In linear equation, The partial sum S₄ based on the information will be 66.67.
What in mathematics is a linear equation?
An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.
An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value.
First, let's write out the first few terms of the sequence:
a₁ = 5(3)¹⁻² = 5/3
a₂ = 5(3)²⁻² = 5
a₃ = 5(3)³⁻² = 15
a₄ = 5(3)⁴⁻² = 45
So, the partial sum S₄ can be calculated as:
S4 = a¹ + a² + a³ + a⁴
= 5/3 + 5 + 15 + 45
= 66.67
Therefore, the partial sum S₄ is 66.67
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
3x + y=5
6x -2y=10 Is it consistent/non consistent and need solution
once i see how to do one ill understand how to do others. thank you
Answer: These are non- consistent and can be solved. The signs of the y terms are the opposite.
Step-by-step explanation: If the signs are the same, and all the terms of one equation are multiples of the other, they are identies, with infinite solutions. We can solve this system by multiplying the first equation by 2, adding the equations to cancel the y terms, and solve for x.
2(3x+y=5) becomes
6x +2y= 10 Add it to the other equation
6x -2y= 10 We are left with
12x = 20 Solve for x
x = 5/3 Substitute for x and solve for y.
3(5/3) + y = 5
5 + y = 5. Subtract 5 from both sides.
y = 0
The solution to this system is (5/3 , 0)
Select the correct answer.
You’re trying to determine what the temperature is outside. The thermometer says it’s 24°C. You convert this temperature to 100°F. If a mistake was made during the conversion process, how did it happen?
A.
You converted Fahrenheit to Celsius instead of Celsius to Fahrenheit.
B.
You added 32 before multiplying by instead of multiplying by and then adding 32.
C.
You multiplied by instead of multiplying by .
D.
No mistake was made.
Answer:
B. You added 32 before multiplying by instead of multiplying by and then adding 32.
PLEASE HELP WILL MARK BRAINLIEST ANSWER!!
Step-by-step explanation:
translation = changing the origin of the graph
moving the graph left right up or down
first image is the normal graph y=x
second image is the graph translated up by 4 to y=x+4
dilation = change in how narrow or spread out the graph gets
compare first image to third
third image is y=3x
see how it become a steeper slope
rotation = moving around the centre point
i think u know that
so with the change to y and x being 17x and 17y
the answer is
please help ive been stuck on this question.
The value of the expression 8 / m - 11 / 3m is 13 / 3m
How to simplify an expression?8 / m - 11 / 3m
Therefore,
8 / m - 11 / 3m
The factor of the denominator is 3m
Therefore,
8 / m - 11 / 3m = 3(8) - 11/ 3m
3(8) - 11/ 3m = 24 - 11 / 3m
24 - 11 / 3m = 13 / 3m
learn more on fraction here: https://brainly.com/question/24161414
#SPJ1
The sum of a number and 3 is less than or equal to 8
Answer:
m ≤ 5
Step-by-step explanation:
I will begin by assuming m to be the number.
Then, the sum of m and 3 is: m + 3.
The symbol for "less than or equal to" is ≤.
So we form an inequality, like this :
m + 3 ≤ 8
To find m subtract 3 on each side:
m ≤ 5
Therefore, m ≤ 5.
Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4
Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m
The correct matches are: 4 in. → 10.2 cm , 7 kg → 15.4 lb
6 gal → 22.7 L and 65 ft → 19.8 m.
What are conversions?Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.
For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.
Here are the conversions:
1 inch = 2.54 cm (approx.)
1 kg = 2.205 lb (approx.)
1 gal = 3.785 L (approx.)
1 ft = 0.3048 m (approx.)
Using these conversions, we can find the equivalent measures:
4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm
7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb
6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L
65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m
To know more about equivalent measures visit:
https://brainly.com/question/29156458
#SPJ1
The product of a number and -3 increased by 8 is no less than 35
The required inequality, of a product of a number and -3 increased by 8 is no less than 35 is -3x + 8 ≥ 35.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
Let the number be x,
According to the question,
The product of a number and -3 increased by 8 is no less than 35.
