(1) The explicit formula and the 21st term for the first sequence are:
aₙ = 10 - 5n and a₂₁ = -95
(2) The explicit formula and the 21st term for the second sequence are:
aₙ = 1.5n + 1.5 and a₂₁ = 33
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
(1)
The given sequence is 5, 0, -5, -10,...
Note the difference between two consecutive terms of the sequence is the same, which is -5.
Therefore, the sequence is an arithmetic sequence with a common difference of d = -5.
The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:
aₙ = a₁ + (n-1)d
Substitute a₁ = 5 and d= -5 into the equation,
aₙ = 5+ (n-1)(-5)
= 5 - 5n + 5
aₙ = 10 - 5n
To find the 21st term, substitute n = 21 into the above equation,
a₂₁ = 10 - 5n
a₂₁ = 10 - 5(21)
a₂₁ = 10 - 105
a₂₁ = -95
Hence, the explicit formula and the 21st term for the first sequence are:
aₙ = 10 - 5n and a₂₁ = -95
(2)
The given sequence is 3, 4.5, 6, 7.5, 9,...
Note that the difference between two consecutive terms is 1.5, therefore, the sequence is an arithmetic sequence with a common difference of
d = 1.5.
The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:
aₙ = a₁ + (n-1)d
Substitute a₁ = 3 and d= 1.5 into the equation,
aₙ = 3 + (n-1)1.5
aₙ = 3+1.5n-1.5
aₙ = 1.5n+1.5
To find the 21st term, substitute n = 21 into the above equation,
a₂₁ = 1.5(21) + 1.5
a₂₁ = 31.5 + 1.5
a₂₁ = 33
Hence, the explicit formula and the 21st term for the second sequence are:
aₙ = 1.5n + 1.5 and a₂₁ = 33
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Erin is a dog groomer. She charges a $6.00 base fee plus an extra $0.50 per pound. If x represents the weight of the dog in pounds, which equation models her income for each dog groomed?
Income = 0.5 x + 6
Income = 5 x + 6
Income = 6 x + 0.5
Income = 6 x + 5
Answer:
the first equation
Step-by-step explanation:
The 6 is the same amount no matter the weight of the dog. .5x represents 50 for each pound.
If a dog weight 20 pounds, it would cost 6 + .5(20)
If a dog weight 30 points it would cost 6 + .5(30) and so on.
Q6. A gas station offers two promotional reusable fountain drink cups over the
summer. The Silver Cup costs $10 and can be refilled all summer for $0.25
each refill. The Gold Cup costs $25 and comes with unlimited refills all summer.
Which inequality can be solved to find x, the number of refills needed to make
the Gold Cup a better value than the Silver Cup?
Answer:
10 + 0.25x < 25Less than 60 refills makes the Gold Cup a better valueStep-by-step explanation:
Let the number of refills be x.
Then the Silver Cup will cost:
10 + 0.25xThe cost of the Gold Cup is $25.
If we need the Gold Cup a better value, then required inequality is:
10 + 0.25x < 25Solve it for x:
0.25x < 25 - 100.25x < 15x < 15/0.25x < 60Answer:
Inequality = 10 + 0.25x < 25
The value of x = x < 60
Step-by-step explanation:
Now we have to,
→ find inequality used to solve for x.
Then the inequality will be,
→ $10 + 0.25x < $25
→ 10 + 0.25x < 25
Required value of x will be,
→ 10 + 0.25x < 25
→ 0.25x < 25 - 10
→ x < 15/0.25
→ [ x < 60 ]
Hence, the value of x < 60.
Hello, please help me answer asap! :) i really need it!!..
Answer: -2.00
Step-by-step explanation:
The parent function for linear functions is y=mx +b.
First, find the slope using the slope formula (y2-y1)/(x2-x1)
(30-10)/(8-3) = 20/5 = 4
Now, plug in known values to solve for "b", which is the y-intercept:
10 = 4(3) + b
10 = 12 + b
10 - 12 = b
-2 = b
an article in the new york times noted that the human population has shown a significant increase in height. when the relationship of height to reproductive success in humans was examined across three decades (1935-1967), height had a positive correlation to the number of children born and the number of surviving children. these observations suggest that
The given observations suggest that the increase in population is directly proportional to the number of children born and the number of surviving children.
