what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ?
Answers
Note that he probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
How did we arrive at this?The percent of eggs total 100.
Based on the frequency, we now that the eggs that are at least 19.75 mm include:
18.75 - 19.75 = 0.8
those that are less than 22.75mm long are:
19.75-20.75 = 4.0
20.75 - 21.75 = 17.3
21.75 - 22.75 = 37.9
Thus, the total of their frequencies are:
0.8 + 4.0 + 17.3 + 37.9 = those that are less than 22.75mm long but at least 19.75 long.
= 60
Thus, the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
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Full Question:
A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.
what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ? See attached image.
Related Questions
that M= 2 2 1 +6 2 -X 2 1 3 find X, for M to be singular
Answers
X must be equal to 0 for M to be singular.
For M to be singular, its determinant must be zero. So, we can set up the equation:
| 2 2 1 |
| 6 2 -x |
| 2 1 3 | = 0
Expanding the determinant along the first row, we get:
2 | 2 -x |
-6 | 1 3 | = 0
Multiplying the determinant of the 2x2 matrix by 2, we get:
4(-x - 3) - (-6)(2) = 0
Simplifying the left-hand side, we get:
-4x - 12 + 12 = 0
Solving for x, we get:
-4x = 0
x = 0
Therefore, X must be equal to 0 for M to be singular.
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Jake hears that 60% of respondents to a recent People Magazine survey said that their favorite fast food restaurant was Taco Bell. Jake believes this is way too high, as Taco Bell just isn't that good.
A SRS of peoples' favorite fast food restaurants is conducted across multiple locations. Of the 1080 respondents, 670 say that their favorite fast food restaurant is Taco Bell.
Conduct a hypothesis test at the a = 0.10 significance level to determine whether this People Magazine survey was true or if Jake has enough evidence to
conclude it wasn't.
Answers
Jake hears that 60% of respondents to a recent People Magazine survey said that their favorite fast food restaurant was Taco Bell. Jake believes this is way too high, as Taco Bell just isn't that good.
An SRS of peoples' favorite fast food restaurants is conducted across multiple locations. Of the 1080 respondents, 670 say that their favorite fast food restaurant is Taco Bell. Therefore, based on the hypothesis test, Jake does now not have enough evidence to finish that the People Magazine survey changed erroneously.
To conduct a hypothesis take a look at this situation, we can set up the following hypotheses:
Null Hypothesis (H0): The percentage of people who recall Taco Bell as their preferred speedy meal-eating place is 60% or better.
Alternative Hypothesis (H1): The share of those who recall Taco Bell as their favorite fast food restaurant is less than 60%.
We will use the binomial test to check those hypotheses. The importance level, alpha (α), is given as 0.10, which means that we need a 90% self-assurance degree for our test.
Let's calculate the p-value based on the furnished sample information and check it in opposition to our importance stage:
Sample length (n) = 1080
Number of respondents who selected Taco Bell (x) = 670
Assuming the null hypothesis is true (p = 0.6), the expected number of respondents choosing Taco Bell is n * p = 1080 * 0.6 = 648.
We can now use the binomial distribution to calculate the p-cost:
p-price = P(X ≤ x) = Σ(C(n, x) * p^x * (1-p)^(n-x)), in which Σ is the sum from 0 to x.
Calculating this sum for x = 670, we want to evaluate the p-fee against our importance stage.
Using statistical software programs or tables, we discover that the p-price is about 0.9995.
Since the p-value (0.9995) is greater than the importance degree (0.10), we fail to reject the null speculation. With this method, there isn't enough proof to conclude that the proportion of folks who don't forget Taco Bell as their favorite speedy meals eating place is less than 60%. Therefore, based on the given pattern, Jake does now not have enough evidence to finish that the People Magazine survey changed erroneously.
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f(x)=2x; g(x)=k·f(x) find K
Answers
As per the given situation, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.
