Answer:
[tex]144.9\leq x\leq 145.5[/tex]
Step-by-step explanation:
Let x represent actual weight of object.
We have been that the weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs.
[tex]|\text{Actual}-\text{Ideal}|\leq \text{Tolerance}[/tex].
Upon substituting our given values, we will get:
[tex]|x-145.2|\leq 0.3[/tex]
Applying absolute value rule [tex]|u|\leq a=-a\leq u\leq a[/tex], we will get:
[tex]-0.3\leq x-145.2\leq 0.3[/tex]
Add 145.2 on each side:
[tex]-0.3+145.2\leq x-145.2+145.2\leq 0.3+145.2[/tex]
[tex]144.9\leq x\leq 145.5[/tex]
Therefore, our required range will be [tex]144.9\leq x\leq 145.5[/tex].
if f(2)=3 and f'(2)=5 find the equation of the tangent line and the normal line to the graph of y=f(x)
The equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
What is tangent and normal to a curve?A tangent is a line touching the curve at one distinct point, and this distinct point is called the point of contact.
The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.
Given is a function f(x) and f(2) = 3 and f'(2) = 5.
We can find the tangent to the curve at x = 2 by finding the value of the derivative of f(x) at x = 2. The slope of the tangent at x = 2 is -
m[T] = (dy/dx) [at x = 2] = f'(2) = 5
Now. the equation of tangent can be written as -
(y - y₁) = m [T] (x - x₁)
and
f(2) = 3
At x = 2, y =3 →
y - 3 = 5 (x - 2)
y - 3 = 5x - 10
y = 5x - 10 + 3
y = 5x - 7
This is the equation of the tangent.
In order to find the slope of Normal at x = 2, use the following formula -
m [T] x m [N] = -1
m [T] = 5
Then -
m [N] = - 1/5
The equation of the normal is given by -
(y - y₁) = m [N] (x - x₁)
(y - 3) = -1/5 (x - 2)
y - 3 = -x/2 + 2/5
y = -x/2 + 2/5 + 3
y = -1/2 x + 3.4
This is the equation of Normal.
Therefore, the equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
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The lines p and q intersect at point O. What is the value of x?
X =
Answer:
The value of x is 16 .
Step-by-step explanation:
Definition of vertically opposite angles
Two lines crosses angles opposite to each other are called vertically opposite angle .
Thus
(2x + 13)° = (3x-3)°
(Vertically opposite angles )
2x + 13 = 3x-3
2x - 3x = -3-13
-x = -16
x = 16
Therefore the value of x is 16 .
mai is saving money to buy a game so far she has saved 20$ which is four fifths of the total cost of the game how much does the game cost
Select all ratios equivalent to 5:15.
2:60, 20:9, 7:21, 1:3
denise bought 5.2 pounds of rice for $5.29. using the unit rate, how much would 2 pounds of rice cost?
Parallelogram ABCD is dilated to form parallelogram EFGH. Side BC is proportional to side CD.
What corresponding side is proportional to segment FG?
what is 475.53 minus 67.37
2/3 of a circle is what percent of a circle
What is the end of the CD account time when the money can be withdrawn?
Maturity date
End date
Completion date
Withdrawal date
Correct Answer: maturity date
Question 8
8 pts + 4 pts for the best answer Thanks!
Question is attached.
How many points are shared by concentric circles?
a. 0
b. 1
c. 2
d. infinite points
Answer:
Option a. 0
Step-by-step explanation:
As we know if we draw two circles with same center but with the different radii, they neither touch each other nor intersect. This is true not only for two circles but for infinite number of the circles having the same center. They never have the common points to share. Set of points lying on each concentric circles are different.
Therefore Option a. 0 points is the correct answer.
Joe paid $14.00 for a board game this is 70% of the original price what was the original price
start off by finding 10% of $14. in order to find 10%, divide it by 70 which gives 2. you now need to make the 30% to add to the 70%, by timesing the 2 by 3to give 6. now all you need to do it add the 6 to 14 to make 20!
so your answer is $20
Answer:
The original price was $20.00
Step-by-step explanation:
Joe paid $14.00 for a board game.
This is the 70% of the original price.