According to the question,
We have the following information:
An article in the New York times noted that the human population has shown a significant increase in height. when the relationship of height to reproductive success in humans was examined across three decades (1935-1967), height had a positive correlation to the number of children born and the number of surviving children.
It means if the number of children born and the number of surviving children is more then the population will also increase.
In other words, it can be said population is directly proportional.
Hence, the given observations suggest that the increase in the population is directly proportional to the number of children born and the number of surviving children.
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a summary measure that is computed to describe a characteristic of an entire population is called... group of answer choices a census. the scientific method. a parameter. a statistic.
A summary measure that is computed to describe a characteristic of an entire population is called a parameter.
Descriptive statistics are those approaches that collect, present, and characterize a set of data in order to accurately describe the different properties of that set of data. A population characteristic can be estimated or a population decision can be made based solely on sample results, according to the definition of inferential statistics.
The totality of the items or things being considered constitutes a population.
The portion of the population that has been chosen for analysis is known as a sample.
A parameter is a summary measure that is computed to describe a characteristic of an entire population.
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Does the equation A=2w represent a proportional relationship?
Answer:
yes
Step-by-step explanation:
as A increases w increases
Need to know if I am correct. Image is provided
Answer:
yes your answer is correct
Haywood collects 85 signatures each day for a
petition. He says he has collected 1,250 signatures
in 15 days. How would you respond to Haywood?
Haywood is wrong because he collected 1,250 signatures in 15 days not 1250 signatures.
Given that, Haywood collects 85 signatures each day for a petition.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Number of signatures Haywood collected in 15 days is
85×15=1275
Since, Haywood said has collected 1,250 signatures in 15 days
So, Haywood is wrong
Therefore, Haywood is wrong because he collected 1,250 signatures in 15 days not 1250 signatures.
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A vertical flagpole, AB,ha a height of 42m. The point B, C and D lie on level ground, and BCD i a traight line Point C i 24 m from the bae of the flagpole. The angle of elevation of the top of the flagpole from point D i 48 degree
Points C and D are 13.82 meters apart.
What is the point in math?
In mathematics, a point (.) is used to indicate an accurate place in space and serves as its representation. It lacks all three dimensions—length, width, and height. It is hence immeasurable. Uppercase letters are typically used to name points.Given : Flag AB, with point B , C ,D lying on ground.
BD = 24 m . AB = 42 m
To find; CD
In triangle ABD, with angle of elevation from D to top of flag pole is 48 degrees.
Tanθ = perpendicular/base
tan 48° = AB/BD
1.1106 = 42/BD
BD= 42/1.1106 = 37.82 m
From the figure:
BD = BC + CD
37.82 m = 24 m + CD
CD = 37.82 m - 24 m = 13.82 m
Points C and D are 13.82 meters apart.
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An airplane
30,000 feet above the
ground begins descending at a rate of
2,000 feet per minute. Write an
equation to model the situation. Find
the altitude of the plane after 5
minutes.
An equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
In this question, an airplane 30,000 feet above the ground.
It begins descending at a rate of 2,000 feet per minute.
We need to write an equation to model the situation. Also, we need to find
the altitude of the plane after 5 minutes.
Let h be the altitude of plane after t hours.
So, we get an equation,
h = 30000 - 2000t
For t = 5 minutes,
h = 30000 - 2000(5)
h = 30000 - 10000
h = 20000 feet
Therefore, an equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
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1. If a truck tire holds 25.0 liters of air at 25.0°C, what will be the volume of air in the tire if the temperature
increases to 30.0 C
Answer:
25.4 L
Step-by-step explanation:
Charles's Law
[tex]\sf \dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}\quad \textsf{(when pressure is constant and temperature is in kelvin)}[/tex]
where:
V₁ = first volume.T₁ = first temperature.V₂ = second volume.T₂ = second temperature.Given:
V₁ = 25 LT₁ = 25.0 °CT₂ = 30.0 °CConvert Celsius to kelvin.
