Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in millions. Write the slope-intercept form of the equation for the line of fit using the points representing 1992 and 2000.
Answer:
278.33X - 553.34222
Step-by-step explanation:
Given the data:
Year, X :
1992
1993
1994
1995
1996
1997
1998
1999
2000
Sales, Y:
1.2
1.4
1.6
1.8
2.2
2.5
2.8
3.0
3.4
Using a linear regression calculator, the regression fit model for the data is
Y = 278.33X - 553.34222
Where, Y = sales in Millions
x = year
Reid found 6 coins that totaled
61¢ in all. What coins did he find?
Answer:
1 quarter, 3 dimes, 1 nickel,1 penny
A pan balance has 3 cubes on one pan and 11 cubes on the other pan. Lucky thinks she should add 7, 8, 9, or 10 cubes to make the pan balance. How can you use the equation 3+c=11 to find the number of cubes Lucy should add
?
The number of cubes Lucy should add is 8.
In mathematics, an equation is a formula that expresses the equivalency of two expressions, by connecting them with the equals sign = .
Given that, a visage balance has 3 cells on one visage and 11 cells on the other visage.
The equation to represent the situation is 3 c = 11
The result of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, c = 11- 3
c = 8
thus, the number of cells Lucy should add is 8.
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Deshawn earned $25 for babysitting his sister. He also earns $8 a week for the trash out. Which equation represents y, the total amount of money that Deshawn earned babysitting and taking out the trash for x weeks
A. y = 8x + 25
B. y = 25x + 28
C. y = 8x
D. y = 25x + 8
Answer:
A
Step-by-step explanation:
25 is by itself and 8 is weekly by an x amount of weeks
Answer:
A. y = 8x + 25
Step-by-step explanation:
y = 8x + 25
8x money he earns for the trash per week
25 money for babysitting.
Simplify: 4(2b + 2) – 3
Answer:
=8b + 5
Step-by-step explanation:
do you need an explantion
Answer:
8b + 5
Step-by-step explanation:
By consulting the table below, you will find how I got 8b + 8, and then
Since 8 and -3 are like terms, I put them together
8 - 3 = 5
So in the simplest form the equation is
8b + 5
The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.
7.) 4, 5, 6
8.) 11, 12, 15
9.) 30, 40, 50
The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.
What is Triangle?Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
7.) This triangle is obtuse.
To see this, we can use the Pythagorean theorem:
4*4 + 5*5 = 16 + 25 = 41
6*6 = 36 m
Since 41 > 36, we know that the triangle is obtuse.
8.) This triangle is right.
To see this, we can again use the Pythagorean theorem:
11*11 + 12*12 = 121 + 144 = 265
15*15 = 225 m
Since 265 = 225 + 40, we know that the triangle is right.
9.) This triangle is also right.
We can use the same method as before:
30*30 + 40*40 = 900 + 1600 = 2500
50*50 = 2500 m
Since 2500 = 2500, we know that the triangle is right.
Therefore, The given triangles are obtuse , right angled and right angled.
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The temperature dropped 24 degrees in 4 hours. What was the average drop in temp per hour?
Answer:
6
Step-by-step explanation:
You have to divide 24 by four.
a one-way anova is performed to compare the means of four populations. the sample sizes are 18, 22, 20, and 22. determine the degrees of freedom for the f-statistic. write your answer in the form (df1 , df2), where df1 is the numerator degrees of freedom and df2 is the denominator degrees of freedom.
A one-way ANOVA is a statistical test used to compare the means of four populations in this case. Thus, the degrees of freedom for the F-statistic in this one-way ANOVA are (df1, df2) \(= (3, 78)\).
The degrees of freedom are essential for calculating the F-statistic, which helps determine whether there are significant differences among the population means.
To calculate the degrees of freedom for the F-statistic, we need to determine the numerator degrees of freedom (df1) and the denominator degrees of freedom (df2). For df1 (numerator degrees of freedom), it is equal to the number of populations (groups) minus 1.
In this case, there are four populations,
So: df1 \(= 4 - 1 = 3\)
For df2 (denominator degrees of freedom), it is equal to the total sample size (N) minus the number of populations (groups).
The total sample size is given as \(18 + 22 + 20 + 22 = 82\).
So: df2 \(= 82 - 4 = 78\)
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Brenton packed 8 peanut bars in each box. If he had 398 peanut bars,
How many boxes were packed?
(ii)
How many bars remained?
