11, sample score.10 is the sample mean.Standard deviation equals 2
sample size, n With n = 5, calculating the z and p values:
z =(11 - 10) / (2 / sqrt(5))z = 1.12The tables show that p(5) = 0.8686.
For n = 6, calculate the z and p values as follows:
z =(11 - 10) / (2 / sqrt(6))z = 1.22The tables show that p(6) = 0.8888.
If both days to occur, the probability that each day will last no more than 11 minutes is as follows:
p total = p(5) * p(6)p total = 0.8686 * 0.8888p total = 0.772learn more about probability click here:
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What is the sign of 37 + (-37)?
Answer:
not positive or negative
Step-by-step explanation:
It is 0 but i would say it is positive nor negative :)
0, It not really postive or negative
37 + -37 = 0 =
Neither negative nor positive
:/
PLEASE HELP ME !!!!!!!
Answer:ok
Step-by-step explanation:
Answer: 1/5 25/48
maybe?
For what value of X is Y= 4 a solution to the equation X-2 =XY+16
If x=-3 and y =2 , then x^y +xy^=?
a) The value of x is -6
b) The value of the expression is -3 .
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a) x-2=xy+16
y= 4 a solution to the equation
Substitute y=4 into the equation.
x-2=x(4)+16
x-2=4x+16
-2-16=4x-x=3x
-18=3x
x=- 18/3= -6
The value of x is -6
b) [tex]x^y+xy^2[/tex]
substitute x= -3 and y =2
(-3)²+(-3)(2)²
= 9 - 12
= -3
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Tara's retirement party will cost $12 if she invites 4 guests. What is the maximum number of guests there can be if Tara can afford to spend a total of $15 on her retirement party?
Please help!!! Complete the flow proof given CM = YJ
Find the slope of the line that passes through (2, 1) and (7, 8).
The slope of the line passing through the point (2,1) and (7,8) is 7/5
What is a slope?
Slope is the inclination of the line with x-axis. measure of how steep a curve or line is. There are various way to calculate the slope of a line. One of the basic way is from coordinates. It is the ratio of difference of y coordinate to the corresponding x- coordinate. it is also known as slope formula
We are given the coordinates as
(2, 1) and (7, 8).
We use the slope formula to find the slope
Slope = (8-1)/(7-2)
Slope = 7/5
Hence the slope of the passing through the given point is 7/5
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