The value of the expression 7x² - 2x + 2 when x = 3 is 59.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Based on the information given, the expression is:
7x² - 2x + 2
Put x = 3
= 7x² - 2x + 2
= 7(3)² - (2 × 3) + 2
= 63 - 6 + 2
= 59
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how many integers can be represented as a difference of two distinct members of the set $\{1, 2, 3\}$?
We can represent 4 integers as a difference of two distinct members i.e. {1, -1, 2, -2}.
What are Integers ?
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
Here, we have 3 distinct positive integers which are {1, 2, 3}.
We can list down the integers as a difference of the two distinct members as follows :
1 - 2 = -1
2 - 1 = 1
2 - 3 = -1
3 - 2 = 1
1 - 3 = -2
3 - 1 = 2
So, we can see clearly it is representing only 4 integers which are {1, -1, 2, -2}.
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what is the expected sum of the numbers that appear when three fair dice are rolled? (enter the value in decimal format.)
The expected sum of the numbers that appear when three fair dice are rolled, is 10.5.
In the given question we have to find the expected sum of the numbers that appear when three fair dice are rolled.
As we know that a dice have six faces. Each faces are mark from the number 1 to 6.
That means if we rolled a dice then there is possibility of coming six numbers. That numbers are 1, 2, 3, 4, 5, 6.
Now the sum of these numbers is
1+2+3+4+5+6 = 21
Total numbers are 6.
So the expected sum of the numbers that appears when one fair dice is rolled
=21/6
=3.5
Since there are three fair dice that are rolled.
So the expected sum of the numbers that appears when three fair dice are rolled = 3*3.5
The expected sum of the numbers that appears when three fair dice are rolled = 10.5
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c. find the mean, median, and standard deviation of heating degree days (hdd), broken down by season, for the california (code 0499). (ignore the first and last rows for the given location, the ones that contain -9999, the code for missing values.) round your answers to two decimal places, if necessary.
mean =1.532
median = 6.98
standard deviation = 3.5
mean for heating degree days and broken down by season for the california
according to the given values we find the mean
mean =
-1.45+ -2.5+-4.5+1.056+3.67+6.98+3.78+2.67+4.87+3.45+2.97+-4.06/12
=1.532
median for heating degree days and broken down by season for the california
according to the given values now we find the median
median = 6.98
standard deviation for heating degree days and broken down by season for the california
according to the given values now we find the standard deviation
standard deviation = square root of ∑([tex]x_{i}[/tex]- μ)^2/n
= 3.5
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A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. It is determined
that the population of bees increases exponentially.
How many bees are will there be after 40 days? Round your answer to the nearest whole number.
After 40 days 4467 bees will be the population after 40 days.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given here: A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. The population of bees also increase exponentially.
let the function that gives the population of bees after given days
f(x)=aˣ27
a⁴×27=45
a= [tex]\sqrt[4]{45/27}[/tex]
a=1.1362
Thus for x= 40 we have f(40)=1.1362⁴⁰×27
= 4465.69
=4467 (approx)
Hence, After 40 days 4467 bees will be the population after 40 days
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suppose a package to be mailed using a certain postal service may not measure more than 114 inches in length plus girth. (length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.) find the greatest volume (in inches cubed) of a rectangular box with square base that may be mailed.
Such a box can hold a maximum volume of (114/2)3 = 9837.4 cubic inches.
A three-dimensional space's occupied volume is measured. [1] It is frequently measured numerically with SI-derived units (like the cubic meter and litre) or with a variety of imperial or US-standard units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its carrying capacity, or the amount of fluid (liquid or gas) that it could hold. A shipment cannot be larger than 114 inches in length plus girth if it is going through a specific postal service. The maximum cubic inch volume of a rectangular box with a square base that can be sent is (114/2)3 = 9837.4.
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name all the corresponding sides and angles below if the polygons are congruent
not sure if i need to add more or if there’s some i missed
Answer:
Step-by-step explanation:
write all your sides and angles down
Corresponding sides:
AC≅JL
CB≅LK
AB≅JK
Corresponding angles:
∠A≅∠J
∠C≅∠L
∠B≅∠K
By using compatible numbers, the estimate is
Use a calculator to multiply 92 × 12. What do you get?
Circle whether the estimates were all less than or greater than
the actual product.
