The probability of committing a Type II error when the mean difference is 55 is 1.
The concept of power in statistical testing is important for understanding the reliability of results. When the power of a statistical test is zero, it means that the test is unable to detect the difference between the means of two groups, even if there is a real difference.
In the given scenario, the mean is 52, the sample size is 25, and the standard deviation is 2.
This means that if the true mean difference between two groups is 55, there is a 100% chance that the test will not detect it. The probability of committing a Type II error is directly related to the power of a statistical test.
The higher the probability of committing a Type II error, the lower the power of the test.
Therefore, it is important to consider the power of a statistical test when interpreting results.
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Your brother Kyle sold half of his comic books and then bought sixteen new ones. Now, he has 36 comic books. Which equation represents the number of comic books Kyle has in his collection?
Answer: 40 divided by 2 (half) = 20+16 = 36
Step-by-step explanation:
Compare the investment below to an investment of the same principal at the same rate compounded annually. principal: $7,000, annual interest: 9%, interest periods:4 , number of years:12 Question content area bottom Part 1 After 12 years, the investment compounded periodically will be worth $ enter your response here more than the investment compounded annually.
[tex]~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}[/tex]
A skating rink charges a rate of $4 plus fee to fee to rent each pair of skates.A faimly rentss 2 pairs of skates and pays a total of $20
The price of each pair of skates is given as follows:
$8.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the cost of a pair of skates.b is the intercept, representing the flat fee.A skating rink charges a rate of $4, hence the intercept b is given as follows:
b = 4.
Hence:
y = mx + 4.
A family rents 2 pairs of skates and pays a total of $20, meaning that when x = 2, y = 20, then the slope m, representing the cost of each pair, is obtained as follows:
20 = 2m + 4
2m = 16
m = 16/2
m = 8.
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what is the maximun of number of people who can stand in each side of the boat
The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.
The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.
Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:
F_B = m_p * g
Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.
To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).
m_b = V * ρ
Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).
m_p = n * m
Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.
n = (F_B) / (m * g)
Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.
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The table represents an exponential function.
x y
1 6
2 4
3 8/3
4 16/9
What is the multiplicative rate of change of the function?
• 1/3
• 2/3
•2
•9
The required multiplicative rate in the given function is 3 / 4.
Option B is correct.
What is an exponential function?The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
From the table of the exponential functions,
The multiplicative factor is given as,
K = y₂/y₁
K = [9 / 8] / [3/2]
K = 3 / 4
Thus, the required multiplicative rate in the given function is 3 / 4. Option B is correct.
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Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(-7,-5), B(-2, 0) ; 1 to 4
Answer:
P = (-6, 4)
Step-by-step explanation:
A = (x1,y1) = (-7,5)
B = (x2,y2) = (-2,0)
m:n = 1:4
P = (x, y)
= ( mx2 + nx1/ m + n , my2 + ny1/ m + n )
= ( 1(-2) + 4(-7)/1+4 , 1(0) + 4(5)/ 1+4 )
= ( -2 - 28 / 5 , 20 / 5 )
= ( - 30 / 5 , 4 )
= ( -6 , 4)
P = (-6, 4)
What is 814 338/698 rounded to the nearest whole number?
The nearest whole number is 814. The value of 338/698 < 0.5
What is whole number?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.
Given mixed number is [tex]814\frac{338}{698}[/tex].
The fraction part of the mixed number is 338/698.
2 times of 338 is 676 < 698.
Thus the value of 338/698< 0.5.
It is necessary to look at the first digit following the decimal point in order to round a number to the nearest whole number. We don't need to do anything if this digit is less than 5 (1, 2, 3, 4), but we must round up if it is 5 or higher (5, 6, 7, 8, 9).
This means the decimal value of the given number is less than 814.5.
Since the digit in the tenth place is less than 5, thus the nearest whole number of the given mixed number is 814.
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Please help. The picture shows the question.
(a) Kenton is running 2.5 miles per day.
(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
The table describes Kenton’s running progress during his training.
In the table, d represents the day number, and t represents the total number of miles he ran since he began training.
From the table,
In a day Kenton ran = 5/2 = 2.5 miles.
2.5 is a common difference.
(a) Kenton is running 2.5 miles per day.
(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d
Therefore, the equation is t = 2.5d
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What are the Types of Triangles in Geometry?
Answer:
isosceles, equilateral, scalene, obtuse, acute, and right triangles.
Step-by-step explanation:
isosceles, equilateral, scalene, obtuse, acute, and right triangles.
Triangles can be classified into six different shapes: right, obtuse, acute, equilateral, scalene, and isosceles. A triangle is said to be isosceles if two of its sides are congruent and one of its sides and angle is distinct.
