The number of months that the manufacturer should offer is given as follows:
51.7 months.
How to obtain the amount using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 60, \sigma = 5.2[/tex]
The z-score associated with the 5.6th percentile is given as follows:
z = -1.59.
Hence the amount of time is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.59 = \frac{X - 60}{5.2}[/tex]
X - 60 = -1.59 x 5.2
X = 51.7 months.
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About 3/4 of a person's weight is water. If a student weighs 70 lb, how much of his weight is water?
Students have 52.5 lb. weight in water.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
A student weighs = 70 lb.
And, About 3/4 of a person's weight is water.
Since, A student weighs = 70 lb.
Hence, Students weighs in water = 3/4 of 70 lb.
= 3/4 × 70
= 52.5 lb.
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Constant Variance Definition
Constant variance, also known as homoscedasticity, is a statistical property where the variance of a variable is equal across all values of the variable.
This means that the variability of the variable is consistent, no matter what the value of the variable is. Mathematically, this is expressed by the formula:
Var(X) = σ^2
where Var(X) is the variance of the variable X, and σ^2 is the same across all values of X.
For example, if we look at the heights of a group of people, we may find that the variance of their heights is equal to 25 cm, no matter what the heights are. In this case, the variance of the heights is 25 cm, and this variance (25 cm) is the same for all the heights in the group.
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Solve the inequality -1/2 > 3/5
To solve the inequality -1/2 > 3/5, we can start by multiplying both sides of the inequality by the least common multiple of the denominators, which is 10, to get rid of the fractions. This gives us:
-1/2 * 10 > 3/5 * 10
-5 > 6
This inequality is not true, since -5 is not greater than 6. So the solution set is the empty set, or { }.
Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth. 15 PTS!!!
The solution for 4ˣ⁺³ = 7 using change of base formula is -1.596
How to solve 4ˣ⁺³ = 7 using the change of base formula log base b of y equals log y over log b?To solve 4ˣ⁺³ = 7 using change of base formula log base b of y equals log y over log b, we are going to use logarithm rules.
If f(x) = g(x), then ln(f(x)) = ln(g(x)). Thus,
ln( 4ˣ⁺³) = ln(7)
Using log rule:
[tex]\log _{a} x^{b} = b \log _{a}(x)[/tex]
ln (4ˣ⁺³) = ln(7)
(x+3) · ln(4) = ln(7)
(x+3) · ln(2²) = ln(7)
(x+3) · 2ln(2) = ln(7)
x+3 = ln(7) / (2ln(2))
x = [ln(7) / (2· ln(2))] - 3
x = -1.596
Thus, the solution is x = -1.596
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Answer:
Did he round up?
Step-by-step explanation:
Which customer has the smallest total bill, including tax and tip?
Customer #2 has the smallest total bill, including tax and tip.
How to know the customer with lowest bill?From the information, three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3.
For customer #1:
(1.06(12.95))(1.15) = 15.79;
The tip is 0.15(1.06(12.95)) = 2.06.
For customer #2:
1.06x = 11.65; x = 10.99; 20%
The tip = 0.2(10.99) = 2.20;
total = 11.65+2.20 = 13.85.
For customer #3:
1.06(11.50) + 0.18(11.50) = 14.26;
The tip is (0.18)(11.50) = 2.07.
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Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.
1. Which customer has the smallest total bill, including tax and tip?
please help me figure this out with an explanation thank you
The three numbers are: 23, 25, 27, The boy is 140 cm tall, the father is 140 + 30 = 170 cm, and the sister is 70 cm tall.
What is an equation?In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.
The terms 3x + 5 and 14 are separated by the word "equal" in the equation 3x + 5 = 14. The three main formats for linear equations are the slope-intercept form, standard form, and point-slope form.
Two expressions are combined with an equal sign to form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. It is possible to solve this equation, and the answer reveals that the value of the variable x is 7.