Answer:
divide 8 and 398 and you will get ur answers
b. Solve -2sinθ =1.2 in the interval 2π ≤ θ ≤ 4 π . How are these solutions related to the solutions in part (a)?
the solutions for -2sinθ = 1.2 in the interval 2π ≤ θ ≤ 4π are approximately:
θ ≈ -0.6435 radians, 5.499 radians, 3.785 radians, and 9.927 radians.
To solve the equation -2sinθ = 1.2 in the interval 2π ≤ θ ≤ 4π, follow these steps:
Step 1: Rewrite the equation in terms of sinθ:
sinθ = -1.2 / 2
Step 2: Check if the right-hand side of the equation is within the range of the sine function, which is -1 to 1. If it is not, then there are no solutions in the given interval. In this case, -1.2/2 = -0.6, which is within the range of the sine function, so we can proceed.
Step 3: Use the inverse sine function (arcsin) to find the value of θ:
θ = arcsin(-0.6) + 2kπ or θ = π - arcsin(-0.6) + 2kπ
where k is an integer (k = 0, ±1, ±2, ...)
Step 4: Substitute the value of k to find all possible solutions within the interval 2π ≤ θ ≤ 4π:
1. For k = 0:
θ = arcsin(-0.6) = -0.6435 radians (approx)
2. For k = 1:
θ = arcsin(-0.6) + 2π ≈ 5.499 radians (approx)
3. For k = -1:
θ = π - arcsin(-0.6) ≈ 3.785 radians (approx)
4. For k = 2:
θ = π - arcsin(-0.6) + 2π ≈ 9.927 radians (approx)
So, the solutions for -2sinθ = 1.2 in the interval 2π ≤ θ ≤ 4π are approximately:
θ ≈ -0.6435 radians, 5.499 radians, 3.785 radians, and 9.927 radians.
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Help please!!
Use the first and last data points to find the slop intercept equation of the trend line.
The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
What is the slope?
The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):
m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333
Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:
b = y₁ - m * x₁
b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666
Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:
y = mx + b
y = 5.3333x + 9.6666
Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
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Answer:
\(y=\dfrac{16}{3}x+\dfrac{29}{3}\)
Step-by-step explanation:
\(\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)
The first and last data points of the given table are:
(1, 15)(7, 47)Substitute the data points into the slope formula to find the slope of the trend line:
\(\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}\)
\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)
Substitute the found slope and the first data point into the slope-intercept formula and solve for b:
\(\implies 15=\dfrac{16}{3}(1)+b\)
\(\implies 15=\dfrac{16}{3}+b\)
\(\implies b=15-\dfrac{16}{3}\)
\(\implies b=\dfrac{45}{3}-\dfrac{16}{3}\)
\(\implies b=\dfrac{45-16}{3}\)
\(\implies b=\dfrac{29}{3}\)
Therefore, the equation of the trend line in slope-intercept form is:
\(y=\dfrac{16}{3}x+\dfrac{29}{3}\)
what is the value of 8+ 2 to the third power times 5
Answer:
48 is the answer
Step-by-step explanation:
Find the Slope of the line that passes through the given points: (5, 2) and (6, 6).
Answer:
You can find slope of line using the slope formula. The slope formula is Y2-Y1/X2-X1. Substitute in the points and solve.
6-2/6-5
4/1
4
The slope of the line is 4.
Hope this helps! :)
Proofs by Counterexample [3 points ] Find the truth of the following statement: There exists a positive integer that can be written as the sum of two different pairs of squares. Think about how a computer can help you find the solution. Provide either a program that you run to solve it or describe your logic of how a computer program can solve this problem.
The statement "There exists a positive integer that can be written as the sum of two different pairs of squares" is false.
To prove the statement false, we need to show that for any positive integer, it is not possible to express it as the sum of two different pairs of squares.
Let's assume the positive integer is represented as "n." We can explore all possible pairs of squares whose sum is equal to n by iterating through values of one of the squares (let's call it a) from 1 to √n. For each value of a, we calculate the corresponding square \((b = n - a^2)\). If b is a perfect square and is different from \(a^2\), we have found a valid pair of squares whose sum is n.
If we exhaust all possible values of a without finding a valid pair, we can conclude that no such pairs exist, and therefore, the statement is false.
Using a computer program to implement this logic can significantly speed up the process of checking all possible pairs of squares for a given positive integer. By leveraging the computational power of a computer, we can iterate through the values of a and check if the corresponding b is a perfect square and different from \(a^2.\) If we find a valid pair, we can immediately stop the program and output the result. Otherwise, we continue the iteration until all values of a have been checked.