What are the six types of triangles?A triangle is said to be isosceles if two of its sides are congruent and one of its sides and angle is distinct.With three congruent sides and three congruent angles, a triangle is said to be equilateral.Triangles without congruent sides or angles are referred to as scalene triangles.Triangles with obtuse angles are referred to as obtuse triangles.Having three acute angles defines a triangle as being acute.Having one right angle defines a triangle as being right.Scalene triangles are those with three different side lengths and three different angle measurements.In a scalene triangle, neither the sides nor the angles are equal. An angle that is exactly correct (90°) defines a triangle as being right. Having a triangle that is scalene and right means that one of its special angles is 90 degrees.To Learn more About Triangles Refer To:
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Write down the percentage multiplier to find 26% of an amount
pls do simple steps/working out :)
Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.
In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.
26% = [tex]\frac{26}{100}[/tex] = 0.26
Hence, 0.26 is the multiplier.
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can two intersecting circles have two common tangents?
Answer:
Yes.
Step-by-step explanation:
They will be either side of the 2 circles.
PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
Identify the coordinates of a point (-7,-6) under the rotation of 90° clockwise around the origin.
The new coordinates of the point (-7, -6) are (-6, 7).
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
(x, y) = (-7, -6)
The rule is given as
A rotation of 90° clockwise around the origin.
Mathematically, this can be represented as
(x, y) = (y, -x)
So, we have
Image = (-6, 7)
Hence, the image is (-6, 7)
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What is the image of ( − 8 , − 12 ) after a dilation by a scale factor of 1 4 centered at the origin?
The image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.
What is dilation?An object can grow in size while preserving its shape through a process called dilation. The object's size can go up or down depending on the scale factor. The scale factor is defined as the ratio of the new image's size to the old image's size. decision-making. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.Given that the image of (8,12) after dilation by a scale factor of 1/4 centered at the origin.
The image of the dilated point will be:-
x : - 8 ⇒ 8 / 4 = 2
y : - 12 ⇒ 12 / 4 = 3
Therefore, the image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.
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Write a recurive rule for the equence. Then write the next two term of the equence. For 1,3,4,7,11
The recursive rule for the given sequence 1, 3, 4, 7, 11 ... is aₙ₊₁ = aₙ + aₙ₋₁.
The next two term of the sequence 1, 3, 4, 7, 11, is equal to 18 , 29.
Recursive rule for the sequence 1, 3, 4, 7, 11, ...... is represented by :
Let us consider before 1 it is 0.
Next term is sum of previous two terms :
0 + 1 = 1
1 + 3 = 4
3 + 4 = 7
4 + 7 = 11
Recursive rule for the given sequence is equal to :
3rd = 2nd + 1st term
4th term = 3rd term + 2nd term .....
aₙ₊₁ = aₙ + aₙ₋₁
Next two terms for the above sequence is equal to:
7 + 11 = 18
11 + 18 = 29
Therefore, the recursive formula to represents the sequence 1, 3, 4, 7, 11 is equal to aₙ₊₁ = aₙ + aₙ₋₁ and next two terms are 18, and 29.
The above question is incomplete, the complete question is:
Write a recursive rule for the sequence. Then write the next two term of the sequence. For 1,3,4,7,11
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What is the solution of second order differential equation?
The second order differential equation:-
[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].
Now, According to the question:
A differential equation is an equation that consists of a function and its derivative. A differential equation that consists of a function and its second-order derivative is called a second order differential equation. Mathematically, it is written as y'' + p(x)y' + q(x)y = f(x), which is a non-homogeneous second order differential equation if f(x) is not equal to the zero function and p(x), q(x) are functions of x. It can also be written as F(x, y, y', y'') = 0. Further, let us explore the definitions of the different types of the second order differential equation.
Hence, The second order differential equation.
[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].
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A central angle measuring 90° Intercepts an arc in a circle whose radlus is 8.
What Is length of the arc of the circle formed by this central angle? Round the length of the arc to the nearest hundredth
of unit.
The length of the arc of the circle formed by the central angle of 90° is approximately 12.57 units
How to determine the length of the arc?The length of an arc in a circle can be found using the formula:
Arc Length = (Central Angle / 360) * (2 * π * Radius)
Given a central angle of 90° and a radius of 8, the arc length can be found as follows:
Arc Length = (90 / 360) * (2 * π * 8)
Arc Length = (1/4) * (16π)
Arc Length = 4π
So, we have
Arc length = 12.57
So, the length of the arc of the circle is 12.57 (rounded to two decimal places).