Let the original price of a board game be x
70% of x = $14.00
0.70x = 14.00
x = [tex]\frac{14}{0.7}[/tex] = $20.00
The original price was $20.00
Simplify i³⁸. [i=√(-1)]
The 38th power, [tex]i^{38[/tex] simplifies to -1.
To simplify [tex]\( i^{38 \),[/tex] you can start by recognizing the pattern that powers of i repeat every four terms. This means that [tex]\( i^{4\),[/tex] equals 1, [tex]\( i^{8 \),[/tex] also equals 1, and so on. Therefore, [tex]\( i^{38 \),[/tex]can be simplified as follows:
[tex]\[ i^{38} = i^{4 \cdot 9 + 2} \][/tex]
Since [tex]\( i^4 \)[/tex] is equal to 1, we have:
[tex]\[ i^{38} = (i^4)^9 \cdot i^2 = 1^9 \cdot (-1) = -1 \][/tex]
So,[tex]\( i^{38} \)[/tex] simplifies to -1.
Complete question is:
Simplify i³⁸. [i=√(-1)]
solve: log 3=.5, then log 1/9=?
What is the range of the function on the graph
Answer:
all real numbers less than or equal to 3
Step-by-step explanation:
The range of the function is set of all y value for which the function is defined
To find out the range we look at the maximum or minimum point on the graph
Maximum point on the graph that is vertex is (-1,3)
x=-1 and y=3
The graph of y is below 3 (vertex)
So the range of the function is set of all real numbers less than or equal to 3
Which relationship between x and y in the equation shows a proportional relationship?
y=3x
y=5(x+3)
y+5=x+3
y=5x+3
What does the equal sign with an arrow mean?
7 × 30 = 7 × ___ tens
7 × 30 = 7 × 3 tens.
To solve 7 × 30 in terms of tens, we first observe that 30 can be written as 3 tens since 30 equals 3 × 10.
Therefore:
7 × 30 can be rewritten as 7 × (3 × 10), which simplifies to 7 × 3 tens.
So, 7 × 30 = 7 × 3 tens.
John invested $400 in a savings account. How much interest will he earn in 5 years if the imterest rate is 7%?
1. Solve for Y 1/2y+4x=z
At a local University 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probability. A) At least one has a computer
B) None have computers
What is the difference between 7 and -8?
If AB is parallel to CD and the slope of CD is -8, what is the slope of AB ?
Answer:
and only if they have the same slope. Any two vertical lines are parallel. Therefore, the slope of AB is -8 if AB is parallel to CD.
Step-by-step explanation:
Solve the equation sin theta = 0.3 to the nearest tenth. Use the restrictions 90degrees < theta < 180degrees.
A)
θ=107.5
B)
θ=162.5
C)
θ=197.5
D)
θ=17.5
The length of a rectangle is 4/5 feet. The width is 5/8 feet. How much greater is the length of the rectangle than the width?
A.)7/40 feet
B.)1/5 feet
C.)3/20 feet
D.)1/3 feet
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the least education?
a. accountant
b. architect
c. pharmacist
d. surveyor
Answer:
D
Step-by-step explanation:
The horizontal axis of the graph is Salary.
Given there is a positive correlation between salary and education, means that as if education increase, salary increase OR if education decrease, salary decrease, and vice versa.
Out of the 4 choices, they wanted to know the one that requires LEAST education. So we will look at the bar that has LEAST salary.
Looking at the graph and bars, out of the 4 choices, Surveyor has the LEAST SALARY, so SURVEYOR would require LEAST EDUCATION. Answer choice D is right.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}.[/tex] Option (d) is correct.
Further Explanation:
Given:
The options are as follows,
(a). Accountant
(b). Architect
(c). Pharmacist
(d). Surveyor
Explanation:
Correlation is a relationship between the two events. The change in one will affect the in change of another one.
There are two type correlations.
A positive correlation mean that if one increases the second event will also increase and if one decreases the second event will also decreases.
A negative correlation mean that if one increases the second event will also decrease and if one decreases the second event will also increase.
There is a positive correlation between salary and education.
The least salary in the given option is of surveyor and has least education.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}[/tex]. Option (d) is correct.
