Write a linear function $f$f with f of 0 is equal to 7$f\left(0\right)=7$f(0)=7 and f of 3 is equal to 1$f\left(3\right)=1$f(3)=1 . $f\left(x\right)=$f(x)=
Answers
The required linear function is
f(x) = -2x+ 7
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Let the linear function f(x) = ax + b
f(0) = 7
a \(\times\) 0 + b = 7
b =7
f(x) = ax + 7
f(3) = 1
3a + 7 = 1
3a = 1 - 7
3a = -6
a = \(-\frac{6}{3}\)
a = -2
The given linear function is
f(x) = -2x+ 7
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Related Questions
the life of light bulbs is distributed normally. the variance of the lifetime is 625 and the mean lifetime of a bulb is 520 hours. find the probability of a bulb lasting for at most 549 hours. round your answer to four decimal places.
Answers
Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.
Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.
To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).
The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.
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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%
Explanation:Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.
To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.
We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.
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(a) Find an angle between 0 = 0° and 9 = 360° that has the same sine as sin(103°) (but is not 0 = 103°) 0= has the same sin as sin(103°). 0° and 0 360° that has the same cosine as cos(242") (but is not 0 = 242") has the same cos as cos(242") Note: Do not include units in your answers. Just give the numerical values.
Answers
An angle between 0° and 360° with the same sine as sin(103°) (but not equal to 103°) is approximately 463°.
An angle between 0° and 360° with the same cosine as cos(242°) (but not equal to 242°) is approximately -118°.
To find an angle between 0° and 360° that has the same sine as sin(103°) and an angle between 0° and 360° that has the same cosine as cos(242°), we can use the periodicity of the sine and cosine functions.
For the angle with the same sine as sin(103°):
Since sine has a period of 360°, angles with the same sine repeat every 360°. Therefore, we can find the equivalent angle by subtracting or adding multiples of 360° to the given angle.
sin(103°) ≈ 0.978
To find an angle with the same sine as sin(103°), but not equal to 103°, we can subtract or add multiples of 360° to 103°:
103° + 360° ≈ 463° (not equal to sin(103°))
103° - 360° ≈ -257° (not equal to sin(103°))
Therefore, an angle between 0° and 360° with the same sine as sin(103°) (but not equal to 103°) is approximately 463°.
For the angle with the same cosine as cos(242°):
Similar to sine, cosine also has a period of 360°. Therefore, angles with the same cosine repeat every 360°.
cos(242°) ≈ -0.939
To find an angle with the same cosine as cos(242°), but not equal to 242°, we can subtract or add multiples of 360° to 242°:
242° + 360° ≈ 602° (not equal to cos(242°))
242° - 360° ≈ -118° (not equal to cos(242°))
Therefore, an angle between 0° and 360° with the same cosine as cos(242°) (but not equal to 242°) is approximately -118°.
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What is x≧6 (six grade inequalities) please help
Answers
Answer:
Step-by-step explanation:
ince
x
=
6
is a vertical line, there is no y-intercept and the slope is undefined.
Slope: Undefined
y-intercept: No y-intercept
Find two points on the line.
x
y
6
0
6
1
Graph the line using the slope, y-intercept, and two points.
Slope: Undefined
y-intercept: No y-intercept
x
y
6
0
6
1
image of graph
f(x,y,z)=x^2+y^2+z^2 s:z=x^2+y^2=49,0≤z≤49
Answers
The given function is F(x, y, z) = x^2 + y^2 + z^2, subject to the constraint z = x^2 + y^2 = 49 and 0 ≤ z ≤ 49.
What is the objective of the given problem and what are the constraints?The objective of the problem is to find the minimum or maximum value of the function F(x, y, z) = x^2 + y^2 + z^2, while satisfying the constraint z = x^2 + y^2 = 49 and the range of 0 ≤ z ≤ 49.
This means that we need to optimize the value of F(x, y, z) within the given constraints.
To solve this problem, we can use the method of Lagrange multipliers. By introducing a Lagrange multiplier λ, we can set up the following equations:
2x = 2λx,
2y = 2λy,
2z = 2λ(z - 49),
x^2 + y^2 - 49 = 0.
