Determine whether the given value is from a discrete or continuous data set.When a car is randomly selected, it is found to have a gas tank that can hold 19.9 gal.
Answers
Explanation
We are asked to determine if the question is a continuous or discrete data set
The discrete data set is a data set that can be counted
Continuous data set are data that can be measured
For the given question, the answer will be option A
Related Questions
Solve the following equation: 5(n + 2) = 3(1 + 2n)
Answers
Answer: n=7
Step-by-step explanation:
First distribute the numbers to get 5n+10=3+6n
Next Subtract 6n from both sides to get -n=10=3
Finally divide both sides my -1 to get rid of the -n to get n=7
Hope this helps :)
Solve 0.005x - 0.03 = 0.01
Answers
Given the equation:
[tex]0.005x-0.03=0.01[/tex]You need to solve for "x" in order to find its value:
1. Apply the Addition Property of Equality by adding 0.03 to both sides of the equation:
[tex]\begin{gathered} 0.005x-0.03+(0.03)=0.01+(0.03) \\ 0.005x=0.04 \end{gathered}[/tex]2. Apply the Division Property of Equality by dividing both sides of the equation by 0.005:
[tex]\begin{gathered} \frac{0.005x}{0.005}=\frac{0.04}{0.005} \\ \\ x=8 \end{gathered}[/tex]Hence, the answer is:
[tex]x=8[/tex]
Determine the length of the line segment shown.
graph of line segment from negative 6 comma negative 5 to 0 comma 3
100 units
25 units
10 units
8 units
Answers
The length of the line segment will be 10 units.
What is Distance?
The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;
D = √( y₂ - y₁)² + (x₂ - x₁)²
Given that;
Two endpoints of the line segment are (6, -5) and (0, 3).
Now,
The length of the line segment is distance between two endpoints (6, -5) and (0, 3).
So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;
D = √(0 - 6)² + (3 - (-5))²
D = √36 + 64
D = √100
D = 10 units
Thus, The length of the line segment will be 10 units.
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A bag contains 2 white balls, 6 orange balls and 2 red balls. If a ball is drawn, find the probability that it is a white or red ball.
Answers
First, let's calculate the total amount of balls:
[tex]2+6+2=10[/tex]Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.
So the probability is:
[tex]p=\frac{red\text{ or }white}{total}=\frac{4}{10}=\frac{2}{5}[/tex]Correct option: A
A garden store sells two types of potted palm trees. The Mediterranean palms sell for $150 each, and the palmetto palms sell for $125 each, including tax. The store wants to sell a total of at least 15 of the plants each day and have total sales of at least $2,000. Which of these systems of inequalities can be used to determine x, the number of Mediterranean palms, and y, the number of palmetto palms, that must be sold?
Answers
The system of inequalities that can be used to determine the number of each type of plant to be sold are :
x + y ≥ 15
$150x + $125y ≥ $2000
What are the system of inequalities?The first step is to determine the inequality signs that would be used in the system of inequalities:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is the greater than or equal to sign, ≥.
Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:
number of Mediterranean palms sold + number of palmetto sold ≥ least number of plants
(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold ≥ least number of sales
x + y ≥ 15
$150x + $125y ≥ $2000
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Hi can you help explain this question. I have trouble writing statement and reasons for this question please. I get lost.
Answers
For the given figure, we will prove the triangles BGH and BDH are congruent.
So, the proof will be as follows:
Statement Reason
1) m∠F = m∠FEG = m∠FGE Given
2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ
3) FG = GE from (2), the definition of equilateral Δ
4) FG = ED Given
5) m∠ GEH = m∠DEH Given
6) EH = EH Reflexive property
7) ΔGEH ≅ Δ DEH SAS postulate
8) GH = DH from (7) CPCTC
9) m∠GHE = m∠DHE from (7) CPCTC
10) m∠GHB = m∠DHB Definition of supplementary angles
11) HB = HB Reflexive property
12) ΔBGH ≅ ΔBDH SAS postualte
13) ΔAGB is an isosceles Δ Given
14)AG = AB Definition of isosceles Δ
15) ΔBCD is an isosceles Δ Given
16) CB = CD Definition of isosceles Δ
17) CB = AG Given
18) m∠CDB = m∠CBD Definition of isosceles Δ
19) m∠ABG = m∠AGB Definition of isosceles Δ
20) m∠CDB = m∠AGB Given
21) m∠ABG = m∠CBD Transitive property
22) Δ AGB ≅ ΔCBD AAS postualte
Find discriminate 7x^2+23x+168=6x^2+3x+7
Answers
The most appropriate choice for Quadratic equation and discriminant will be given by -
Discriminant = -244
What is Quadratic equation and discriminant?