By using compatible numbers, the estimate is 900
Using a calculator, the actual product is 1104The estimates were less than the actual product.How to estimate the product expression?From the question, we have the following expression that can be used in our computation:
92 x 12
From the question, we are to make use of compatible numbers
This means that we have the following approximation
92 = 90
12 = 10
Next, we estimate the product using approximated values
i.e.
Product = Approximation of 92 x Approximation of 12
Substitute the known values in the above equation, so, we have the following representation
Product = 90 x 10
Evaluate the products
Product = 900
Using a calculator, we have
Product = 92 * 12
Evaluate the products
Product = 1104
900 is less than 1104
Hence, the estimate is less than the actual product
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Use the information given to enter an equation in standard form.
Slope is 7, and (1, 8) is on the line.
The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant b.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
Put m = 7 , x = 1 and y = 8
8 = 7(1) + b
b = 1
Thus, y = 7x + 1
Hence "The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1".
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What is the equation of the line that passes through the point (4,6)(4,6) and has an undefined slope?.
Answer:
x = 4
Step-by-step explanation:
A line with undefined slope is a vertical line.
Vertical lines have equation in the form:
x = anumber
In this case they gave you the info you need (4,6) The 4 is the x and the 6 is the y. (4,6) is in the form (x,y).
So x is 4.
x = 4
A cyclist travels 40km between two villages with an average speed of 18km\hr. Find how long the journey takes.
Here the time taken to complete the journey is2 hour 20 minutes
To find it we need to use the formula which include speed, time and distance of total journey.
Speed=Distance/Time
Here we put the number based on the formula,
18km/hr=40km/time
Time=40km/18km/hr
Time=2.2hr or 2 hour 20 minutes
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The average time it takes Greg to mown a lawn can be defined by the expression 28x + 5
The number 28 represented by the equation A = 28x + 5 is the average time it takes to mow one lawn
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be = A
Now , the equation A is given as
A = 28x + 5
where x is the number of lawns to mow
Now , A is the average time required to mow a lawn
So , the number 28 is the average time required to mow a single lawn
Therefore , the number 28 average time it takes to mow one lawn
Hence , The number 28 represented by the equation A = 28x + 5 is the average time it takes to mow one lawn
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circle the number that are divisible by both 5 and 2 (25,40,55,70,80,95)
Answer:
40, 70, 80
Step-by-step explanation:
It would have to be numbers that end in 0. Numbers that are divisible by 5 end in 0 or 5, but numbers divisible by 2 do not end in 5, so only the numbers that end in 0 are divisible by 2 and 5.
if the correlation between two variables is close to 0, you can conclude that a scatterplot would show
Scatterplots would show no straight‑line pattern, but there might be a strong pattern of another form.
The correlation coefficient between the values is close to 0, which means that there is no pattern of any form, hence, the scatterplot would show a cloud of points with no visible pattern
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. One more variable can be shown if the points are color-, shape-, or size-coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable and its position on the vertical axis by the value of the other variable.
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Plot the points (-5, 3) and (-4, 9) and find the slope.
Answer:
Slope M=6
Step-by-step explanation:
a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.
The side length of the original cube for the given measurements and condition is equal to 8.6ft.
As given in the question,
Let 'x' be the side of the original cube.
Volume of original cube = x³
As given 8ft thick slice is cut from the top of the cube.
Volume of the thick slice = 8x²
Volume of the resulting rectangular box = 44
⇒ x³ - 8x² = 44
⇒ x³ - 8x² -44 =0
Plot the graph of the function.
Graph is attached.
From the graph approximate value of side length 'x' = 8.6 ft.
Therefore, the side length of the original cube is equal to 8.6ft.
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Colin buys a car for £45500.
It depreciates at a rate of 6% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny
where appropriate.
if you have 200 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
1600 square meters is the greatest area that may be enclosed.
Rectangle.
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
If fencing is required for 200 meters, then the enclosed area's perimeter is 200 meters.
Perimeter of rectangle = 2(L + B)
2(L+B) = 200
Divide both sides by 2
L+B = 100
L = 100 - B
Here,
Area(A) = L X B
Substitute L = 100 - B into the equation above
A = (100 - B) x B
A = 100B - B²
At maximum area dA/dB = 0
dA/dB = 100 - 2B
100 - 2B = 0
2B = 100
B = 100/2
B = 50m
So L = 100 - 50
L = 50m
Maximum area to be enclosed = 50 x 50
Maximum area to be enclosed = 2500 square meters
In conclusion, the 2500 square meters of space that the fence will enclose
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the equation x^3-6x=72 has a solution between 4 and 5
The solution of the given equation is between 4 and 5.