By solving these equations simultaneously, we can find the values of x, y, z, and λ that satisfy the equations and the given constraints.
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The algebra question is in the image
Answers
Answer:
B
Step-by-step explanation:
A or constant is the answer
Simplify.
(6^2)^4
O 6^6
O 6^8
O 36^4
0 6^2
Answers
Answer:
its b and c dude
Step-by-step explanation:
Answer:
6^8
Step-by-step explanation:
Hope that helped!
Plz, mark brainiest, only 3 more till I level up!
Have a great day!!
A business traveler was wondering how the taxi meters in a particular city work. She kept track of the distance traveled on each of her taxi rides and the amount
she paid for each of her fares. She then plotted the data points and found that while they didn't exactly form a line (probably due to varying times spent stuck in
traffic), they could be approximated by the line y = 1.75x+2.25, where x is the distance traveled in miles and y is the fare in dollars. According to the model, about
how much will a 3 mile ride cost?
A. $5.25
B. $6.75
С. $7.50
D. $8.50
Answers
please help quickly i really need this bad whoever get it correct ill give brainliest
Answers
Answer:C
Step-by-step explanation: Two negatives makes a positive so it would be a positive answer witch would make the answer 10000 so it would be C
Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of x = 1 + r. $1,000 is deposited at the start of the first year, an
additional $300 is deposited at the start of the next year, and $500 at the start of the following year.
Write an expression for the value of the account at the end of three years in terms of the growth factor x.
Answers
The polynomial expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500x
Interest earned per year, x = 1 + r
First year :
deposit = $1000Year end balance = 1000 × x = 1000x
Second year :
Initial balance = 1000x + 300Year end balance = (1000x + 300)x = 1000x² + 300x
Third year :
Initial balance = 1000x² + 300x + 500Year end balance = (1000x² + 300x + 500)x = 1000x³ + 300x² + 500x
Therefore, the expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500
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Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be placed in the corner of a city park. The garden is a right triangle with base 25, and height 30.
Draw the garden such that 1 unit on the grid below represents 5
Answers
Answer:
Given that the garden is a right triangle with base 25m start and height 30 m The length of the hypothenus can be achieved by using pythagorean theorem. Please find the attached file for the diagram. I made a large unit for the sake of clarity.
Answer:
6.0 on the left side 5.0 at the bottom 7.8 on the right side
Step-by-step explanation:
The coach of a college basketball team categorizes the number of points
scored by the team in each game, with the categories being 51-57, 58-64,
65-71, and 72 or more. If the following data represent the numbers of
points scored in the last 10 games, how many games were in the 58-64
category?
51, 70, 63, 59, 56, 75, 60, 55, 67, 64
O A. 1
OB. 4
O C. 3
OD. 2
Answers
A graph is a way to represent a lot of data in a visual format. thus the number of games in the category 51-57 are 3.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. the line of the graph is a function that follows the graph.
The categories and the data points can be arranged as;
51 - 57 = 51, 56, 55
58 - 64 = 63, 59, 60, 64
65 – 71 = 70, 67
72 or more = 75
Therefore, the number of games in the category 51-57 are 3.
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Simplify:
3x^3+ 2y^3 + 6x^3 + 5y
A) 9x^3+2y^3+5y
B) 9x^6+2y^3+5y
C) 5xy^3+6x^3+5y
D) 9x^6+7y^4
Answers
Answer:
\(9x^3 +2y^3 + 5y\)
Step-by-step explanation:
\(3x^3+ 2y^3 + 6x^3 + 5y\)
Combine like terms:
\(3x^3+ 2y^3 + 6x^3 + 5y\)
\((3x^3+6x^3) +2y^3 + 5y\)
\(9x^3 +2y^3 + 5y\)
Hope this helps!
explanation: combine like terms.
3x^3+6x^3= 9x^3
Lolly wrote a total of 10 pages over 5 hours. How many hours will Lolly have to spend writing this week in order to have written a total of 20 pages?