Let the the first number is : x
So, the other two numbers are :x+2, x+4
a) x+(x+2)+(x+4)=75
3x+6=75
3x=69
X=23
The three numbers are: 23, 25, 27
b)The sister's height is denoted as x. Two times, since the boy is twice as tall. His height is 2x + 30 because the father is 30 centimeters taller than the boy. The total height is 3.8 meters, or 380 centimeters. You can now create an equation.
x + 2x + 2x + 30 = 380
assemble similar terms
5x = 350
x = 70
The boy is 140 cm tall,
the father is 140 + 30 = 170 cm,
and the sister is 70 cm tall.
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X/3+10=15 what is x.
Answer:
15
Step-by-step explanation:
x/3+10=15
(x+30)/3=15
x+30=15×3
x+30=45
x=45-30
x=15
Answer:
First you need to put the variable, x, in a fraction
[tex]\frac{x}{3} + 10=15[/tex]
In this case, 10, is a positive integer, so because its a whole number, we put it with 15 on the other side of the equal sign. Then the +10 will become -10.
[tex]\frac{x}{3} =15-10[/tex]
Then its easier to calculate, 15 - 10 is 5.
[tex]\frac{x}{3} =5[/tex]
After that you put 5 over 1 and crisscross the equation.
[tex]\frac{x}{3} =\frac{5}{1}[/tex]
x times 1 is x itself, and 3 times 5 is 15
[tex]x=15[/tex]
So in the end x = 15
Have a wonderful day! :-)
Two bridges, A and B, run parallel to each other over a narrow river. Bridge A crosses the river at an exterior angle of (2x) . Bridge B crosses at angle of (4x-6). These two angles are supplementary.
What is the measure of the angle represented by the expression (4x-6)?
The measure of angle B crossing the river perpendicularly is 110°.
What are supplementary and complementary angles?When the sum of the two angles is 180° they are said to be supplementary.
When the sum of the two angles is 90° they are said to be complementary.
Given, Bridge A crosses the river at an exterior angle of (2x), Bridge B crosses at an angle of (4x-6) and these two angles are supplementary.
So, The sum of these two angles are 180°.
Therefore,
4x - 6 + 2x = 180°.
6x = 174°.
x = 174°/6.
x = 29°.
So, The measure of the angle B is (4(29) - 6)°.
= 116 - 6.
= 110°.
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Is this correct? 4.8%=4.888%=488.8
The value of the expression of the percentage as the friend details is; 0.04888....... and as such the friend is not correct
How to find the percentage?Percentages are usually calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Now, we are given the number 4.8% with 8 having a bar over it.
A bar over a number is called vinculum and it means that the number is being repeated indefinitely after a decimal point.
This tells us that our given number can now be expressed as;
4.888.....%
This is because from the definition of vinculum , 8 is repeated indefinitely. Thus, this can be simplified as;
4.888...../100 = 0.04888.......
Thus, the friend is not correct in conclusion.
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What are the 7 forms of gender inequality?
Gender inequality refers to the unequal distribution of rights, opportunities, and resources between individuals based on their gender. There are many forms of gender inequality, but some common ones include economic inequality, educational inequality, health inequality, political inequality, violence against women, social inequality and intersectionality.
Economic inequality: This refers to the unequal distribution of wealth, income, and resources between men and women. This can manifest in various forms, such as the gender pay gap and lack of representation in leadership positions.
Educational inequality: This refers to the unequal access to education and the resulting disparities in literacy rates and educational attainment between men and women.
Health inequality: This refers to the unequal access to healthcare and the resulting disparities in health outcomes between men and women.
Political inequality: This refers to the underrepresentation of women in politics and leadership positions, as well as the lack of policies and laws that promote gender equality.
Violence against women: This refers to the widespread problem of physical, sexual, and emotional abuse against women.
Social inequality: This refers to the unequal distribution of social status, power, and privilege between men and women, which can manifest in various forms of discrimination, prejudice, and bias.
Intersectionality: This refers to the ways in which gender inequality intersects with other forms of inequality, such as race, class, and sexuality, creating complex and interconnected forms of disadvantage for certain individuals and groups.
It's important to note that Gender inequality can manifest in various forms and it can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life. Therefore, it's crucial to understand and address gender inequality in all its forms.
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PLEASE HELP! the graph of y=x^3… (picture provided)
Answer:
Step-by-step explanation:
second one
How does the substitution method works for solving a two order system of equations?
The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.