In mathematics, a function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are often represented using function notation.
To find k, we need to know the value of g(x) for a specific value of x. Let's say we want to find k when x = 3. Then:
g(3) = k · f(3)
g(3) = k · 2(3)
g(3) = k · 6
If we know the value of g(3), we can solve for k:
g(3) = 15
15 = k · 6
k = 15/6
k = 2.5
Therefore, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.
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Look at the Box and Whisker Plot below, then identify the parts of the plot.
Identify:
Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
Interquartile Range:
Answers
Answer:
For the Box and Whisker Plot, these are the answers for all of the parts of the plot:
Minimum: The minimum is the lower end of the whisker which is 2
Maximum: The maximum is the upper end of the whisker which is 16
Median: The median is the thick line you see that goes down through the box plot which is the number 8
First Quartile: The lower end line of the box plot which is 4
Third Quartile: Known as the Second Quartile, this is the upper end line of the box plot which is 14
Interquartile Range: The Interquartile Range is the numbers that starts from the First Quartile to the Third Quartile which is the numbers from 4 to 14
Therefore, the answers are 2, 16, 8, 4, 14, and 4-14. Hope this helps with your homework or assignment!
-5th Grade Honors Student who learned this yesterday
Find the area of the below shape in mm^2
Answers
Answer:
(1600 + (3200π)/3) mm²
Step-by-step explanation:
1 cm = 10mm. (1cm)² = (10²)mm = 100mm²
area of rectangle = 2 X 8 = 16cm² = 1600mm²
radius of circle = 8cm.
area of full circle would be = π r² = π (8)² = 64π cm²
360° in full circle
area of triangular sector = (60/360) X (64π) = (32π)/3 cm² = (3200π)/3 mm²
total area = (1600 + (3200π)/3) mm²
help pls, will give brainliest
Find the perimeter of the figure. Simplify your answer.
Answers
The perimeter of the figure is 9k² + 13k - 8
Finding the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The perimeter of the figure is the sum of the side lengths
Using the above as a guide, we have the following:
Perimeter = -k + k² - 2 + 2k² + 5k + 2 + k² - 2 - k + 5k² + 10k - 6
When the expression is evaluated, we have
Perimeter = 9k² + 13k - 8
Hence, the perimeter of the figure is 9k² + 13k - 8
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Plan the media elements that you will use in your presentation. Think about what types of media
elements, such as charts or diagrams, could be used to support your ideas.
Provide at least three
media examples in the table below.
Media Type
Media Use
Important Idea to Communicate
Answers
Media Type: Chart
Media Use: To illustrate the growth of the company's revenue over the past five years
Important Idea to Communicate: The company has experienced significant growth in revenue over the past five years and is on an upward trajectory.
Media Type: Diagram
Media Use: To explain how a new product works
Important Idea to Communicate: The new product is innovative and easy to use, and it solves a common problem that many people face.
Media Type: Infographic
Media Use: To demonstrate the impact of climate change on the environment
Important Idea to Communicate: Climate change is a serious and pressing issue that affects all of us, and we need to take action to mitigate its effects.
The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2. Find the number
Answers
The number in the mathematical statemnent is 1 1/2
Calculating the value of the numberFrom the question, we have the following parameters that can be used in our computation:
The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2
Represent the number with x
So, we have the following equation
x + x/6 + 5x/2 + 7 = 12 1/2
So, we have
x + x/6 + 5x/2 = 5 1/2
Multiply through by 6
This gives
6x + x + 15x = 33
Evaluate the like terms
22x = 33
Divide through by 22
So, we have
x = 33/22
This gives
x = 1 1/2
Hence, the number is 1 1/2
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The value of the number is 1.5
How to determine the valueFirst, we have that;
Let the number be x
From the information given, we have that;
The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2. Find the number
This is represented as;
x + 1/6x + 5/2x + 7 = 25/2
find the LCM, we get;
42x + 7x + 105x + 294 /42 = 25/2
collect the like terms, we have;
154x + 294/42 = 25/2
cross multiply the values, we have;
(154x + 294) = 25 × 21
154x = 231
Divide both sides by the coefficient
x = 1. 5
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(8) = 21 B. h(-3) = -1 C. h(2) = 16 D. h(13) = 18
Answers
Answer:
The given function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we also know that h(8) = 19 and h(-2) = 2.