At first it is important to know about equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
If [tex]ax^2 + bx + c = 0[/tex] ([tex]a\neq0[/tex]) is a quadratic equation, discriminant is given by
[tex]D = b^2-4ac[/tex].
Here,
The given equation is
[tex]7x^2+23x+168=6x^2+3x+7[/tex]
[tex]7x^2 - 6x^2 + 23x - 3x + 168 - 7 = 0 \\x^2 + 20x +161 = 0\\[/tex]
Discriminant = [tex]20^2 - 4 \times 1 \times 161[/tex]
= [tex]400 - 644[/tex]
= -244
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help me these two questions please
Answers
The values are given as;
1. - 2a - 9 = 6a + 15, a = -3
2. 14 + 3n = 5n - 6, n = 10
What is an algebraic expression?An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;
ParenthesesAdditionsubtractionBracketDivisionMultiplicationThey are also known to be made up of terms, variables, constants, factors and coefficients.
Given the algebraic expression;
- 2a - 9 = 6a + 15
Let's take the following steps;
collect like terms
- 2a - 6a = 15 + 9
add or subtract like terms
-8a = 24
Make 'a' the subject
a = 24/-8
Find the quotient
a = -3
14 + 3n = 5n - 6
collect like terms
3n - 5n = -6 - 14
-2n = -20
Make 'n' the subject of formula
n = 10
Hence, the values are -3 and 10
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HELPPppppp PLS AOUHF
Answers
As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.
Area of triangle:
In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,
Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}
As the area is always positive.
Given,
Here we have the triangle VWX,
And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).
Now we have to find the area of the triangle.
To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).
Now, we have to apply the values on the formula, in order to get the area of the triangle,
=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|
When we expand the terms, then we get,
=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|
Further simplify the expression will gives you the following,
=> A = 1/2 |27 - 20 + 12|
=> A = 1/2 |19|
Therefore, the area of the triangle is 9.5 square units.
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Which of the following represents the polar equation r = (tan 2θ)(csc θ) as a rectangular equation?
Answers
We will have the following:
[tex]r=\tan ^2(\theta)\csc (\theta)\Rightarrow r=(\frac{\sin(\theta)}{\cos(\theta)})^2(\frac{1}{\sin(\theta)})[/tex][tex]\Rightarrow r=\frac{\sin^2(\theta)}{\sin(\theta)\cos^2(\theta)}\Rightarrow r=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]Now, we corroborate with one of the expression, in our case we will analyze y = x^2:
[tex]r\sin (\theta)=(r\cos (\theta))^2\Rightarrow r\sin (\theta)=r^2\cos ^2(\theta)\Rightarrow r=\frac{\sin (\theta)}{\cos ^2(\theta)}[/tex]So, the expression taht represents the value given is:
[tex]y=x^2[/tex]Ellen renovates the foyer of an old farmhouse. The foyer is 15 feet long and 8 feetwide. Calculate the area of the foyer.foyer60 square feet46 square feet120 square feet23 square feet240 square feet
Answers
Data
Length = 15 ft
Width = 8 ft
Area
a jar contains 22 red marbles number 1 to 22 and 52 blue marbles number 1 to 50 to a marble is drawn at random from the drawer find the probability of the given event around solution to three decimal places
Answers
We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
[tex]P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}[/tex]This gives,
[tex]\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}[/tex]Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
[tex]P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}[/tex]We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
[tex]\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}[/tex]The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
[tex]P(r\cup o)=P(r)+p(o)-p(r\cap o)[/tex]Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
[tex]\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}[/tex]This implies that,
[tex]\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}[/tex]Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
[tex]P(b\cup e)=p(b)+p(e)-p(b\cap e)[/tex]From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
[tex]\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}[/tex]p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
[tex]\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}[/tex]p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
[tex]\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}[/tex]Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
(6-6)x 6=0
(6 + 6):6=2
6? 6?6 = 4
Answers
Answer:
I don't know if you can use permutations but
(6P2-6)/6=4 ????
