Construct both a 98% and a 95% confidence interval for B1. B₁ = 40, s = 5.4, SSzz = 53, n = 16 98%
Answers
The 98% confidence interval for B₁ is (38.037, 41.963), and the 95% confidence interval for B₁ is (38.586, 41.414).
To construct a confidence interval for B₁, we need the standard error of B₁, denoted SE(B₁). Using the information, B₁ = 40, s = 5.4, SSzz = 53, and n = 16, we can calculate SE(B₁) as SE(B₁) = s / sqrt(SSzz) = 5.4 / sqrt(53) ≈ 0.741.
For a 98% confidence interval, we use a t-distribution with (n - 2) degrees of freedom. With n = 16, the degrees of freedom is (16 - 2) = 14. Consulting the t-table, the critical value for a 98% confidence level with 14 degrees of freedom is approximately 2.650.
Using the formula for the confidence interval, the 98% confidence interval for B₁ is given by B₁ ± t * SE(B₁) = 40 ± 2.650 * 0.741 = (38.037, 41.963).
For a 95% confidence interval, we use the same SE(B₁) value but a different critical value. The critical value for a 95% confidence level with 14 degrees of freedom is approximately 2.145.
The 95% confidence interval for B₁ is given by B₁ ± t * SE(B₁) = 40 ± 2.145 * 0.741 = (38.586, 41.414).
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Related Questions
helpppp plsss
How can you tell without doing division if a number is a multiple of 9?
Answers
1. List out the prime numbers of 9.
The prime numbers of 9 is 3.2. To prove, you can multiply 3 by 3.
3 x 3 = 9
6 3/4 ÷1 1/8
HELP ME PLEASE
Answers
Answer: 6
Step-by-step explanation:
6 3/4 x 1 1/8
27/4 x 8/9
Your answer is 6
a. For what value of c is the quantity Sum(x_1- c)^2 minimized? [Take the derivative with respect to c, set equal to 0, and solve.]
b.Using the result of part (a), which or the two quantities Sum(x, - x)^2 and Sum(x_i - mu)^2 will be smaller than the other (assuming that x yu,)?
Answers
Minimizing the Sum of Squared Deviations
In statistics, the objective of many analyses is to identify the values of parameters that minimize the sum of squared deviations between observed and expected values. A common example of this is finding the mean (average) of a set of values. In this context, the deviations are calculated as the difference between each observed value and the mean.
In the problem stated above, we have a sum of squared deviations given by the expression (x_1 - c)^2. The goal is to find the value of c that minimizes this expression. To do this, we will take the derivative of the expression with respect to c, set it equal to 0, and solve for c.
Taking the derivative with respect to c:
The derivative of (x_1 - c)^2 with respect to c is 2 * (x_1 - c) * (-1) = 2 * (c - x_1). Setting this equal to 0 and solving for c:
2 * (c - x_1) = 0
c = x_1
So, the value of c that minimizes the expression (x_1 - c)^2 is equal to x_1.
Comparing Sum(x_i - mu)^2 and Sum(x_i - x_1)^2:
Now, let's consider the two quantities Sum(x_i - mu)^2 and Sum(x_i - x_1)^2. Assuming that mu is the population mean and x_1 is a sample mean, we can say that Sum(x_i - mu)^2 will always be equal to or larger than Sum(x_i - x_1)^2. This is because the sample mean is an unbiased estimator of the population mean and has a smaller variance than the population mean. In other words, the sample mean will be closer to the observed values, on average, than the population mean, leading to smaller deviations and a smaller sum of squared deviations.