Kelvin = Celsius + 273.15
[tex]\implies \sf T_1= 25 + 273.15 = 298.15 \;K[/tex]
[tex]\implies \sf T_2 = 30 + 273.15 = 303.15\; K[/tex]
Substitute the given values into the formula:
[tex]\implies \sf \dfrac{25}{298.15}=\dfrac{V_2}{303.15}[/tex]
[tex]\implies \sf V_2 =303.15 \cdot \dfrac{25}{298.15}[/tex]
[tex]\implies \sf V_2 =\dfrac{7478.75}{298.15}[/tex]
[tex]\implies \sf V_2 =25.41925205...L[/tex]
Therefore, the volume of air in the tire if the temperature increases to 30.0 °C is 25.4 L (nearest tenth).
2x + 7 < -11 or -3x - 2 < 13
The value of x is in the range (-∝,-9)∪(-5,∝)
Given inequalities :
2x + 7 < -11 or -3x -2 < 13
⇒ 2x < -11 -7 or -3x < 13+2
⇒ 2x < -18 or -3x < 15
⇒ x < -9 or -x < 5
⇒ x < -9 or x > -5
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Fatima has a total of $12 to spend to make some fruit smoothies. She will use mango and strawberries. Strawberries cost $4 per pound and mango costs $2 per pound. Let x = the number of pounds of strawberries and y = the number of pounds of mango.
A) Write a linear equation in standard form that could model how many cups of fruit she can buy: __x+__=__
B) What is the greatest number of pounds of strawberries can she buy if she doesn't buy any mango? ____ pounds
C) What is the greatest number of pounds of mangoes can she buy if she doesn't buy any strawberries? ____ pounds
D) If Fatima buys 2.5 pounds of strawberries, how many pounds of mangoes can she buy? ____ pounds
Help fill in the spaces.
Answer:
B 2020 on edge
Step-by-step explanation:
Can u help me with this problem?
Answer:
No because the determinant of A is 0 .
Step-by-step explanation:
A starts the a -85 so n32 -24 = A- because 540i.7 is a so 0 so a is 0
Can anyone help me This is for math
The value of x is 1.94 units approximately.
Since the triangle is equilateral and each side is [tex]\sqrt{10}[/tex].
we know that, in equilateral triangle base is bisected by the perpendicular drawn from the opposite vertex.
So here for one small triangle by Pythagoras theorem,
[tex]x^2+(\frac{\sqrt{10}}{2})^2=(\sqrt{10})^2\\x^2+\frac{10}{4}=10\\x^2=10-\frac{10}{4}=\frac{30}{4}=\frac{15}{2}\\x=\frac{\sqrt{15}}{2}\approx1.94[/tex]
Hence the value of x is 1.94 units approximately.
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A sign company is building a sign with the dimensions shown. What is the area, in square feet, of the sign.
A.) 65ft^2
B.) 60ft^2
C.) 130ft^2
The area of the triangle will be 60ft².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Now using the Pythagoras theorem we can find out the length of the other wall
b²+p²=h²
So here h=13ft and b=5ft
p²= h²-b²
= 13²-5²
=169-25
p = √144 = 12ft
So the area of the trinagle is = 1/2*b*p
1/2(10*12)= 60ft²
Hence the area of the triangle will be 60ft².
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the sum of three numbers is 2020. the first is four times the sum of the other two. the second is seven times the third. what is the product of all three?
28 is the product of all three numbers .
What are the algebraic expressions ?An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. The multiplied value before the variable is the coefficient.
Calculation3rd = x
2 nd = 7x
1 st = 4(x + 7x ) = 32x.
x + 7x + 32x = 20
x = 1/2.
we are looking for product = x*7x*32x = 1/2 * 7 * 1/2 * 32*1/2 = 1/2 * 1/2 * 1/2 * 32 * 7 = 28.
28 is the product of all three numbers
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What is the range of this relation?
Answer:
{-4, -3, 2, 4}
Step-by-step explanation:
range are he y values so, find the y values of the points on the graph
hopes this helps please mark brainliest
Which statement correctly compares the function shown on this graph with
the function y = 3x - 6?