Rajesh obtain 93 marks in English out of 100 marks but Sita obtained 82 marks.Convert their marks in a fraction and calculate who got more marks?How many parts more marks then other.Also write their grade by asking with your teacher
Answers
Answer:
Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.
Answer 2: 11/100 more marks
Answer 3: Rajesh got an A, while Sita got a B-
Step-by-step explanation:
Put the 93 on top of 100, and do the same for 82.
Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.
which of the following graphs could be the graph of g (x)= (x+1) (x-2) (x+5)
Answers
D
1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial
g (x)= (x+1) (x-2) (x+5)
g(x) =x³+4x²-7x-10
As the coefficient is positive, then we'll have
Examining the options, we have as the roots S={-5,-1,2} So the answer is D
a survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. a sample 20 employees is selected and the data is given below. education (no. of years) length of tenure in current employment (no. of years) age (no. of years) annual income ($) 17 8 40 124,000 12 12 41 30,000 20 9 44 193,000 14 4 42 88,000 12 1 19 27,000 14 9 28 43,000 12 8 43 96,000 18 10 37 110,000 16 12 36 88,000 11 7 39 36,000 16 14 36 81,000 12 4 22 38,000 16 17 45 140,000 13 7 42 11,000 11 6 18 21,000 20 4 40 151,000 19 7 35 124,000 16 12 38 48,000 12 2 19 26,000 10 6 44 124,000 for two people a and b with the same years of education and age, suppose a's length of tenure is 2 more years than b, what would the salary difference between a and b? group of answer choices -4387.76 2193.88 2689.24 10011.92 none of the choices
Answers
The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.
What is linear regression model?The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model. The response variable is another name for the dependent variable. Explanatory or predictive variables are other names for independent variables. Models with a single predictor are known as simple linear regression. Multiple predictor models are known as multiple linear regression. Models for numerous response variables using multivariate linear regression. Finding the weights (namely, W0 and W1) that result in the best-fitting line for the input data (i.e., the X characteristics) that we have is how linear regression functions. The line with the lowest price is chosen to be the greatest fit.Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
According to the general form of a multiple linear regression model:
-143481.1924 = intercept(c) ; where regression line crosses the origin
10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3
y = predicted variable
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The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled 684 dollars. How many children how many adults were admitted?
Answers
Answer:
176 children and 105 adults.
Explanation:
Let's call x the number of children and y the number of adults.
If 281 people entered the park, we can write the following equation
x + y = 281
If they collected 684 dollars, we can write the following equation
1.5x + 4y = 684
because it cost $1.5 for children and $4 for adults.
Now, we have the following system of equations
x + y = 281
1.5x + 4y = 684
First, we need to solve the first equation for y, so
x + y = 281
x + y - x = 281 - x
y = 281 - x
Then, replace this expression on the second equation
1.5x + 4y = 684
1.5x + 4(281 - x) = 684
1.5x + 4(281) - 4(x) = 684
1.5x + 1124 - 4x = 684
-2.5x + 1124 = 684
Finally, we can solve the equation for x
-2.5x + 1124 - 1124 = 684 - 1124
-2.5x = -440
-2.5x/(-2.5) = -440/(-2.5)
x = 176
So, the value of y is equal to
y = 281 - x
y = 281 - 176
y = 105
Therefore, they admitted 176 children and 105 adults.
Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-7, -1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, -1), 6 units
Answers
The coordinates for the center of the circle is (-7,-1) and the length of the radius is 6 units , the correct option is (D) .
If the equation of the circle is x² + y² + 2fx + 2gy + c = 0
then the center is (-f,-g)
and the radius is √(f²+g²-c)
In the question ,
it is given that the
equation of the circle is x² + y² + 14x + 2y + 14 = 0
So , on comparing it with the general form of equation , we get
2f = 14
f = 7
and 2g = 2
g = 1
hence, the center is (-7,-1) .
the radius is √(7² + 1² - 14)
= √(49 + 1 - 14)
= √(50 - 14)
= √36
= 6
Therefore , The coordinates for the center of the circle is (-7,-1) and the length of the radius is 6 units .