So,
-3x + 8 ≥ 35
Thus, the required inequality, of a product of a number, and -3 increased by 8 is no less than 35 is -3x + 8 ≥ 35.
Learn more about inequality here:
brainly.com/question/14098842
#SPJ2
Graph the system of equations on your graph paper to answer the question.
{y=x−4y=−x+6
What is the solution for this system of equations?
Answer: (5 , 1)
Step-by-Step explanation:
hihi your problem is a system of question y = x-4 and y = -x+6 okay so graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!
y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right
y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left
once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!
the solution is x = 5 and y = 1 which is also (5 , 1)
hopefully this was helpful !
Find the Slope And Y Intercept
PLEASE HELP
Answer:
The y-intercept is -2
the slope is 2.5/1 or 2.5
Explantation:
The slope formula is m=y2-y1/x2-x1
we can use the points (1,0.5) and (0,-2) (i got these points from the graph)
m=-2-0.5/0-1
m=2.5 or 2.5/1
One of the assumptions underlying the theory of control charting is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is 0.07. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly
Answer:
P(at least 1 wrong in 10) =0.5160
Step-by-step explanation:
Let A be the event that there is a problem in the proces. Then the probability of problem with the process is P ( A) = 0.07
Let B be the event that the process is without the problem. Then the probability of without problem is P ( B) = 0.93
Now we want to find the 10 successive points of event B. Since the events are independent we can find this as
P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)
or
P(B)^ 10= .93^10=0.48398
As we have to calculate at least 1 in 10 then we will subtract it from 1.
P(at least 1 wrong in 10) = = 1 - .93^10 =1- 0.48398=0.5160
Write a quadratic function in standard form, with a leading coefficient of 1, given x-intercepts 7 and 10. Use "y" as the dependent variable
and "x" as the independent variable.
Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
Learn more about quadratic function here
brainly.com/question/27958964
#SPJ1
plz quick solve for f
Answer: f = 100
Step 1.
We'll need to expand 3(f - 91) by multiplying a term and an expression. The following product distributive property will be used: A(B + C) = AB + AC.
In the example, the expression will consist of 2 terms.
First term: 3 and f.
Second term: 3 and -91
Rewrite 3(f - 91) like this.
3f - 3 × 91
Step 2.
Multiply 3 by 91.
3 × 91 = 273
Hence, the answer is 100.
Find the unknown coordinate so the line through the
points has the given slope
Answer:
#1 (0,-4)
#2 (5,0)
#3 (3,1)
Step-by-step explanation:
#1. (-3, 2) (0, y) slope = -2
slope = rise/run therefore slope = -2/1 or down 2 and over 1
so from -3 to 0 you are going over 3 units (or 3 times) Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6 so 2-6 = -4
so y intercept (b) = -4 0r (0,-4)
#2 (-7,-4) (x,0) slope (m) = 1/3 -7+12=5 x=5
#3 (4,-3) (x, 1) slope (m) = -4 (4/-1) Moving one unit in slope means
-3=4=1 for Y and 4-1=3 for X therefore the point is (3, 1)
A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Evelyn, Amelia and Ava start with 17, 16 and 15 tokens, respectively. How many rounds will there be in the game?
The number of rounds that can be played is given by the product of three
and the least number of tokens a player has at the start.