Since we know the range of h(x) is 1 ≤ h(x) ≤ 25, statement B cannot be true because it suggests a value of h(x) outside of this range.
Statement A suggests that h(8) = 21, which is outside the given range for h(x). Therefore, statement A cannot be true.
Statement C suggests that h(2) = 16, but we do not have any information about the value of h(x) at x = 2. Therefore, statement C may or may not be true.
Statement D suggests that h(13) = 18, but 13 is outside the domain of h(x). Therefore, statement D cannot be true.
Thus, the only statement that could be true for h is B. However, we cannot be certain that statement B is true without more information about the function h.
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Step-by-step explanation:
A land owner is planning to build a fenced in rectangular patio behind his garage, using his garage as one of the "walls." He wants to maximize the area using 60 feet of fencing. The quadratic function A(x) = x(60 - 2x) gives the area of the patio, where × is the width of one side. Find the maximum area of the patio (in f2).
A2
Answers
The maximum area of the patio is, 450 feet²
Now, Lets remove the brackets from the function's expression
A(x) = -2x² + 60x
So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max
As we know ,
X (max) = (X₁ + X₂)/2 ,
where X₁ and X₂ are the roots of the function A(x)
Lets find X₁ and X₂
x (60 - 2x) = 0
Hence, x₁ = 0
And, 60 - 2X₂=0
x₂ = 30
So, X max= (0 + 30)/2 = 15
So A max= A(15) = 15 (60-2 x 15) = 15 (60 - 30) = 15 x 30 = 450 feet²
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Find the value of a in parallelogram STUV a+6 a+17 a
Answers
Hello
S a T
2a + 6 / /
/ / a + 17
/ /
V a U
you want ST = VU (it's good) and SV = TU (not good)
2a + 6 = a + 17
2a - a = 17 - 6
a = 9
Power companies typically bill customers based on the number of kilowatt-hours used during a single billing period. A kilowatt is a measure of how much power (energy) a customer is using, while a kilowatt-hour is one kilowatt of power being used for one hour. For constant power use, the number of kilowatt-hours used is calculated by kilowatt-hours = kilowatts • time (in hours). Thus, if customers use 5 kilowatts for 30 minutes, they’ll have used 5 kilowatts • 1/2 hours = 2.5 kilowatt-hours.
Suppose the power use of a customer over a 30-day period is given by the continuous function P = f(t), where P is kilowatts, t is time in hours, and t = 0 corresponds to the beginning of the 30 day period.
A. Approximate, with a Riemann sum, the total number of kilowatt-hours used by the
customer in the 30-day period, and explain why your Riemann sum is an approximation of the desired property.
B. Derive an expression representing the total number of kilowatt-hours used by the
customer in the 30-day period, and explain your reasoning. (This expression should not be an approximation.)
C. Consider the following table of data for the function f(t)
f(t)
0 2.3
1 2.5
2 2.1
3 3.9
4 3.6
5 5.5
6 4.5
7 5.6
8 1.2
9 1.0
10 1.8
Recall that f(t) represents the number of kilowatts being used by a customer at time t hours from the beginning of the billing period. Estimate the number of kilowatt-hours the customer uses in this 10-hour period, and explain your method.
Answers
Answer:
30 wats due to electrocorrespond period of time
Step-by-step explanation:
according to plan b ratio 89 quart to a million
Power usage over time can be approximated by a Riemann sum or computed exactly by integrating the function representing the power usage. For the given 10-hour data, the total power usage can be estimated by summing up the products of the power usage and time interval.