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If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6
Answers
Since y varies directly with x then
[tex]\begin{gathered} \frac{y}{x}=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}[/tex]So,
[tex]\frac{y}{x}=\frac{-3}{-12}=\frac{3}{12}=\frac{1\cdot3}{4\cdot3}=\frac{1}{4}[/tex]Then, 1/4 is the constant of proportionality. So that,
[tex]\begin{gathered} \frac{y}{x}=\frac{1}{4} \\ \frac{-6}{x}=\frac{1}{4} \\ -\frac{6}{x}\cdot x=\frac{1}{4}\cdot x \\ -6=\frac{x}{4} \\ 4\cdot-6=\frac{x}{4}\cdot4 \\ -24=x \end{gathered}[/tex]Solve for x in terms of the other pronumerals
ax+ b/4 = x+c/3
Answers
Answer:
[tex]x=\cfrac{4c-3b}{3a-4}[/tex]==============================
Given expression[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]Solve it for x in steps below[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex] Given
[tex]3(ax+b)=4(x+c)[/tex] Cross-multiply
[tex]3ax + 3b=4x+4c[/tex] Distribute
[tex]3ax-4x=4c-3b[/tex] Collect terms with x
[tex]x(3a-4)=4c-3b[/tex] Factor out x
[tex]x=\cfrac{4c-3b}{3a-4}[/tex] Divide both sides by 3a - 4
A heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope. What are the horizontal and vertical components of the force?
Answers
The vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
What is the resolution of the forces?Resolution of forces is the process of separating a force into two or more pieces so that the combined effect on the body is the same as if it had been a single force. We can analyze motion individually in different directions thanks to the resolution of forces.
Given that a heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope.
The vertical component and the horizontal component will be calculated as:-
Vertical component = 80sin60=69.28 N
Horizontal component = 80cos60 = 40 N
Therefore, the vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
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write equations for the horizontal and vertical lines passing through the point (-7,7)
Answers
The vertical line's equation is x = -7, and the horizontal line's equation Is y = 7.
Where the given coordinate is (--7, 7).
What do the vertical and horizontal lines represent?A vertical line is a straight, up and down line in a coordinate plane that is parallel to the y-axis. The horizontal line, on the other hand, is parallel to the x-axis and goes straight, left, and right.Here,
The value of x, is -7, will never change for a vertical line. This holds true for any y value. As a result, x = -7 is the equation for a vertical line passing through this point.
Similarly, the value of y, is 7, will never change for a horizontal line. This holds true for any x value. As a result, the equation for a horizontal line passing through this point is as follows: y =7
As a result, the vertical line's equation is x = -7 and the horizontal line's equation is y = 7.
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what are the appropriate measures of central location for interval data? mean and median median and mode mean, median, and mode what are the appropriate measures of variability for interval data? range, interquartile range, variance, standard deviation, and coefficient of variation variance coefficient of variation what are the appropriate measures of relative standing for interval data? interquartile range percentiles and quartiles none
Answers
The appropriate measures of central location for interval data are Mode, median, and average
The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.
Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.
The data point in the middle of the data collection is known as the median.
It can be obtained by halving the data set, which will show where the median is located.
Simply put, mode refers to the data that occurs most frequently.
Each of these provides positional information on the data, as can be seen from the definition.
The one value that other values in the data center around is given by the mean.
Therefore, the correct options are Mode, median, and average
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Janice is cutting ribbon to decorate a present. She has 7/8 foot of ribbon. She needs to make pieces that are 3/8 foot each. How many 3/8-foot pieces will she get from the 7/8-foot ribbon?
Enter the correct answer in the box.
Answers
Based on the length of the ribbon, and the length of the pieces Janice needs to make, the number of 3/8 foot pieces she can make would be
How to find the number of pieces?To find the number of pieces that Janice can get from the 7/8 foot ribbon, you need to divide this length by the length of each piece of ribbon.
The length of each of these pieces is 3/8 so the number of pieces of ribbon that Janice can get from the 7/8 foot ribbon is:
= 7 / 8 ÷ 3 / 8
= 7 / 8 x 8 / 3
= 56 / 24
= 2.33 ribbons
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Janice can make 2 pieces of ribbon from 7/8 feet of ribbon each measuring 3/8 feet.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Janice is cutting the ribbon to decorate a present. She has 7/8 feet of ribbon.