By employing this approach, we can systematically verify the statement for various positive integers efficiently.
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(a) On the grid above, draw the line x = 3
The Graph will look like this:
The graph will show a vertical line crossing the x-axis at x = 3 and extending infinitely in both the positive and negative y-directions.
The equation x = 3 represents a vertical line that passes through the point (3, 0) on the Cartesian coordinate system. This means that for every value of y, the corresponding x-coordinate is always 3. Since the line is vertical, it extends infinitely in both the positive and negative y-directions.
To visualize the line x = 3 on a graph:
1. Draw two perpendicular axes, the horizontal x-axis, and the vertical y-axis.
2. Since x = 3, draw a vertical line passing through the point where x = 3 on the x-axis (at x = 3) and extending through the entire y-axis.
The resulting graph will show a vertical line crossing the x-axis at x = 3 and extending infinitely in both the positive and negative y-directions.
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AHHH CAN YOU HELP ME?
FOR 100 points and brainlest
Step-by-step explanation:
The answer is -9
Answer:
-9
Step-by-step explanation:
Which phrase represents the algebraic expression for n – 4?
A. The quotient of a number and four.
B. Four less than a number.
C. Four minus a number.
D. Four more than a number.
Step-by-step explanation:
B. Four less than a number.
Kennedy is a salesperson who sells computers at an electronics store. She makes a base pay of $100 each day and then is paid a $10 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Kennedy's total pay on a day on which she sells xx computers.
Answer:
Step-by-step explanation:
Rombos BA(5x-11). AD(6x-18)
The value of x is 7.
And every side of the rhombus is 24 unit.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given:
ABCD is a rhombus.
BA = 5x - 11
And AD = 6x - 18
Then, BA = AD
5x - 11 = 6x - 18
x = 7
Therefore, the value of x is 7.
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what is the slope- intercept form of 4x+5y=20
Answer:
y = -4/5x + 4
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Standard Form: 4x + 5y = 20
Step 2: Rewrite
Subtract 4x on both sides: 5y = 20 - 4xDivide 5 on both sides: y = 4 - 4/5xRearrange: y = -4/5x + 4approximately 85% of statistics students do their homework in time for it to be collected and graded. each student does homework independently. in a statistics class of 60 students, what is the probability that at least 50 will do their homework on time? students are selected at random.
The probability that at least 50 will do their homework on time is 65%.
To solve this problem, we need to first determine the probability of a single student doing their homework on time. We are given that approximately 85% of students do their homework on time, so the probability of any given student doing their homework on time is 0.85.
Now, we need to determine the probability of at least 50 out of 60 students doing their homework on time. To do this, we can use a binomial distribution. A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In this case, we have 60 independent trials (60 students), and each trial has a probability of success of 0.85 (the probability that a student does their homework on time). We want to find the probability of at least 50 successes (students doing their homework on time). To do this, we can use the binomial cumulative distribution function (CDF), which gives us the probability of getting k or fewer successes in n trials:
\(P(X \leq k) = \sum^{ i=0}_{k} (n^C_a * p^a * q^{n-i})\)
where X is the number of successes, k is the number of successes we want (in this case, 50 or more), n is the total number of trials (60), p is the probability of success (0.85), q is the probability of failure (1-p, which is 0.15), and ⁿCₐ is the binomial coefficient, which represents the number of ways to choose i successes out of n trials.
Using this formula, we can calculate the probability of getting 50 or more successes out of 60 trials:
P(X ≥ 50) = 1 - P(X < 50) = 1 - Σa =0 to 49 (60Cₐ * 0.85ᵃ * 0.15⁽⁶⁰⁻ᵃ⁾)
When we apply the value of a as 5, then we get the probability as 0.65 or 65%.
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In ΔDEF, the measure of ∠F=90°, the measure of ∠D=66°, and EF = 32 feet. Find the length of FD to the nearest tenth of a foot.
Answer:
14.3
Step-by-step explanation:
Remark
Make a rough sketch of the triangle.
Make F the right angle
Make <D = 66
E is the other angle.
Givens
EF = 32
<F = 90
<D = 66
Equation
Tan(D) = EF/FD
Solution
Tan(66) = 32/FD Multiply both sides by FD
FD*Tan(66) = 32
Tan(66) = 2.246
2.246 * FD = 32 Divide by 2.2246
FD = 32/2.246
FD = 14.25
FD = 14.3
Please Help
Which of the following is a continuous random variable?