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an experiment requires a measurement before and after the presentation of a stimulus to 20 subjects. in the analysis of the data collected from this experiment, how many degrees of freedom are there in the test?
In a repeated measures design with 20 subjects, each subjected to 2 measurements (before and after stimulus presentation), the degrees of freedom in the test would be 19.
DF in Repeated Measures ExperimentThe problem is about an experiment in which a measurement is taken before and after a stimulus is presented to 20 subjects. The aim is to determine the number of degrees of freedom in the data analysis of the experiment.
Degrees of freedom (df) are a measure of the amount of variability in a set of data that is free to vary in the calculation of a statistical test. In a repeated measures design, the degrees of freedom are calculated as the number of subjects minus 1. In this case, with 20 subjects, the degrees of freedom would be 19.
The concept of degrees of freedom is used in both mathematics and physics, but the specific context of a t-test for dependent samples is commonly used in statistical analysis, particularly in the social sciences, psychology, and education research. So, it is more related to mathematics.
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a town is designing a rectangular park that will be 600 feet wide by 1000 feet long. on a scale drawing, the dimensions of the park are 12 inches wide by 20 inches long. a rectangular area of the park for swing sets is 0.5 inch wide by 2 inches long on the scale drawing. what is the actual length of the swing set area of the park?
The actual length of the swing set area is 0.5 * 20 feet = 10 feet.
Since the scale drawing represents the actual dimensions of the park,
We can use the ratio of the scale drawing dimensions to the actual dimensions to find the actual length of the swing set area.
Let's call the actual length of the swing set area L.
Then, on the scale drawing, the length of the swing set area is 0.5 inches.
The ratio of the actual length to the scale drawing length is 20 inches : L feet.
We can set up an equation to find L:
L * (20 inches / L feet) = 0.5 inches
Solving for L, we find:
L = (0.5 inches * L feet) / (20 inches / L feet)
= (0.5 * L feet) / (20 / L feet)
= (0.5 * L feet) / (20 / L feet)
= 0.5 * (L feet / 12 inches/foot)
= 0.5 * 20 feet
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Answer:
The answer is 100 feet. I took the quiz and it was 100 feet.
Step-by-step explanation:
HELP ASAP (40 points if correct)
How many solutions does the system of linear equations represented in the graph have?
A. One solution at (−2, 0)
B. One solution at (0, −2)
C. Infinitely many solutions
D. No solution
The equation has one solution at (0, -2) for the system of linear equations represented in the graph.
What is the Solution to a Linear Equation?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Given the graph,
and the line passes from (0, -2) and (4, 0)
since the line passes from (0, -2) and (4, 0),
so one of the solutions is at (0, -2),
and another solution is at (4, 0).
according to the options equation has (0, -2) as one of the solutions.
Hence option B is correct.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer: x =13
Step-by-step explanation:
subtract 7 from both sides
7-7= 0
-7+20=13
x=13
Answer:
[tex] \sf \: x = 13[/tex]
Step-by-step explanation:
Given equation,
→ x + 7 = 20
Now the value of x will be,
→ x + 7 = 20
→ x = 20 - 7
→ [ x = 13 ]
Hence, the value of x is 13.
Find the value of h in the graph
Thanks
Answer:
See below
Step-by-step explanation:
The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)
so 4^x is now 4^(x+1)
then 4^(x+1) = 4^(x-h)
would mean h = - 1
3. What is the probability an individual student likes between 5.5 and 8.5 songs from Eminem?
This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.
Explain about the probability?The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.
There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.
How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
To find:
P(X < 5.5)
Z = -1.0
However;
P(X< 5.5) = P(Z < -1.0)
P(X< 5.5) = 0.1587
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I really need help! Find P(green and odd).
The Probability P(Green and odd) for given Sample Space is 1/5.
What is probability?The likelihood of an event is expressed by probability. A random event's occurrence is the subject of this mathematical field of study. From zero to one, the value is available. In mathematics, probability is used to forecast the likelihood that events will take place.
The likelihood of something happening is referred to as a probability. The probability distribution also makes use of this basic concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event occurring.
Event's likelihood of occurring P(E) = The number of positive outcomes divided by the total number of outcomes
Now,
Total number of outcomes=10
No. of Box that are green and marked odd=2
Hence, the probability
P(Green and odd)=2/10=1/5
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Why in distributed system relational algebra is enough?
relational algebra is a sufficient tool for manipulating data in a distributed system because it provides a uniform and consistent way to access and manipulate data.
Regardless of where it is stored in the system, and because it is a declarative language that abstracts away implementation details, making it easier to maintain and evolve the system.