A quadratic equation is a second-order equation written as ax² + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
To solve two order system of equations using substitution, follow these steps:
Step 1. Choose one equation and solve it for either of the one variables.
Step 2. In the other equation, substitute the value get from step 1.
Step 3. Solve the new equation.
Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.
Step 5. Check the solution in both original equations.
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Solve for x.
Enter your answer.
A square with side lengths 5 times x centimeters and diagonal length of 50 centimeters.
The value of x in the square is 5√2 centimetres.
How to find the side of a square?A square is a quadrilateral with 4 sides equal to each other. The square has side length 5 times x centimetres and the diagonal length is 50 centimetres.
Therefore, the side x can be found using Pythagoras's theorem as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
50² = (5x)² + (5x)²
2500 = 25x² + 25x²
2500 = 50x²
divide both sides by 50
x² = 2500 / 50
x² = 50
square root both sides of the equation
x = √50
x = √25 × 2
x = 5√2 centimetres
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What is the average rate of change of
g
gg over the interval
−
8
≤
x
≤
−
2
−8≤x≤−2minus, 8, is less than or equal to, x, is less than or equal to, minus, 2?
The average rate of change of g over the interval −8 ≤ t ≤ 2 is equal to -0.5 or -1/2.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(t) over the interval [-8, 2]:
a = -8; g(a) = 1
b = 2; g(b) = -4
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (-4 - 1)/(2 - (-8))
Average rate of change = -5/10
Average rate of change = -0.5 or -1/2.
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Complete Question:
What is the average rate of change of g over the interval −8 ≤ t ≤ 2?
May someone explain this to me in step-by-step? I'd greatly appreciate it!
Thank you.
Answer:
x = 9
Step-by-step explanation:
x = the missing side
24/8 = x/3
8(x) = 24(3)
8x = 72
x = 9
====================================================
Explanation:
The slanted left-most sides of the figures are 24 and 8, when moving from left to right.
Let's reverse the direction and move from right to left. The jump from 8 to 24 is "times 3", which is the scale factor when moving from the smaller figure to the larger figure.
The smaller figure has 3 up top. Apply the "times 3" scale factor to get 3*3 = 9 as the top side length of the larger figure.
In other words, every side of the smaller figure is tripled to get the larger figure.
----------------
Here's another way to solve.
24/8 = x/3
24*3 = 8*x .... cross multiplying
72 = 8x
8x = 72
x = 72/8
x = 9 is the final answer.
Which of the following is a solution of the linear equation 2x 3y 5?
Step-by-step explanation:
Solution
The correct option is A Yes, it is.
Given Line:
2
x
+
3
y
=
5
Standard Line :
a
x
+
b
y
=
c
Given line has two variables
x
and
y
where both
x
and
y
have power of
1
similar to standard form of line. So,
2×+3y=5 is a line in two variables.
A tool box is a rectangular solid with sides of 19 in. , 12 in. , and 9 in. What is its volume? 4,104 1,026 2,052 80.
The volume of a rectangular solid tool box would be 2,052 cubic inches.
Rectangular solids are three-dimensional shapes with six equal rectangles for sides. To find the volume of the rectangular solid tool box, we can use this following formula:
Volume = length x breadth x height
In this case, we are given that:
The length of the tool box = 19 in
The breadth of the tool box= 12 in
The height of the tool box= 9 in
We can find the volume by using the formula above:
Volume = 19 in x 12 in x 9 in
Volume = 2052 in³
As the result, the volume of the rectangular tool box would be 2052 cubic inches.
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this is the last question
The resulting quadrilateral have the following vertices: A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5), D'(x, y) = (1, 1). (Correct choice: B)
How to find the coordinates of the vertices of a polygon by rigid transformation
Herein we have the case of a quadrilateral, that is, a polygon with four vertices: A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2), D(x, y) = (4, 4), whose image is the result of a dilation with a scale factor of 1 / 4 about the origin on Cartesian plane. The polygon is contracted by contracting each of five vertices, whose formula is shown below:
P'(x, y) = k · P(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Imagek - Scale factorIf we know that k = 1 / 4, A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2) and D(x, y) = (4, 4), then the coordinates of the resulting polygon:
A'(x, y) = 0.25 · (- 4, 6)
A'(x, y) = (- 1, 1.5)
B'(x, y) = 0.25 · (- 2, 2)
B'(x, y) = (- 0.5, 0.5)
C'(x, y) = 0.25 · (4, - 2)
C'(x, y) = (1, - 0.5)
D'(x, y) = 0.25 · (4, 4)
D'(x, y) = (1, 1)
The vertices of the resulting quadrilateral are A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5) and D'(x, y) = (1, 1).