What is solution of an 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.
Consider the given equation,
x^3 - 6x = 72
Subtract 72 from both sides,
x^3 - 6x - 72 = 72 - 72
x^3 - 6x - 72 = 0
After solving this equation we get
x ≈ 4.63902
This value is exactly between the 4 and 5.
Hence, the solution of the given equation is between 4 and 5.
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for each pair of points below think about the line that joins them. for which pairs is the line parallel to the x-axis?
Pair of points representing parallel line to the x-axis from the given pairs is equal to option a. (3.2, 7) and (5, 7).
As given in the question,
Line parallel to the x-axis has slope = 0
Calculate the slope of each pair of points :
a. (3.2, 7) and (5, 7)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 7- 7) / ( 5 - 3.2)
= 0
Pair of points represents parallel line to x-axis.
b. (8, 8.4) and (8, 8.8)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 8.8- 8.4) / ( 8 - 8)
= not defined
Pair of points is not parallel to x-axis.
c. (6 1/2, 12) and (6.2, 11)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 11- 12 / ( 6.2 - 6.5)
= 1/ 0.3
= 10/3
Pair of points is not parallel to x-axis.
Therefore, pair of points represents parallel line to x-axis is equal to
option a. (3.2, 7) and (5, 7).
The complete question is:
For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the x-axis? Circle your answer(s). Without plotting them, explain how you know.
a. (3.2, 7) and (5, 7)
b. (8, 8.4) and (8, 8.8)
c. (6 1/2, 12) and (6.2, 11)
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Determine whether the equation 3(4g+6)=2(6g+9) has one solution, no solution, or infinitely many solutions.
Answer:
one solution
Step-by-step explanation:
Question-2
What is the distance between the zeros of the function defined by
6 (2x²+2-8)-2x (2x - 1)?
Answer:
(2x−1=2x−1) (mark me brainliest) <3!
A synthetic fiber used in manufacturing carpet has tensile that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. (a) Find the probability that a random sample of n = 6 fiber specimens will have a sample mean tensile strength that exceeds 75.75 psi. 75.75 - р X- р M P[X > 75.75] = P o In o Tn 75.75 – 75.5 P[X > 75.75] = P2> 3.5 va = P[Z > 0.175] = 1-0(0.175) = 0.4325 BC (b) How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 to n = 49?
The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
Given that,
The tensile strength of a synthetic fiber used to make carpet is regularly distributed, with a mean of 75.5 psi and a standard deviation of 3.5 psi. We have to determine probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi.
We know that,
The Z score is used to determine how far the raw score deviates from the mean, either above or below.
z = (score - mean) / (standard deviation ÷ √sample)
Mean 75.5 psi and standard deviation 3.5 psi. n = 6.
For > 75.75:
z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17
P(z>0.17) = 1-P(z<0.17)
= 1-0.5675
= 43.25%
Therefore, The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
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I am in 6th grade, can somebody answer in 6th grade skill? Here is an incomplete equation of 534 divided by 6. I only have 4 minutes left and I am stressed out!!!!
The answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
534 divided by 6
[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace8\emptyspace9\:\:\:\:\:\:\:\:\:\:\:\:\\ 6\overline{|\smallspace534}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace4\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace5\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
The A = 48
B = 54
C = 54
After applying the concept of arithmetic operation.
Thus, the answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.
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the tigers beat the sharks 2 out of the 3 times they played. they then played more times, and the sharks ended up winning at least 95% of all the games played. what is the minimum possible value for ?
37 is the minimum possible value for N.
Given,
Sharks' current winning percentage is 1/3*100, or 33.33%.
Since Shark's winning rate must be at least 95%, we must determine the lowest number of N that can be used. Sharks must thus win every one of the N games in order to reduce N.
Total matches therefore equal N+3.
When sharks have a 95% winning percentage, tigers will have a 5% winning percentage. And they'll only triumph in two games overall.
Therefore,
2 matchups represent 5% of all matches.
As a result, there were 40 total matches (2/5*100).
So,
N+3 = 40 => N= 37
As an alternative, you can determine the solution by solving the following equation.