A. X= number of incoming flights at the local airport
B. T=winning time in the man's 100 meter dash at the 2016 Olympics
C. P=number of points scored by Stephen curry in a game
D.H=The number of hats sold on Tuesday
Answer:
option A
Step-by-step explanation:
because it is not limited to anything while option b is limited to the men's hundred meter dash and 2016, and to the Olympics
C is limited to one game and stephen curry
D is limited to tuesday
since option a isn't confined to one day, person, or specific event there can be endless numbers assigned to the variable
Fill in the tables and create a recursive and explicit equation for all three questions.
Answer:okay
Step-by-step explanation:hm
consists of abnormal behaviors identical to those in schizophrenia that have persisted for at least 1 month but fewer than 6 months.
The description refers to the diagnosis of brief psychotic disorder, which consists of abnormal behaviors identical to those in schizophrenia lasting for at least 1 month but fewer than 6 months.
Brief psychotic disorder is a psychiatric diagnosis characterized by the presence of psychotic symptoms, such as hallucinations, delusions, disorganized thinking, or grossly disorganized or catatonic behavior. These symptoms are similar to those seen in schizophrenia, but the key distinction is that brief psychotic disorder lasts for a shorter duration, specifically between 1 month and 6 months.
During this period, individuals with brief psychotic disorder may experience a sudden onset of symptoms that significantly impact their thoughts, emotions, and behavior. However, unlike schizophrenia, the duration of symptoms in brief psychotic disorder is limited, typically resolving within a few weeks to a few months.
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Glass bottles are formed by pouring molten glass into a mold. The molten glass is prepared in a furnace lined with firebrick. As the firebrick wears, small pieces of brick are mixed into the molten glass and finally appear as defects (called "stones") in the bottle. If we can assume that stones occur randomly at the rate of 0.00001 per bottle, what is the probability that a bottle selected at random will contain at least one such defect?
The probability that a bottle selected at random will contain at least one defect can be found using the complement probability of having no defect.
Let us denote the probability of having at least one defect in a bottle as P(A). P(A') is the probability of not having any defect in the bottle. Since the probability of an event occurring plus the probability of it not occurring is equal to 1, then \(P(A') = 1 - P(A).\)
Thus, the probability of having no defect in a bottle is
\(P(A') = (1 - 0.00001) = 0.99999\)
.Since a bottle has either no defect or at least one defect,
\(P(A) = 1 - P(A') = 1 - 0.99999 = 0.00001.\)
Therefore, the probability that a bottle selected at random will contain at least one such defect is \(0.00001 or 1/100,000.\)
This means that on average, only 1 bottle in 100,000 will contain such a defect.
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A television game show has 12 doors, of which the contestant must pick 2. Behind 3 of the doors are expensive cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 2 doors she selects. Determine the probability that the contestant wins at least one car.
\(the \: answer \: is \: \frac{1}{10} \)
\(\blue{———hope it helps———}\)
\(\large{ \pink{ \underline{ { \sf{Answer}}}}}\)
\(the \: answer \: is \: \frac{1}{10} \)
I need help !! this is geometry hw
Answer:
angle a=64, longest side AV : shortest side: TV
angle c=55 longest side: BW shortest side: CB
angle z =24 longest side: XZ shortest side: XP
Step-by-step explanation:
Evaluate (-1)x(-2)x(-3)x(-4)x(-5).
Answer:
\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)
Step-by-step explanation:
By the rule of Integer multiplications,
\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)
\(= [2] \times [12] \times (-5)\)
\(= -120\)
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What is the area of a triangle whose vertices are J(-2, 1), K(0, 3), and L(3,-4)?
Enter your answer in the box.
units²
Answer: 10 units²
Step-by-step explanation:
To find the area of a triangle when given its vertices, we can use this formula:
\(\displaystyle \frac{Jx(Ky - Ly) + Kx(Ly - Jy) + Lx(Jy - Ky) }{2}\)
We will plug in our coordinate points and solve. The area will be the absolute value simplification of this expression.
J(-2, 1) is (Jx, Jy), K(0, 3) is (Kx, Ky), and L(3,-4) is (Lx, Ly).
\(\displaystyle \frac{Jx(Ky - Ly) + Kx(Ly - Jy) + Lx(Jy - Ky) }{2}\)
\(\displaystyle \frac{-2(3 - -4) + 0(-4 - 1) + 3(1 - 3) }{2}\)
\(\displaystyle \frac{-14+ 0-6}{2}\)
\(\displaystyle \frac{-20}{2}\)
\(\displaystyle -10,\;\;|-10|=10\)