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What is the exponential value of 3?
The exponential value of 3, also known as [tex]e^3[/tex] is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 3.
To calculate [tex]e^3[/tex] , we would use the following formula:
[tex]e^3[/tex]= e x e x e = 2.71828 x 2.71828 x 2.71828 = 20.0855
So, the exponential value of 3 is approximately 20.0855.
It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.
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the diameter of a wheel is 3 feet. what is the distance around the wheel
Answer: 9.42 Feet or 9 Feet 5.04 Inches
Step-by-step explanation: To solve for the circumference, the equation you must use is C = 2πr (Circumference = 2pi(3.14)radius(half of the diameter)).
Jim began a 167-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour, find the amount of time he spent on the bicycle.
The amount of time he spent on the bicycle is 5.5 hours.
How to find the amount of time he spent on the bicycle?Jim began a 167-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking.
The whole trip took 6 hours. Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour.
The amount of time he spent on the bicycle can be calculated as follows;
speed = distance / time
distance = speed × time
Therefore, total distance is as follows:
let
x = time spent walking
167 = 4x + 30(6 - x)
167 = 4x + 180 - 30x
167 = -26x + 180
167 - 180 = -26x
x = -13 / -26
x = 1 / 2
Time spent on bicycle = 6 - 0.5 = 5.5 hours.
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1
The graph shows an image of a dilation about the origin with a scale factor of 2.
-10-8-6-4-
2
40
1
What are the coordinates of the pre-image of A', point A?
(-8,-12)
01
8 10 X
As a result, the answer to the provided coordinate plane problem is only choice C), which is the right answer.
What is a coordinate plane?The term "coordinate plane" refers to a two-dimensional region that consists of two number lines. It emerges when the X-axis & Y-axis intersect at a location known as the origin. Using the numbers on a coordinate grid, one can locate points.
Here,
Since, If there is a coordinate plane with both parallel lines, go with option A.
Therefore, there is no cure.
There are hence a finite number of solutions that could be found.
If two lines cross, there is only one potential result for Option B. Consequently, the quantity of potential solutions is.
According to Option C, there must be an endless number of solutions to the system because there are two coinciding lines that provide us an infinite number of junction sites.
The difference between Option D) and Option B) is noted.
Only choice C) is hence the proper one.
Therefore , the solution to the given problem of coordinate plane comes out to be Only choice C) is hence the correct one.
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Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). it is called by ____
Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). It is called by GEMS.
An effective acronym for teaching pupils the hierarchy of operations is PEMDAS.
The PEMDAS rule explains to pupils how to solve multi-step arithmetic problems and in what sequence to complete the operations to arrive at the right solution.
Groupings, Exponents, Multiplication or Division, Subtraction or Addition is referred to as GEMS. All grouping symbols, including parentheses, brackets, and braces, are referred to as groupings. The acronym GEMS has been adopted to take the role of PEMDAS. These can be used in place of one another.
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Ryan invests $7,171 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. How long will it take for the account balance to reach $11,688.69?
Round your answer to the nearest whole year.
It will take 7 years for the account balance to reach $11,688.69.
To find how long will it take for the account balance to reach $11,688.69
we will use the compound interest formula that is
[tex]$ \text A = \text P(1 + \frac{\text r}{\text n})^{\text {nt}}[/tex]
where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Given that, P = $7,171
A = $11,688.69
r = 7%
n = 12
t = to find
Substitute the details in the formula and we get
[tex]$11688.69 = 7171(1 + \frac{0.07}{12})^{12t}[/tex]
[tex]$ \text t=\frac{\log _{\frac{1207}{1200}}\left(\frac{1168869}{717100}\right)}{12}[/tex]
t = 7.000003 = 7 years
Thus, It will take 7 years for the account balance to reach $11,688.69.