Explanation:The power use of a customer over a 30-day period is given by a continuous function P = f(t), and we are asked to find the total number of kilowatt-hours used by the customer using Riemann sums and an exact formula.
A Riemann sum would be an approximation of the definite integral of the function P(t) from 0 to the total hours in a 30-day period, which can be obtained by adding up the products of the function values and the time intervals over the period. However, this is only an approximation because the actual power usage P may change within each time interval.The total number of kilowatt-hours can be computed exactly, without approximation, by integrating the function P(t) from 0 to the total hours in a 30-day period. This would give the exact total power usage because the integral essentially sums up all the instantaneous power usage over time, taking into account all the variations of P within each time interval.For the given power usage data over a 10-hour period, one can estimate the total power usage by using the Riemann sum, which is the sum of the products of the given power usages and the respective time intervals, i.e., 1 hour each.Learn more about Power usage calculation here:https://brainly.com/question/32137172
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Find out Monomials and Binomials from the following algebraic expressions:
**+9x²+7x-35, ln x, - 3x3 + 2x, x, x³, √x, 18x14x + 14,7x-1, 1
Sin (x), x³-5, e*, (x + 4)², - 3n+2y + 2x + 1, √x +y, 3-x.
Answers
Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms.
Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms. These terms can be added or subtracted, and they may contain variables, constants, and exponents. Binomials are commonly used in algebra to represent equations, formulas, and functions.
Monomials:
- 9x²
- 7x
- ln x
- -3x³
- 2x
- x
- x³
- √x
- 18x14x
- √x
- 7x-1
- 1
- Sin (x)
- x³
- e*
- √x +y
- 3-x
Binomials:
- 18x14x + 14
- (x + 4)²
- - 3n+2y + 2x + 1
- x³-5
Here are the monomials and binomials from the given algebraic expressions:
Monomials:
- ln x
- x
- x³
- √x
- 1
- Sin(x)
- e*
- 3-x
Binomials:
- +9x²+7x-35
- -3x³ + 2x
- 18x¹⁴x + 14
- 7x-1
- x³-5
- (x + 4)²
- -3n+2y + 2x + 1
- √x + y
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Suppose you invest $150 a month for 4 years into an account earning 8% compounded monthly.
After 4 years, you leave the money, without making additional deposits, in the account for another 23 years. How much will you have in the end?
Answers
Answer:
You will approximately have about 48,297.74
Step-by-step explanation:
Find the value of h for the parallelogram to the right. Find the value of h for the parallelogram to the right.
H=
Answers
The length of h in the parallelogram is 17.0 units.
How to find the side of a parallelogram?A parallelogram is a quadrilateral that has opposite sides equal to each
other and opposite sides parallel to each other.
Therefore, let's find the value of h in the parallelogram as follows:
Using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
18² - 6² = h²
h² = 324 - 36
h = √288
h = 16.97
Therefore,
h = 17.0 units
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can someone help me with this??
Answers
Help pleaseee!! I will give brainlist
Answers
The length FE in the circle is 6 units
The arc AE has a measure of 64 degrees
Calculating the length FEFrom the question, we have the following parameters that can be used in our computation:
The circle
Given that the lengths from the center to either chords are equal
This means that
FE = 6 units
Calculating the measure of arc AEFor the other circle, we have
BC = 58 degrees
AB = ED
The arc AE is calculated as
AE = 180 - BC - ED
Where
AB = ED = BC = 58 degrees
So, we have
AE = 180 - 58 - 58
Evaluate
AE = 64
Hence, the arc AE is 64 degrees
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PLS HELP Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5). Determine the vertices of image L′M′N′ if the preimage is rotated 180° counterclockwise about the origin.
L′(5, 1), M′(0, 1), N′(5, 2)
L′(−1, −5), M′(−1, 0), N′(−2, −5)
L′(−5, −1), M′(0, −1), N′(−5, −2).