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a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
Answers
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
\(\pi\)(R +3)^2
Area of the pool is:
\(\pi R^2\)
Now, Our equation is:;
\(\pi\)(R +3)^2 - \(\pi R^2\) = 198
\(\pi\)((R+3)^2 - \(R^2\)) = 198
Open the inner bracket :
\(\pi\)(\(R^2+6R+9-R^2\)) = 198
\(\pi\)(6R +9) = 198
6R+9 = 198/\(\pi\)
6R = 198/\(\pi\) - 9
R = (198/\(\pi\) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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Write the equation of the line that is parallel to y-axis and passing through the point (3,-5)
Answers
Answer:
\(x=3\)
Step-by-step explanation:
Because this line is parallel to the y-axis, it is a vertical line. This is a special case where the formatting of its equation is different:
\(x=d\) where d is the x-intercept, or the value of x when the line crosses the x-axis
We're given that the line passes through the point (3,-5). Because this is a vertical line, the x-coordinates of the points it passes through will always stay the same. Therefore, the x-intercept (d) is 3.
\(x=3\)
I hope this helps!
The problem is 44+(7x+12)=180, what is x?
Answers
Answer:
x=
124 /7
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
Actually, the problem is 44+2(7x+12)=180. (There are two angles that equal 7x+12).
44+14x+24=180
68+14x=180
14x=180-68
14x=112
x=8
Consider the scalar function ψ(x, y, z) = x^2 + z e^y. What is the value of the contour surface passing through the point (1,0,2)? Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work. x = 2t3 + 3t2 - 12t y = 2t3 + 3t2 + 1 (a) Find the points on the curve where the tangent is horizontal. ( , ) (smaller t) ( , ) (larger t) (b) Find the points on the curve where the tangent is vertical. ( , ) (smaller t) ( , ) (larger t)
Answers
The value of the contour surface passing through the point (1, 0, 2) is ψ(1, 0, 2) = 1^2 + 2e^0 = 1 + 2 = 3.
To find the points on the curve where the tangent is horizontal, we need to determine the values of t that satisfy the condition for a horizontal tangent, which is when the derivative of y with respect to t is equal to 0.
Given the parametric equations:
x = 2t^3 + 3t^2 - 12t
y = 2t^3 + 3t^2 + 1
Taking the derivative of y with respect to t:
dy/dt = 6t^2 + 6t
Setting dy/dt equal to 0 and solving for t:
6t^2 + 6t = 0
t(6t + 6) = 0
From this equation, we have two possible solutions:
t = 0
6t + 6 = 0, which gives t = -1.
Therefore, the points on the curve where the tangent is horizontal are (0, y(0)) and (-1, y(-1)). To find the corresponding y-values, substitute the values of t into the equation for y:
For t = 0:
y(0) = 2(0)^3 + 3(0)^2 + 1 = 1
For t = -1:
y(-1) = 2(-1)^3 + 3(-1)^2 + 1 = -2 + 3 + 1 = 2
Hence, the points on the curve where the tangent is horizontal are (0, 1) and (-1, 2).
To find the points on the curve where the tangent is vertical, we need to determine the values of t that satisfy the condition for a vertical tangent, which is when the derivative of x with respect to t is equal to 0.
Taking the derivative of x with respect to t:
dx/dt = 6t^2 + 6t - 12
Setting dx/dt equal to 0 and solving for t:
6t^2 + 6t - 12 = 0
t^2 + t - 2 = 0
(t + 2)(t - 1) = 0
From this equation, we have two possible solutions:
t + 2 = 0, which gives t = -2
t - 1 = 0, which gives t = 1.
Therefore, the points on the curve where the tangent is vertical are (x(-2), y(-2)) and (x(1), y(1)). To find the corresponding x-values and y-values, substitute the values of t into the equations for x and y:
For t = -2:
x(-2) = 2(-2)^3 + 3(-2)^2 - 12(-2) = -16 + 12 + 24 = 20
y(-2) = 2(-2)^3 + 3(-2)^2 + 1 = -16 + 12 + 1 = -3
For t = 1:
x(1) = 2(1)^3 + 3(1)^2 - 12(1) = 2 + 3 - 12 = -7
y(1) = 2(1)^3 + 3(1)^2 + 1 = 2 + 3 + 1 = 6
Hence, the points on the curve where the tangent is vertical are (20, -3) and (-7, 6).