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Answer:
7 years-----------------------------
Use compound interest equation:
A = P(1 + r/n)^(nt), where A - future amount, P- investment, r - interest rate, n- number of compounds, t - time in yearsSubstitute the given to find the value of t:
11688.69 = 7171(1 + 0.07/12)^(12t)1.0058333333^(12t) = 11688.69 /71711.0058333333^(12t) = 1.62999442198ln 1.0058333333^(12t) = ln 1.6299944219812t = ln 1.62999442198 / ln 1.005833333312t = 84 (rounded)t = 7is 60/77 and 17/6 Proportional
Find the range for the measure of the third side of a triangle when the measures of the other two sides are 13 in. And 27 in.
Answer: The measure of the third side of a triangle, when the measures of the other two sides are 13 in and 27 in, must be greater than the difference between the measures of the other two sides (which is 27 in - 13 in = 14 in) and less than the sum of the measures of the other two sides (which is 27 in + 13 in = 40 in).
This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.
Therefore the range of the measure of the third side of a triangle with side lengths 13 in and 27 in is:
(14 in < x < 40 in)
or
[x > 14 in and x < 40 in].
It is also important to note that any value of x within this range will produce a valid triangle, however any value less than 14 in or greater than 40 in will not.
Step-by-step explanation:
solve the systems. 3r=1-s and 7s=4-6r
The left side of the equations is equal to the right side for the values (3/14,5/14).
What is a system of equations?
A system of equations is a set of two or more equations that contain multiple variables. The goal is to find the values of the variables that make all the equations in the system true at the same time. There are different methods to solve a system of equations, such as substitution, elimination, and graphing.
To solve the system of equations given, we can use the substitution method:
1-s = 3r
7s = 4 - 6r
We can start by solving the first equation for one of the variables.
1-s = 3r
s = 1 - 3r
Now we can substitute this expression of s into the second equation
7(1 - 3r) = 4 - 6r
7 - 21r = 4 - 6r
-14r = -3
r = 3/14
Now we can substitute this value of r into either equation to find the value of s
s = 1 - 3r
s = 1 - 3(3/14)
s = 1 - 9/14
s = 5/14
So, the solution of the system of equations is (r,s) = (3/14,5/14)
We can check by substituting the solution into the original equations.
3r = 1 - s = 1 - 5/14 = 9/14
7s = 4 - 6r = 4 - 6(3/14) = 4 - 18/14 = -14/14 = -1
The solution is correct, since the left side of the equations is equal to the right side for the values (3/14,5/14)
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A graphed line passes through the points (12, 5) and (12, 9) A graphed line passes through the points (12, 5) and (12, 9)
The line that passes through (12, 5) and (12, 9) is a vertical line, and its equation is:
x = 12
How to find the equation of the line?We know that we have a line that passes through points (12, 5) and (12, 9).
Notice that the x-value of the two points is the same one, then we will have a vertical line of the form:
x = a
The x-value in both points is 12, then the constant value of the line is 12, thus the equation for the line that passes through these two points is:
x = 12.
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Anyone who genius math? Help me, ty
Answer:
B) -3
Step-by-step explanation:
(y - y₁) / (x - x₁) = slope
(8-2) / (m-5) = -3/4
cross-multiply to get:
-3(m-5) = 24
distribute -3 to get:
-3m + 15 = 24
subtract 15 from each side to get:
-3m = 9
m = -3
What does the y-intercept of the line of best fit represent?
The y-intercept indicates the y-value when the x-value is 0.
What does the y-intercept look like?
When a linear equation is expressed in slope-intercept form (y=mx+b), the constant variable b stands in for the y-intercept. As an illustration, the variable b corresponds to the number 8 in the equation y=6x+8. The y-intercept is shown here.
In regression, what does the y-intercept stand for?
In regression analysis, the point at which the regression line crosses the y-axis is known as the constant term. The y-intercept is another name for the constant.
The easiest way to depict the overall picture of what the collected data is indicating is with a straight line, which is what a linear regression does. It aids in our ability to determine whether the two things under investigation are related or have a correlation.
Learn more about the y-intercept
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