She needs to make pieces that are 3/8 feet each.
To obtain the no. of pieces we have to divide the total length of the ribbon by the length of each piece.
∴ (7/8)/(3/8).
= (7/8)×(8/3).
= 7/3 pieces.
But he can only make 2 pieces as pieces must be in integers.
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A graph of a linear function has a slope of -1/3 and contains the point (0, 2). Which of these represents the equation of this function?
Answers
slope intercept equation is represented below
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 2=-\frac{1}{3}(0)+b \\ b=2 \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]a total of tickets were sold for the school play. they were either adult tickets or student tickets. there were 53 more student tickets sold than adult tickets. how many adult tickets were sold?
Answers
Total 250 adult tickets are sold.
Let a = number of adult tickets sold
Let s = number of student tickets sold
a + s = 553
s = a + 53
From above equations;
a + a + 53 = 553
2a = 553 - 53
2a = 500
a = 250
Total 250 adult tickets are sold.
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Please help me will give brainly Thanks
Answers
The required equation of line would be 2y = 5x - 8 which is shown in the given graph.
What is the slope of the line?The slope of a line is defined as the angle of the line.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, -4).
The value of the x-coordinate is 2 when y-coordinate is 1.
Here the line passes through the points (0, -4) and (2, 1).
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = -4
x₂ = 2, y₂ = 1
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 1 = (1 - (-4))/(2 - 0 )[x -2]
⇒ y - 1 = 5/2[x -2]
⇒ 2y - 2 = 5[x -2]
⇒ 2y = 5x - 10 + 2
⇒ 2y = 5x - 8
Therefore, the required equation of line would be 2y = 5x - 8 which is shown in the given graph.
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Every computer that a business owner purchases will lose most of its value after 5 years of use. The owner plans to purchase a computer for $2,100 and replace it after 4 years.Part BMethod 2 of determining the computer's value is to reduce its value by 30% after each year of use.Which function, g(n), represents the value of the computer after years of use for Method 2?g(n) = 0.3n(2,100)g(n) = 0.7 (2.100)g(n) = 2.100(0.3)^ng(n) = 2.100(0.7)^n
Answers
Answer:
D. g(n)=2100(0.7)^nD. g(n)=2100(0.7)^
Explanation:
• The purchase price, i.e. the initial value of the computer = $2100.
,• The rate at which its value reduces = 30%.
To determine the computer's value after n years of use, we use the depreciation formula below:
[tex]A(n)=P(1-r)^n[/tex]In this case:
• The Principal, P = $2100
,• The rate, r = 30%
Substitute these values into the formula.
[tex]\begin{gathered} g(n)=2100(1-30\%)^n \\ =2100(1-\frac{30}{100})^n \\ =2100(1-0.3)^n \\ \implies g(n)=2100(0.7)^n_{} \end{gathered}[/tex]The function g(n) that represents the value of the computer after n years of use is Option D.
If the first term of gp is 1 and 4th is 27 find the ratio term and the 9th term
Answers
The ratio term of given geometric progression is 3 and the 9th term of the GP is 6561.
What is Geometric Progression?
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54,_ _ _ _ has a common ratio of 3.
Given in question,
first term of the GP is 1,
4th term of the GP is 27,
[tex]4^{th} term = ar^3[/tex]
[tex]ar^3 = 27[/tex]
Therefore, the ratio term of geometric progression, r = 3
We know that, [tex]a_n = ar^{n-1}[/tex]
[tex]a_9 = ar^8[/tex]
[tex]a_9 = 3^8[/tex]
a9 = 6561
Therefore, the 9th term of given geometric progression is 6561.
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if 6x-1=29, what is the value of x2+x
Answers
We are given
[tex]6x-1=29[/tex]Therefore the value of x can be gotten by simplifying the above equation
[tex]\begin{gathered} 6x=29+1 \\ 6x=30 \\ x=\frac{30}{6} \\ x=5 \end{gathered}[/tex]Given that x is 5, we can proceed to find the value of the expression.
[tex]\begin{gathered} x^2+x \\ \Rightarrow(5)^2+5 \\ \Rightarrow25+5 \\ \Rightarrow30 \end{gathered}[/tex]This implies that
[tex]x^2+2\Rightarrow30[/tex]