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In one of its Spring catalogs , Bean advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once.
A. In words, define the random variable X.
B. List the values that X may take on.
C. How many pages do you expect to advertise footwear on them ?
D. Calculate the standard deviation .
Answers
A) The random variable X is The number of pages that advertise footwear
B) X = 1, 2, 3.....20
C) On average 3.02 pages expect to advertise footwear on them
Bean advertised footwear on 29 of its 192 catalog pages.
we randomly survey 20 pages
the random variable X is
X = The number of pages that advertise footwear
It is given that 20 pages have been surveyed
so, X = 1, 2, 3.....20
The average value for binomial distribution can be calculated as follows
μ = np
= 20 (29/192)
= 580/192
=3.02
On average 3.02 pages expect to advertise footwear on them
Therefore, A) The random variable X is The number of pages that advertise footwear
B) X = 1, 2, 3.....20
C) On average 3.02 pages expect to advertise footwear on them
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what is the best way to solve ratios
Answers
When looking at a ratio problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole amount or a part of the whole and what you are trying to work out.
If you have been given the whole amount you can follow these steps to answer the question:
Add together the parts of the ratio to find the total number of shares.
Divide the total amount by the total number of shares.
Multiply by the number of shares required.
If you have been been given a part of the whole you can follow these steps:
Identify which part you have been given and how many shares it is worth.
Use equivalent ratios to find the other parts.
Use the values you have to answer your problem.
the cube root of 64 is 4. how much larger is the cube root of 65.1? estimate using the linear approximation.
Answers
The exact difference is 0.022916
Given that the cube root of 64 is 4
We need to find how much larger is the cube root of 65.1 using the linear approximation.
Linear approximations:
They are ways to define a line tangent to a curve. At a particular range near the tangent point, the line can serve as an approximation for the function. However, linear approximations are determined through a combination of differentiation.
Here, when the tangent point is defined at x=a
then the linear approximation of a function is defined as f(x) ≈ f(a)+f′(a)(x−a)
Consider a = 64 f(x) = x^(1/3)
f'(x) = 1/3 x ^(-2/3)
So linear approximation is f(x) = 4 + 1/3 (64)^(-2/3) * (x-64)
x = 65.1
f(65.1) = 4 + 1/3 (64)^(-2/3) * (65.1 - 64)
f(65.1) - 4 = 1/3 1.1 (64)^(-2/3) = 1/3 * 1.1 * 1/16 = 1.1 / 48 = 0.0229
The exact difference is 0.022916
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Help=pts 3and4!!!!!!!!
Answers
See picture. If it’s sideways, use the rotate button.
an acme bearings manager wants to compare the average ball bearing sizes from two different machines. she suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. she takes two independent, random samples of size 50, one from each machine. the mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. the mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. run a hypothesis test consistent with her suspicions. be sure to a. check all necessary assumptions; b. state the null and alternative hypotheses; c. decide whether or not to pool and explain why; d. calculate the test statistic and p-value; e. state your conclusion in a complete sentence based on the p-value.
Answers
a. The necessary assumptions are the population variances are equal and combine the two sample variances into one.
b. The null and alternative hypotheses are defined.
c. The sample sizes are equal, and the sample standard deviations are approximately equal, we can safely assume equal variances and pool the sample variances.
d. The value of test statistic is 3.15 and p value is 0.05.
e. The mean diameter of bearings from machine 2 is greater than that of machine 1 at a 5% level of significance.
To begin the hypothesis test, the manager needs to state the null and alternative hypotheses. The null hypothesis (H0) is the statement of "no difference" between the mean diameters of bearings from the two machines. The alternative hypothesis (Ha) is the statement that the mean diameter of bearings from machine 2 is greater than that of machine 1.