Answers
Answer:
10 hours
Step-by-step explanation:
since she spent 5 hours writing 10 pages. you just have to multiple by 2 to know how long it will take to write 20 pages
What is the factorization of 2x^2 + 7x + 6?
Answers
Answer:
( x + 2)(2x + 3)
Step-by-step explanation:
\(2 {x}^{2} + 7x + 6 \\ \\ = 2 {x}^{2} + 4x + 3x + 6 \\ \\ = 2x(x + 2) + 3(x + 2) \\ \\ = ( x + 2)(2x + 3)\)
Plz someone answer these!
Answers
Describe a pattern in the sequence of numbers. Predict the next number.
1.) 256, 64, 16, 4, ... ________.
2.) 2, 6, 18, 54, ... _______
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
In the first sequence,
let's take ratio of the next term with its preceding term, so we will get the common ratio ~
\(\qquad \sf \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)
So, we can imply that The next term of the sequence is 1/4 times the previous term.
hence, the unknown term will be 1/4 times of previous term.
That is : 1/4 × 4 = 1Therefore, the next term here is 1
In the second sequence,
Do the same procedure as above, we will get common ratio as :
\(\qquad \sf \dashrightarrow \: \cfrac{18}{6} = 3\)
So, the next term is 3 times the preceding term, that is :
3 × 54 = 162Therefore, the next term is 162
pattern: divide by 4
next term: 1
2.
pattern: multiply by 3
next term: 162
Water runs from a hose into a bucket at a steady rate. The amount of water in the bucket for the time it is being filled is shown in the graph.
The point (12, 5) is on the graph. What do the coordinates tell you about the water in the bucket?
Your answer:
Answers
The point (12, 5) on the graph indicates that the bucket has been filled with 5 units of water after 12 units of time.
What is graph?
In mathematics, a graph is a visual representation of a set of data or mathematical relationships between variables.
The coordinates (12, 5) on the graph indicate that after 12 units of time, the amount of water in the bucket is 5 units.
This means that the bucket is being filled at a steady rate, and the rate at which the water is being added to the bucket is consistent over time.
The horizontal axis, usually the x-axis, represents time while the vertical axis, usually the y-axis, represents the amount of water in the bucket.
The graph provides a visual representation of the relationship between the amount of water in the bucket and time, which can be used to make predictions about the amount of water in the bucket at different points in time.
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What is the range of this function?
6802
10
12
OA. (-8, -3, 5, 7}
B. (-3, 7, 8, 12)
C. (-8, -3, 5, 6, 7, 8, 10, 12}
D. (6, 8, 10, 12)
or wo
-7
Answers
Answer:
Step-by-step explanation:
it is
Suppose 1 and 2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 5, x = 113.7, s1 = 5.01, n = 5, y = 129.9, and s2 = 5.33. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.)
Answers
The 95% confidence interval for the difference between the true average stopping distances for cars equipped with system 1 and system 2 is approximately (-32.68, 0.28)
To calculate the 95% confidence interval (CI) for the difference between the true average stopping distances for cars equipped with system 1 and system 2, we can use the formula:
CI = (x1 - x2) ± t * sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
- x1 and x2 are the sample means of system 1 and system 2, respectively.
- s1 and s2 are the sample standard deviations of system 1 and system 2, respectively.
- n1 and n2 are the sample sizes of system 1 and system 2, respectively.
- t is the critical value from the t-distribution for the desired confidence level and degrees of freedom.
We have:
x1 = 113.7, s1 = 5.01, n1 = 5 (for system 1)
x2 = 129.9, s2 = 5.33, n2 = 5 (for system 2)
The critical value of t for a 95% confidence level with (n1 + n2 - 2) degrees of freedom can be found using a t-distribution table or a statistical software.
For simplicity, let's assume it to be 2.262 (which is close enough for a sample size of 5).