Learn more:
Learn more about normal distribution https://brainly.com/question/12698949 Learn more about standard normal distribution https://brainly.com/question/13006989 Learn more about confidence interval of meanhttps://brainly.com/question/12986589
Answer details:
Grade: High School
Subject: Statistics
Chapter: Correlation
Keywords: correlation, salary, education, positive correlation, based, careers, least education, accountant, architect, pharmacist, surveyor, negative correlation, average salaries, personal trainer,
show that cos(3theta) = cos^3(theta)-3 cos(theta)sin^2(theta) ... use this to find an equation in rectangular coordinates for the curve r= 4 cos (3theta)......
ANY HELP ? ...?
18 is 240% of what? basic percent equation ...?
The recipe calls for 1 egg, which makes 8 slices of pumpkin pie. how many eggs would be needed to make 56 slices of pumpkin pie ?
To find the number of eggs needed for 56 slices of pumpkin pie when the recipe calls for 1 egg for 8 slices, simply set up a proportion and solve. In this case, you would need 7 eggs for 56 slices of pie.
To determine how many eggs are needed to make 56 slices of pumpkin pie, we use a proportion. Given that 1 egg makes 8 slices of pie, we set up the proportion as follows:
1 egg / 8 slices = x eggs / 56 slicesSolving for x, which represents the number of eggs needed for 56 slices, we get that x = 7 eggs.
GRAPHING EXPONENTIAL FUNCTIONS
1. If (-1, y) lies on the graph of y = 3^x+1, then y =
a) 0
b) 1/3
c) 1
2. If (x, 1/100) lies on the graph of y = 10^x, then x =
a) 2
b) -1/2
c) -2
3. If (-1, y) lies on the graph of y = 2^2x, then y =
a) -4
b) 1/4
c) 1
4. What is the relationship between the graphs of y = 2^x and y = 2^-x?
a) reflections over the x-axis
b) reflections over the y-axis
c) reflections over y = x
5. If (3, y) lies on the graph of y = -(2x), then y =
a) 1/8
b) -6
c) -8
6. Which of the following equations is not exponential?
a) y = 1x
b) y = (1/2)x
c) y = -2x
7. If (-2, y) lies on the graph of y = 4^x, then y =
a) -16
b) 1/16
c) 16
8. If (-3, y) lies on the graph of y = 3^-x, then y =
a) -27
b) 1/27
c) 27
9. If (-3, y) lies on the graph of y = 3^x, then y =
a) 1/27
b) -1
c) -27
10. If (-3, y) lies on the graph of y = (1/2)^x, then y =
a) 8
b) 1/8
c) -8
The detailed answer provides the solutions to a series of questions involving finding specific values for y given x in various exponential equations, as well as recognizing the relationship between graphs of exponential functions and identifying which equations are not exponential.
1. If (-1, y) lies on the graph of y = 3ˣ+1, then y equals the value of the function when x is -1. Therefore, y = 3⁻¹ + 1 which simplifies to y = 1/3 + 1 = 4/3, which is not one of the provided options.
2. If (x, 1/100) lies on the graph of y = 10ˣ, then we need to find the value of x such that 10ˣ equals 1/100. 10ˣ = 1/100 is equivalent to 10ˣ = 10⁻², so x = -2.
3. If (-1, y) lies on the graph of y = 2²ˣ, we substitute x with -1. Then y = 2²*⁻¹ = 2⁻² = 1/4.
4. The relationship between the graphs of y = 2ˣ and y = 2⁻ˣ is that they are reflections over the y-axis. When x is replaced by -x in the function, the resulting graph is a reflection over the y-axis.
5. If (3, y) lies on the graph of y = -(2ˣ), then y is the negative value of 2 raised to the power of 3, which is -8. So, y = -8.
6. Among the given equations, y = -2ˣ is not exponential because it lacks the variable as an exponent. So, y = -2ˣ is not exponential.
7. If (-2, y) lies on the graph of y = 4ˣ, then y = 4⁻² = 1/16.
8. If (-3, y) lies on the graph of y = 3⁻ˣ, then y = 3⁻⁽⁻³⁾ = 3³ = 27.
9. If (-3, y) lies on the graph of y = 3ˣ, then y = 3⁻³ = 1/27.
10. If (-3, y) lies on the graph of y = (1/2)ˣ, then y = (1/2)⁻³ = 2³ = 8.