In symbols,
H0: μ1 = μ2 (where μ1 is the mean diameter of machine 1 and μ2 is the mean diameter of machine 2) and
Ha: μ2 > μ1.
Before conducting the hypothesis test, we need to check some assumptions.
The next step is to calculate the test statistic and p-value. We use a t-test to compare the means of two independent samples. The test statistic is calculated as:
t = (x₁ - x₂) / [s_p x √(2/n)]
where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, and n is the sample size.
Plugging in the numbers, we get:
t = (3.355 - 3.302) / [0.050 x √(2/50)] = 3.15
Using a t-distribution table with 98 degrees of freedom (n₁ + n₂-2), we find that the p-value associated with a t-value of 3.15 is less than 0.01.
Finally, we need to state our conclusion based on the p-value. Since the p-value is less than our significance level of 0.05, we reject the null hypothesis.
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Dunkin donuts is selling a 12 muffins for $3.60. What is the unit price per muffin? **
Answers
Answer:
30 cents per muffin
Step-by-step explanation:
3.60 divided by 12=.30
Answer: $0.30
Step-by-step explanation:
You have just signed up for a broadband home internet service that uses coaxial cable. which connector type will you most likely use?
Answers
Answer:
F type connector
Step-by-step explanation:
Use an F-type connector for broadband cable connections that use coaxial cable.
The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,
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F type connector
The F-connector is a coaxial RF connector commonly used for "wireless" terrestrial television, cable television, and common for satellite television and cable modems, usually with RG-6/U cable or with RG -59 / U.F connector is also known as threaded connector. There are two main types: 7mm (6.8mm) is the most common and used in coaxial cable, and 5mm connector is used in thin coaxial cable commonly used in satellite system.
The F-connector is an accessory that connects a coaxial cable to an electronic device or wall outlet.
Type F connectors are highly mechanical and electrically stable coaxial screw connectors for cable television (CATV), set-top boxes, cable modems and satellite television applications up to 4 GHz
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Which of the following is equal to the number sentence listed below?
(21 × 25) + (21 × 12)
Answers
21 + 25 = 46
21 + 12 = 33
46 + 33 = 79
therefore the answer is 79
Step-by-step explanation: thank you for listening
.
The price p of a pizza is $6.75 plus $0.75 for each of the t toppings on the pizza.
Answers
While hanging out at Yum Yum's, you observe the following ice cream orders.
Chocolate
Mint Chip
Chocolate
Chocolate
Vanilla
Blueberry
Mint Chip
Mint Chip
Vanilla
Chocolate
Chocolate
Vanilla
[You will use the above data to answer this question and the next question.]
Choose the correct statement.
The relative frequency of Vanilla is 3 and its absolute frequency is 0.25.
The absolute frequency of Vanilla is 3 and its relative frequency is 0.33.
The relative frequency of Vanilla is 3 and its absolute frequency is 0.33.
The absolute frequency of Vanilla is 3 and its relative frequency is 0.25.
Answers
The correct statement is: The absolute frequency of Vanilla is 3 and its relative frequency is 0.33.
In the given ice cream orders, Vanilla appears 3 times. This count of 3 represents the absolute frequency of Vanilla. Absolute frequency refers to the actual number of occurrences of a particular observation or event. To calculate the relative frequency of Vanilla, we divide its absolute frequency by the total number of observations. In this case, the total number of ice cream orders is 12. Thus, the relative frequency of Vanilla is 3/12, which simplifies to 0.25 or 25%.
Relative frequency represents the proportion or percentage of the total observations that a specific event or observation constitutes. It provides a standardized measure that allows for comparison across different data sets. In this context, Vanilla comprises 25% of the ice cream orders, indicating its relative popularity compared to other flavors in the sample.
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Please help due in 10 minutes
Answers
Answer:
I got B or number 2
Step-by-step explanation:
Answer
(5-5)x
Step-by-step explanation:
the rest of the equal -5(x-1) and this one equals 0
so D
Spare an answer sir?