7
6
6
4
1
5432/1 1 2 3 4 5
A. The function shown on the graph has a smaller rate of change, but
a higher starting point.
B. The function shown on the graph has the same rate of change, but
a higher starting point.
C. The function shown on the graph has the same rate of change, but
a lower starting point.
D. The function shown on the graph has a smaller rate of change and
a lower starting point.
The graphed function's rate of change is the same, however
a lesser base line.
What is meant by mathematical expression?A mathematical expression shows the value of something by combining numbers, variables, and operators. A mathematical statement known as an equation involves setting two expressions equal to one another.
Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
In the mathematics curriculum and in mathematics in general, algebraic expressions are crucial. Students must be proficient in computations and the manipulation of algebraic expressions in order to advance and do well in mathematics. They must also be able to understand and write expressions.
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In scientific notation, 170.04 is written as?
Answer: It would be 1.7 × 10^2.
Step-by-step explanation:
18.9x{2x2.7}-4.6} - to the second power
The equivalent value to the expression 18.9 x [(2 x 2.7) - 4.6] - 2² is given by the following option:
C. 11.12.
How to obtain the equivalent value to the expression?The equivalent value to an expression is given by the solution to the expression.
The expression in this problem is given as follows:
18.9 x [(2 x 2.7) - 4.6] - 2²
The brackets take precedence, hence the first operation to be solved is of:
(2 x 2.7) - 4.6
The parenthesis take precedence relative to the subtraction, hence:
(2 x 2.7) - 4.6 = 5.4 - 4.6 = 0.8.
Then the expression is given by:
18.9 x [(2 x 2.7) - 4.6] - 2² = 18.9 x 0.8 - 2².
The square takes precedence, hence:
18.9 x 0.8 - 4.
Then the multiplication takes precedence, which means that the equivalent result is of:
18.9 x 0.8 - 4 = 15.12 - 4 = 11.12.
Given by option C.
Missing InformationThe problem is given by the image shown at the end of the answer.
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A hula hoop has a circumference of 110 centimeters.What is the diameter of the hula hoop
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 26.35°. What is the measure of ∠P?
127.3°
153.65°
26.35°
76.825°
50 POINTS
The measure of angle P as well as angle Q is 76.825. Hence, option D is correct.
What is an angle?When two lines converge at a point, they produce an angle. The word "angle" refers to the length of the "gap" between these two rays. The symbol is used to denote it.
Radians, a unit of roundness or rotation, and degrees are the 2 most common units used to measure angles. In daily life, angles are present.
As per the given data from the question,
Angle P and Q are congruent and,
Angle, ∠R = 26.35°
Suppose ∠P = a
The sum of all the three angles of a triangle is 180°.
x + x + 26.35° = 180°
2x = 180° - 26.35°
x = 76.825°.
Therefore, ∠P will be equal to 76.825°.
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It's a picture. Sorry if it isn't explained well.
Answer:
A: y=3x-1
Step-by-step explanation:
we can use slope formula to get the rate of change
y2-y1/x2-1
3-1/1-0
2/1
2 is the rate of change
so A has the rate of change of 3 so it’s the only one with the greater one
Hopes this helps please mark brainliest
A bread company makes two types of wheat bread, light whole wheat and regular
whole wheat. A loaf of light whole wheat bread requires 2 cups of flour and 1
egg. A loaf of regular whole wheat bread requires 3 cups of flour and 2 eggs. The
bakery has 90 cups of flour and 80 eggs on hand. The profit on the light bread is
$1 per loaf and on the regular bread is $1.50 per loaf. In order to maximize
profits, how many of each loaf should the bakery make?
By the equations, he should make 70 whole wheat bread that would earn a profit of $105 that is maximum he can earn with the given amount of flour and egg.
What is system of equation?simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. When there are multiple unknowns and there is sufficient data to set up equations in those unknowns, systems of equations are used to solve applications. In general, we need sufficient information to construct equations in the n unknowns.
Here,
Let x be light whole wheat and y be the regular whole wheat.
given,
A loaf of light whole wheat bread requires 2 cups of flour and 1 egg.
A loaf of regular whole wheat bread requires 3 cups of flour and 2 eggs.