Relational algebra is a powerful mathematical tool used to manipulate data in a relational database. It provides a way to perform operations on data in a structured and organized manner.
In a distributed system, where multiple nodes store and process data, relational algebra is still sufficient because it provides a uniform and consistent way to access and manipulate data across the entire system.
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!30 POINTS!
Solve the system of equations by using the elimination method
-3x + 14y = -28
-2x + 7y= -14
Please show your work!
Answer: -6x + 21y = -42Now we can solve for y:21y = -42 + 42
y = 0Substitute y = 0 back into one of the original equations:-3x + 14(0) = -28
-3x = -28
x = 9/1So the solution to the system of equations is (x, y) = (9, 0).
Step-by-step explanation:
Adrian is going to an amusement park. The price of admission into the park is $35, and once he is inside the park, he will have to pay $3 for every ride he rides on. How much money would Adrian have to pay in total if he goes on 12 rides? How much would he have to pay if he goes on r rides?
The amount of money that Adrian will pay if he goes on the given amount of ride would be =$71
How to calculate the cost per ride?An amusement park is defined as the park where different recreational activities are being carried out.
The price of admission in the park = $35
The amount he pays for each ride at the amusement park= $3.
The amount for 12 rides= 3×12 = $36
Therefore the total amount of money that Adrian will pay if he goes to the amusement park for 12 rides would be = $36 + $35 =$71
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Exponential growth: what it is, why it matters, and how to spot it
An expansion within a population that happens at the same pace across time is represented by the function of exponential growth.
What is exponential growth?It is reasonable to suppose that data grows exponentially as populations double or triple in size. Exponentially decaying data is the reverse of exponentially growing data. When your data are visualized on a graph, the pattern an exponential function displays appears as an ascending curve. f(x) = a(1 + r)x is another formula you may use to compute exponential growth.F(x) stands for the function and is a term.The starting value of your data is indicated by the a variable.Growth rate is indicated by the variable r.Period of time is represented by the x variable.Examples :
The analyst can determine the possible returns after three, five, and ten years if the customer deposits an initial starting capital of $5,000 into their compound savings account. The analyst decides: Using a 5% interest rate
Upon completion of three years: ($5,000)(1 + 0.05)(3) = $5,788
Upon completion of five years: ($5,000)(1 + 0.05)(5) = $6,381
A decade later, ($5,000)(1 + 0.05)(10) = $8,144
The Complete Question is exponential growth.
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There i only one carton of pear. Jo want to buy 3/4 of it, and Max to buy 1/3 of it. Will there be enough?
The only one carton of pear is not enough because the sum of both Jo and Max requirement is max than the one.
There is only one carton of pear.
Jo want to buy 3/4 of it, and Max to buy 1/3 of it.
To check whether one carton of pear is enough for both Jo and Max we firstly add the part of Jo and Max to find the total pear they want. Then we check the one pear is enough y subtracting.
Now finding the total pear that Jo and Max want:
Total Pear they want = Jo want + Max want
Total Pear they want = 3/4 + 1/3
To add we equal the denominator.
Multiply and divide by 12 on both number
Total Pear they want = 3/4 × 12/12 + 1/3 × 12/12
Total Pear they want = 9/12 + 4/12
Total Pear they want = (9 + 4)/12
Total Pear they want = 13/12
Total Pear they want = 1 1/12
As we can see that the sum of both Jo and Max requirement is max than the one pear. So the only one carton of pear is not enough.
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Jim is going to order rose bushes from a local nursery. The delivery charge is $15.00. Each rose bush costs $18.75. What is the greatest number of rose bushes lim can he buy with 80.
Answer: 3 rose bushes
Step-by-step explanation:
1. First we must identify the unknown. We do not know how many rose bushes he can get, we will use "x" to represent this number.
2. We must set up an equation with the given information. We know the delivery fee will remain constant.
3. 15+18.75(x)=80
4. Subtract 15 from both sides and it leaves you with 18.75x=65
5. Then you must divide both sides by 18.75, which leaves you with x=3.46
6. We cannot buy .46 of a plant so we must round down to 3
7. Jim can buy 3 rose bushes
Can someone PLEASE help me fill this chart? I’m not sure how to even get the -5?
Answer:
See below
Step-by-step explanation:
This is very easy once you understand what to do kiddo. They give you a x term, in this case -2, all you have to do is plug in this value into the equation y = x² -2x -3 which will give you your y value in this case +5 not - 5.
Heres the extra work
[tex]y = x^2 - 2x -3\\y = (-2)^2 -2(-2) -3\\y = 4 + 4 -3\\y = 5[/tex]