Answers
Answer:
yes
Step-by-step explanation:
3+ 9*4 = 3 + 36 = 39
39 is bigger than 15
Answer:
yes
Step-by-step explanation:
Just you will subsititute by the point in the inequality
(3, 9) the first number is x and the second is y
then
3 + 4 * 9 = 39
for sure 39 > 15
I hope this is hlepful to you
Which expression is equal to 6(r2 – 3) + 2(r2 + 1)?
8r squared - 20
6r squared -2
8r squared -16
6r squared +2r-16
pls, help 20 points!
Answers
Answer:8r squared -16
Step-by-step explanation:
**Determine if the lines are parallel, perpendicular or neither**
Line A 9x – 3y = 6
Line B 6x – 2y = 8
O perpendicular
O parallel
O neither
O No answer text provided.
Answers
Answer:
a parrallel
b parrallel
find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n= 60, p= 0.3
Answers
The mean is just the multiplication of \(n\) and \(p\) so \(60 * 0.3\) = \(18\)
Variance is \((1 - p) * n * p\) so \(0.7 * 60 * 0.3 = 12.6\)
So the variance is \(12.6\)
The standard deviation is just the root of the variance so: \(\sqrt{12.6}\) = \(3.55\) rounded to the nearest hundredth. :D
Use the method of Lagrange multipliers to find the dimensions of the rectangle of the greatest area that can be inscribed in the ellipse x^2/16+y^2/9=1 with sides parallel to the coordinate axes.
Answers
The dimensions of the rectangle with the largest area that can be inscribed in the ellipse using the Lagrange multipliers approach are 2a = 2x = 16/√(145) and 2b = 2y = 12/√(145).
We want to find the dimensions of a rectangle with sides parallel to the coordinate axes that have the greatest area and can be inscribed in the ellipse x²/16 + y²/9 = 1. Let the rectangle's measurements be 2a and 2b, where an as well as b are the lengths of the ellipse's semi-axes.
The area of the rectangle is A = 4ab. We want to maximize A subject to the constraint x²/16 + y²/9 = 1.
We set up the Lagrangian function L(x,y,λ) = 4ab + λ(x²/16 + y²/9 - 1), where λ is the Lagrange multiplier. Taking the partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we get:
∂L/∂x = 2λx/16 = 0
∂L/∂y = 2λy/9 = 0
∂L/∂λ = x²/16 + y²/9 - 1 = 0
The first two equations give x = y = 0, or λ = 0. However, these are not the maximum points, since they correspond to a rectangle with zero areas.
We solve the third equation for λ in terms of x and y: λ = 16/(16x²/9 + 9y²/16). Substituting this into the first two equations, we get:
x/8 = y/6
x²/16 + y²/9 = 1
Solving these equations simultaneously, we get x = ±8/√(145) and y = ±6/√(145). Hence, 2a = 2x = 16/√(145) and 2b = 2y = 12/√(145) are the dimensions of the rectangle with the largest area that can be inscribed in the ellipse (145).
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In an effort to save money, Zoe decides to cut back on the number of meals she eats at restaurants each month. She tracks the
number of meals she eats out each month for a year. The data is recorded in the dot plot below.
O
1
2
3
4
5 6 7 8 9 10 11 12 13 14 15
Number of Meals
Which statement about the data is true?
0
The data is skewed left with an outlier.
a
The data is skewed left with no outlier.
The data is skewed right with an outlier.
The data is skewed right with no outlier.
Answers
Answer:
The data is skewed left with an outlier.
Explanation:
Skewness occurs when the entries of the data set are either distributed more to the left or more to the right on the number line. In this case, most of the entries lie to the right, so the data set is skewed left.
We are given that angle ABC and are congruent, and that angle GHI and angle DEF are congruent. By the , the measure of angle ABC is equal to the measure of angle DEF, and the measure of angle GHI is equal to the measure of angle DEF. By the substitution property, the measure of angle ABC is equal to .