Substituting the values into the formula, we get:
CI = (113.7 - 129.9) ± 2.262 * sqrt((5.01^2 / 5) + (5.33^2 / 5))
CI = -16.2 ± 2.262 * sqrt(5.01^2 / 5 + 5.33^2 / 5)
CI = -16.2 ± 2.262 * sqrt(25.0502 + 28.1082)
CI = -16.2 ± 2.262 * sqrt(53.1584)
CI = -16.2 ± 2.262 * 7.2847
CI = -16.2 ± 16.4812
CI ≈ (-32.68, 0.28)
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−3.5(8.5+5.5y)=−15.5
Answers
Answer: y= -14.25/19.25
Step-by-step explanation:
−3.5(8.5+5.5y)=−15.5 can be write as
-29.75 - 19.25y= -15.5
-19.25y = 14.25
y= -14.25/19.25
Four years ago, Sam invested in Grath Oil. She bought three of its $1,000 par value bonds at a market price of 93.938 and with an annual coupon rate of 6.5%. She also bought 450 shares of Grath Oil stock at $44.11, which has paid an annual dividend of $3.10 for each of the last ten years. Today, Grath Oil bonds have a market rate of 98.866 and Grath Oil stock sells for $45.55 per share. Use the scenario above to consider which statement best describes the relative risk between investing in stocks and bonds.
Answers
Answer:
C. The market price of the bonds is more stable than the price of the company's stock.
Step-by-step explanation:
In the context, Sam bought some bonds at the market price from Grath Oil and also invested in buying corporate shares which paid a dividend of $3.10 for each share annually for a period of ten years.
At present the market value of the bonds of Grath Oil is more. The market price of the bond is the amount of the money to be paid in an open market to buy a bond.
So the bond's market price is much more stable than the price of the company's stock. It is riskier to invest in company stocks.
Answer:
ik you dont need it no mo but its c
Step-by-step explanation:
i just want the points
How does place value
help me subtract decimals?
Answers
Place Value helps you subtract decimals because without it it would be a mess. Everything has to be in order if not you get the wrong answer
3. Determine the width of a picture frame if the length is
11 inches and its diagonal length is 14.2 inches.
U
14,2
Answers
The width of the frame is = 156.2 inches.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The length = 11 inchesThe diagonal = 14.2 incheslength * diagonal = 11 * 14.2156.2 incheslearn more about unitary method click here:
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Pls help with this answer
Answers
When b is 3, the value of the expression \(2b^3 + 5\) is 59.
To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.
Given that b = 3, we substitute this value into the expression:
\(2(3)^3 + 5\)
First, we evaluate the exponent, which is 3 raised to the power of 3:
2(27) + 5
Next, we perform the multiplication:
54 + 5
Finally, we add the two terms:
59
Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.
In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.
It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.
It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.
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PLS HELP (its an image by the way :) )
Answers
The diameter is 7.2. What is the circumference?
Answers
Answer:
22.62 cm exactly or limited to de precision of this calculator (13 decimal places). Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.
Answer:
22.6
Step-by-step explanation:
circumference is pi x diamter so:
7.2 x pi (3.142)
=22.61
round it so 22.6
Please hurry I will mark you brainliest
Grandpa khan’s age is 8 years is more than five times his grandson's age. The sum of their ages is 88 years. How old are they? Write an equation and “let statements”
Answers
\(\boxed{\large{\bold{\blue{ANSWER~:) }}}}\)
see this attachment
Step-by-step explanation:
age of grandpa=72
age of grandson =16
A shipping company uses a formula to determine the cost for shipping a package: c = 2.79 + 0.38p, where c is the cost of shipping and p is the number of pounds. What is the cost of shipping a package that weighs 8 pounds?
Answers
Using the formula they gave us:
Cost of shipping = 2.79 + 0.38(8)
Cost of shipping = 2.79 + 3.04
Cost of shipping = 5.83(currency unit)
What is the mean medium and mode of $0.99,$0.99,$1.49,$1.49,$1.49,$1.99,$1.99,and$2.49
Answers
Mean: $1.615
Median: $1.49
Mode: $1.49
Given the graph below, what is the zero(s)?
Answers
Answer:
-2 and 2
Step-by-step explanation:
The term 'zeros' refers to the roots/x-intercepts of the function. In this instance, the zeros of the function are -2 and 2.