The bakery has 90 cups of flour and 80 eggs on hand.
So the system of equation will be,
2x+3y=90
x+2y=80
multiply the second equation by 2,
2x+4y=160
2x+3y=90
subtract the equations,
y=70
by this,
x=-60
So by this he should make 70 whole wheat bread that will make him earn a profit of,
=70*1.5
=$105
According to the calculations, he should produce 70 loaves of whole wheat bread for a profit of $105; this is the most he can make with the supplied quantities of flour and egg.
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How to do x+5x-7(2+x)=7?
Answer:
x=-21
Step-by-step explanation:
x+5x-7(2+x)=7 so 6x-14-7x=7
-x=21 so x=-21
Which of the following statements explains how you should round 213.709?
A.
Since the digit in the hundreds place is less than 5, keep the digit in the hundredths place. Then drop the digits on the right.
B.
Since the digit in the hundredths place is less than 5, keep the digit in the tenths place. Then drop the digit in the hundredths and thousandths places.
C.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
D.
Since the digit in the hundredths place is less than 5, leave the digit in the hundredths place and drop all the numbers on the right.
Option C is correct. Since the digit in the thousands place is 5 or greater than 5.
Given that in option C:
Since the digit in the thousandth place is greater than or equal to 5, increase the digit in the hundredth place by 1. Then drop the digit in the thousandth place.
Also, 213.709 is given in the question in which we have to round off these digits.
The digit which is just after the decimal is called tenths and just after that is hundredths and just after that is called thousandths.
Seeing the value in option C is correct as it tells the value of thousandths is greater than or equal to 5 is correct as 9 is in thousandths place and is greater than 5.
Increasing the value in the hundredth which is zero to one and dropping the digit in the thousandth place is correct as it makes the value 213.71.
All the other options don't satisfy the round of the value 213.709.
Hence, 213.71 can be rounded as per the statement written in option C.
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Complete the frequency distribution table.
Score: 6, 9, 7, 8, 5, 9, 8, 7, 8, 7, 6, 9, 5, 8, 7, 6, 10, 10
According to the given frequency distribution table the values are as follows:
Frequency of 6 is 3
Frequency of 7 is 4
Frequency of 8 is 4
Frequency of 9 is 3
Frequency of 10 is 2
What is statistics?Statistics is the field concerned with collecting, organizing, analyzing, interpreting and presenting data to draw conclusions by analyzing it.
In Mathematics, statistics is the branch which is concerned with collecting, analyzing, interpreting, and presenting large amounts of numerical or quantitative data.
What does frequency mean in Statistics?It is the number of times a data or figure occurs in a set of given or collected data.
Which frequency distribution does the table have?In order to make the provided data more meaningful and understandable, it can be organized using a frequency distribution table. There are two or three columns in a frequency distribution table. All of the results are represented as individual values or as class intervals in the first column.
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what is result of evaluating the following expression? (45 / 6) % 5 group of answer choices 2.5 3 7 2
The result of the given expression is 2.5.
We are given a mathematical expression. Let the expression be denoted by the variable "E". The expression is given below.
E = (45 / 6) % 5
We need to simplify the expression and find its value. First of all, we will solve the brackets.
E = (7.5) % 5
Now we will solve the modulus operator. The modulus operator "%" gives us the remainder after the division of the two numbers. After dividing one number by another, the modulo operation yields the remainder, or signed remainder, of the division.
E = 2.5
Hence, the value of the expression is 2.5.
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Sally had 36 guests coming for Thanksgiving dinner. 1/3 of the guests brought a dessert. Each dessert could serve 6 people. How many servings of dessert were there?
Sally will get a total of 72 servings for her Thanksgiving dinner.
How to determine the quantity of servings for a Thanksgiving dinner
In this problem we knows that Sally has 36 guests for Thanksgiving dinner, one third of which, that is, 12 guests, brought a dessert and each dessert could serve 6 guests. The total number of servings (r) is equal to the number of desserts (n) and the expected quantity of guests per dessert (q), that is:
r = n · q
r = 12 · 6
r = 72
There are a total of 72 servings.
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