Answers
Answer:
By the Substitution property, the measure of angle ABC is equal to GHI.
Step-by-step explanation:
According to the Question,
Since we have,
Angle ABC and angle DEF are congruent ⇒ ∠ABC = ∠DEF-------(1 ) Similarly,angle GHI and angle DEF are congruent ⇒ ∠GHI = ∠DEF------(2)On substituting the value of from equation (1) to equation (2)
We get, ∠ABC = ∠GHI ∴ ∠ABC ≅ ∠GHI
Thus, By the Substitution property
The measure of angle ABC is equal to angle GHI.
Please help me with this question, suppose a fair die is rolled
successively ten times in a row. Write a formula for the
probability of rolling exactly three numbers greater than four.
Answers
The probability of rolling exactly three numbers greater than four when a fair die is rolled successively ten times in a row is approximately 0.0902.
Let X be the number of times a number greater than four appears when a fair die is rolled ten times in a row.
Then X follows a binomial distribution with parameters n = 10 and p = 2/6 = 1/3, as each roll has six equally likely outcomes, and two of those outcomes correspond to a number greater than four.
To find the probability of rolling exactly three numbers greater than four, we need to calculate P(X = 3).
Using the formula for the binomial distribution, we have:
P(X = 3) = C(10, 3) * (1/3)³ * (2/3)⁷
where C(10, 3) = 10!/(3!7!) is the number of ways to choose 3 rolls out of 10 that give us a number greater than four.Thus,
P(X = 3) = C(10, 3) * (1/3)³ * (2/3)⁷ = (10*9*8)/(3*2*1) * (1/3)³ * (2/3)⁷ = 120 * (1/27) * (128/2187)≈ 0.0902
So, the probability of rolling exactly three numbers greater than four when a fair die is rolled successively ten times in a row is approximately 0.0902.
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The father is three times as old as his son, Joe. Joe is four years older than his sister, Alexa. Alexa is twice as old as Rocky. Let R equal Rocky's age. Write an algebraic expression. Please Help!
Answers
Answer:
R=(F/3-4)/2
Step-by-step explanation:
Father = F
Joe = J
Alexa = A
R= Rocky
F=3J
A+4=J
A=2R
F/3=J
A=J-4
A=F/3-4
2R=F/3-4
R=(F/3-4)/2
Hope this helps!
Find the size of the final unknown interior angle in a polygon whose other interior angles are:
162°, 110°, 115°, 138°, 105° and 98°.
the answer is 172 sorry
Answers
The measure of the final unknown interior angle in the polygon is 172°.
What is the missing interior angle of the polygon?Given the other interior angles of the polygon to be:
162°, 110°, 115°, 138°, 105° and 98°
If we are to find the final interior angle, it means the polygons have 7 interior angles.
Hence, it is a heptagon.
Sum of the interior angle of a heptagon equals 900 degrees.
Let, the final interior angle be x:
Hene:
162° + 110° + 115° + 138° + 105° + 98° + x = 900°
Solve for x:
728 + x = 900
728 - 728 + x = 900 - 728
x = 900 - 728
x = 172°
Therefore, the missing interior angle is 172°.
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The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.
Filling Water Tank
Place the segments in the correct order from the least to the greatest rate of increase in the water level.
A
0
B
→x
Answers
Answer: BCA
Step-by-step explanation:
what is the equation of the mjddle for the function f(x)?
f(x)=3cos(x)-2.5
Answers
please give brainliest
Answer:
To shift the graph of the function f(x) = cos(x) downward by 2.5 units, you can subtract 2.5 from the function. The equation of the middle for the shifted function would be:
f(x) = cos(x) - 2.5
Answer:
y=-2.5
Step-by-step explanation:
f(x) =0 -2.5
y=-2.5
Hope this helped buddy
peace ️