Response;45 roundsReasons for arriving at the above value;A round is when the player with the most tokens gives one token to each of the other players, and one placed in the discard pile, we have;
First three round17 - 3 = 14
16 + 1 = 17
15 + 1 = 16
17 - 3 = 14
14 + 1 = 15
16 + 1 = 17
17 - 3 = 14
14 + 1 = 15
15 + 1 = 16
The above values follow a number series such that we have;
Fourteenth three rounds4 - 3 = 1
2 + 1 = 3
3 + 1 = 4
4 - 3 = 1
1 + 1 = 2
3 + 1 = 4
4 - 3 = 1
2 + 1 = 3
1 + 1 = 2
Fifteenth three rounds3 - 3 = 0
1 + 1 = 2
2 + 1 = 3
3 - 3 = 0
0 + 1 = 1
2 + 1 = 3
3 - 3 = 0
0 + 1 = 1
1 + 1 = 2
Therefore, after the fifteenth three rounds, which is 15 × 3 = 45 rounds Ava runs out of token, ending the game.
Learn more about number series here:
https://brainly.com/question/4163549
At noodles and Company Restaurant, the probability that a customer will order a non-alcoholic beverage is .34. Find the probability that in a sample of 9 customers none of the 9 will order a non alcoholic beverage
Answer:
0.0238
Step-by-step explanation:
look at the picture for steps
I’m thinking -15+1/8x. Let me know if I’m wrong.
Answer:
Your incorrect
Step-by-step explanation:
How can you use the order of operations to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x + 5) - x = 42
Answer:
Step-by-step explanation:
The distributive property tells us that the term in the inside the parentheses will by multiply by the term on the outside of the parentheses first. Example:
3(x + 5) means that (x + 5) + (x + 5) + (x + 5) = 3x + 15
So 7(x + 5) - x = 42 ; without the distributive property you would have to write what is inside the parentheses seven times then complete solving the problem
7( x + 5) -x = 42
(x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) - x = 42 by definition
(x + x + x + x + x + x + x) + (5 + 5 + 5 + 5 + 5 + 5 +5) -x = 42 (x + 5) Associative and Commutative
7x + 35 - x = 42 Addition
6x + 35 = 42 Associative and Commutative
6x = 7 Subtraction
x =7/6 Division
Now with the Distributive property
7(x + 5) - x = 42
7·x + 7 · 5 - x = 42 Distributive property
7x + 35 - x = 42 Multiplication
6x + 35 = 42 Associative and Commutative
6x = 7 Subtraction
x = 7/6 Division
I need help I don't really understand this
Answer:
Should be -5/3
Step-by-step explanation:
at 1,1 the line meets and go down 5 spaces and the 3 to the right and it meets again(rise over run)
Assume that T is a linear transformation. Find the standard matrix of T. T: R2→R2 first reflects points through the line x2-x1 and then reflects points through the line x2-x1 A= (Type an integer or simplified fraction for each matrix element)
the standard matrix of T. T: R2→R2 is [ 0 1 ]
[ 1 0]
We must locate the pictures of the standard basis vectors of R2 under T and translate those images into columns of a 2x2 matrix in order to get the standard matrix of T.
Let's start by thinking about the reflection along the line x2 - x1. The point (x1, x2) is mapped to the point via this reflection (x2, x1).
We apply T to the first standard basis vector, e1 = (1,0), to determine its image:
T(e1) = (0,1) (0,1)
We also use T: to determine the image of the second standard basis vector, e2 = (0,1).
T(e2) = (1,0) (1,0)
Hence, (0,1) and (1,0) are the images of the standard basis vectors, These photos can now be expressed as columns in a matrix:
[0 1]
[1 0]
This is the standard matrix of T.
learn more about standard matrix
brainly.com/question/17585333
#SPJ4
if 7 men and 5 womean have applied for job and 3 applicants are randomly selected from the probability that 2 are men
The probability that 2 men are selected is 49/144
Probability is the likelihood or chance that an event will occur.
If 7 men and 5 women have applied for job, the total number of people that applied will be 12 people
Pr(2 men are selected) = 7/12 * 7/12Pr(2 men are selected) = 49/144Hence the probability that 2 men are selected is 49/144
Learn more on probabaility here:https://brainly.com/question/24756209
A student multiplies (4+5i) (3-2i) incorrectly and obtains 12-10i. What is the student's mistake? Select the two correct answers. A. They multiplied the second number by the real part of the first number. B. In the multiplication of the imaginary parts, the student forgot to square the i. C. The student has only multiplied the real parts and the imaginary parts. D. The student has added the real parts and multiplied the imaginary parts. E. The student has multiplied the second number by the imaginary part of the first number.