2/(N+3) = 5/100
You will obtain N = 37 by solving.
That is,
The minimum possible value for N is 37
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suppose that two players are playing the following game. player 1 can choose either top or bottom, and player 2 can choose either left or right. the payoffs are given in the following table: where the number on the left is the payoff to player a, and the number on the right is the payoff to player b. if each player plays their maximin strategy, the outcome of the game will be player b player a left right top 8 1 2 6 bottom 3 5 4 2 group of answer choices top/left top/right bottom/left bottom/right
A) Player 1 does not have a dominant strategy because if player 2 plays left, then player 1 should play bottom but if player 2 plays right then player 1 should play top. For a dominant strategy to existing player 1 would have to chose top or bottom regardless of what player 2 does.
B) Player 2 has a dominant strategy of left because this always produces a better outcome for this player. Specifically, if player 1 plays top player 2 is better off playing left (since 5 > 4) and if player 1 plays bottom player 2 is still better off playing left (since 4 > 3)
C) i) Top/Left is not a Nash Equilibrium because if player 2 plays left then player 1 would be better off playing bottom and it only takes one player wanting to deviate to ruin a potential Nash Equilibrium.
Simplest 3 varieties of stresses can exchange the composition of an equilibrium aggregate: (1) a change inside the concentrations (or partial pressures) of the additives by using adding or doing away with reactants or merchandise, (2) an alternate in the general strain or quantity, and (three) an exchange within the temperature of the gadget.
To learn more about A) Player 1 does not have a dominant strategy because if player 2 plays left, then player 1 should play bottom but if player 2 plays right then player 1 should play top. For a dominant strategy to existing player 1 would have to chose top or bottom regardless of what player 2 does.
B) Player 2 has a dominant strategy of left because this always produces a better outcome for this player. Specifically, if player 1 plays top player 2 is better off playing left (since 5 > 4) and if player 1 plays bottom player 2 is still better off playing left (since 4 > 3)
C) i) Top/Left is not a Nash Equilibrium because if player 2 plays left then player 1 would be better off playing bottom and it only takes one player wanting to deviate to ruin a potential Nash Equilibrium.
Simplest 3 varieties of stresses can exchange the composition of an equilibrium aggregate: (1) a change inside the concentrations (or partial pressures) of the additives by using adding or doing away with reactants or merchandise, (2) an alternate in the general strain or quantity, and (three) an exchange within the temperature of the gadget.
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what is 4 times (5+3) divided by 8-2
Answer: 5.3
Step-by-step explanation: First, you have to use PEMDAS and then you will get 32 divided by 6, which is 5.3 repeating
What is the slope of the black line?
What is the slope of the blue line?
Answer:
Blue line: -1/2
Black line: 3/4
Step-by-step explanation:
The slope of the blue line is a negative cause its a negative slope and the slope of the black line is positive cause its a positive slope.
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help help help help help
The y value of the y-intercept is 146 feet while the slope is -4 feet per second
How to find the y value of the y-intercept and the meaning?it was given that Kaliel starts at a height of 142 feet. That means at time 0 second (the start), he is at height 142 feet. So this is y-intercept i.e. time = 0 (x-axis), height = 146 (y-axis)
Thus, the y value of the y-intercept is 146 feet
In this case, the slope is defined as the rate of change in height with time i.e the rate at which he descends
Slope = Change in height / Change in time
From the table, the time given is 8 and 13 when the height is 110 and 94. Slope will be:
Slope = (94-110) /(12-8)
Slope = -16/4
Slope = -4
This implies he descends at a rate of 4 feet per second.
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Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model f(t)=89−17log10(t+1),0≤t≤24 where t is the time in months.
(a) What is the average score on the original exam? (b) What was the average score after one year? (c) After how many months would it take for it to predict that the average dropped to 82? (Assume that the the model could continue past two years, if necessary)
Answer:
Step-by-step explanation:
a problematic case may occur when two variables measured on a sample of individuals have a correlation of less than 1. on average, individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called
Individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called regression towards the mean.
What is regression?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable and one or more independent variables.
If one sample of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. This is known as regression toward the mean.
Background A statistical phenomenon called regression to the mean (RTM) can cause natural variation in repeated data to appear as actual change. It occurs when measurements that are frequently followed by ones that are more typical of the range are unusually large or small.
Hence, individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called regression towards the mean.
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