Answer:
B. In the multiplication of the imaginary parts, the student forgot to square the i. C. The student has only multiplied the real parts and the imaginary parts.Step-by-step explanation:
Before we figure out the student mistake, let us find the product of the complex numbers ourselves first.
(4+5i) (3-2i)
open the parenthesis
= 4(3)-4(2i)+3(5i)+5i(-2i)
= 12-8i+15i-10i²
Note that in complex number, i² = -1, hence the expression will become;
= 12-8i+15i-10(-1)
= 12-8i+15i+10
collect like terms by separating the real from imaginary part
= 12+10-8i+15i
= 22+7i
From the students answer i.e 12-10i, it can be concluded that;
In the multiplication of the imaginary parts, the student forgot to square the i and the student has only multiplied the real parts and the imaginary parts 4 and 3 to get 12
A spinner is divided into three sections: red, blue, and green. The red section is 2/5 of the area of the spinner. The blue section is 1/2 of the area of the spinner. Give the probability for each outcome. Express your answers as fractions.
Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).
Meaning of probability :
Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.
The analysis of events governed by probability is called statistics.
According to the given information :
Red section = \(\frac{2}{5}\)
multiply numerator and denominator by \(2\) we get
Red section = \(\frac{4}{10}\)
Blue section = \(\frac{1}{2}\)
multiply numerator and denominator by \(5\) we get
Blue section = \(\frac{5}{10}\)
Green section = \(1\)- Red section - Blue section
Green section =\(1-\frac{4}{10} -\frac{5}{10}\)
Green section = \(\frac{1}{10}\)
Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).
Learn more about Probability
https://brainly.com/question/11234923
#SPJ1
make e the subject
e-5=2f
Answer:
e-5=2f
take '-5' to the other side where '2f' is
e=2f+5
Which of the following circles has an area greater than 400 square meters and less than 600 square meters? Use 3.14 for π. Select all that apply.
A.Radius: 8 meters
B.Radius: 12 meters
C.Radius: 14 meters
D.Diameter: 12 meters
E.Diameter: 22 meters
F.Diameter: 26 meters
Answer:d
Step-by-step explanation:fkjfkjfkjfkjfkjf
Keeping the properties of exponents in mind, to what power must you raise the expression 7; to get 7 as the
result?
Write 11/80 as decimal Round to four decimal places as needed
The fraction is given
\(\frac{11}{80}\)ExplanationTo determine the decimal form .
\(\frac{11}{80}=0.1375\)AnswerHence the answer in decimal form is 0.1375.
Elyas is on holiday in Greece.
He wants to buy a pair of sunglasses for €90
The exchange rate is €1 = £0.875
Elyas says, "The sunglasses cost less than £70"
Using a suitable approximation, show that Elyas is wrong.
Answer:
To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.
To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.
Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.
We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds
Step-by-step explanation:
Evaluate the expression $-8x+5-2x-4+5x$ when $x=2$ before and after simplifying.
Answer:
-9
Step-by-step explanation:
First combine like terms.
-8x+5-2x-4+5x -8x-2x+5x=-5x
-8x+5-2x-4+5x 5-4=1
Now plug in 2 for x
-5x+1
↓
-5(2)+1= -10+1=-9
If this is wrong, I'm sorry for the misguidance.
(7+3)^5 please help and can i get the explaintion
Answer:
100000
Step-by-step explanation:
Brainliest plz
Solve the inequality below.
2x < 12
To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:
2x < 12
x < 6
Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:
<=======()------6-------------->
The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.
In summary, the solution to the inequality 2x < 12 is x < 6.
I'm 15 BTW