L′(1, −5), M′(1, 0), N′(2, −5)
Answers
The coordinates of the triangle after transformation are:
L′(1, −5), M′(1, 0), N′(2, −5)
What are the coordinates after transformation?There are different methods of transformation such as:
Translation
Rotation
Reflection
Dilation
Now, a rotation of 180 degrees counterclockwise about the origin is equivalent to the coordinate transformation given as (x, y) → ( −x, −y) . Meanwhile, a rotation of 270 degrees counterclockwise about the origin is equivalent to the coordinate transformation (x, y) → ( y, -x) .
Applying the rule for rotation of 180 degrees counterclockwise to the coordinates L(−1, 5), M(−1, 0), N(−2, 5) gives us:
L'(1, -5), M'(1, 0), N'(2, -5)
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Help Quickly! The table shows bear population data gathered by researchers in the Wild Horse Forest. If the total bear population was 2,008 bears in May 2002, estimate the number of total bears counted in 2002 to complete the chart. (Zoom click the picture to see it better)
Answers
The estimated total number of bears in 2002 will be 1060.
How to estimate the population sizeTo estimate the population size, the mark-recapture formula is applied. This formula is used to determine the unknown population size. First, a selected sample from the population of bears has the number marked initially and the total population. The formula is: N = MC/R
In the given question,
M = 2008
C = 38
R = 72
So, N = (2008)(38)/72
= 76304/72
1059 which is estimated at 1060.
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Mrs. Golden wants to cove her 6.5 foot by 4 foot bulletin board with silver paper that comes in 1 foot squares. How many squares does Mrs. Golden need to cover her bulletin board? will there be any fractional pieces of silver pater left over? Explain why or why not.
Answers
Mrs. Golden will not have any Fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.
To cover Mrs. Golden's bulletin board, we need to calculate the total area of the board and then divide it by the area of each silver paper square to get the total number of squares required.
The area of the bulletin board can be calculated by multiplying its length and width:
Area of bulletin board = 6.5 ft x 4 ft = 26 sq. ft.
Since the silver paper comes in 1 ft squares, the area of each square is 1 sq. ft.
Therefore, the total number of silver paper squares required to cover the bulletin board can be calculated by dividing the area of the bulletin board by the area of each square:
Total number of squares required = Area of bulletin board / Area of each square
= 26 sq. ft / 1 sq. ft
= 26 squares
So, Mrs. Golden will need 26 silver paper squares to cover her bulletin board.
As the area of the bulletin board is not exactly divisible by the area of each silver paper square, there will be some fractional pieces of silver paper left over. The leftover fractional area will be equal to the remainder obtained when the area of the bulletin board is divided by the area of each square. In this case, the remainder is 0 sq. ft since the area of the bulletin board is exactly divisible by the area of each square.
Therefore, Mrs. Golden will not have any fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.
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Which of the following is equivalent to (3x+2)(3x+2)(3x-2)
Answers
Answer (3x−2)(3x+2)^2
Step-by-step explanation:
What is 64x625 in standard form
Answers
You are 22 years old and are starting a savings plan and will deposit $200 every 2 months until you retire. The account will give you 7% interest. How much do you expect your account to be worth when you retire at 67 years old?
Answers
The expected of your account to be worth when you retire at 67 years old is $1,118,473.61.
To calculate the future value of your savings account, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value of the account
PV = Present Value of the account
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the present value (PV) is zero because you haven't started saving yet. The interest rate (r) is 7% per year, or 0.07 as a decimal. You will be depositing $200 every 2 months, which means 6 times a year (n=6). You have 45 years until you retire (t=45), and want to find the future value (FV) of the account.
We can start by calculating the total number of deposits you will make:
45 years * 12 months/year / 2 months/deposit = 270 deposits
Each deposit will be for $200, so the total amount you will deposit is:
270 deposits * $200/deposit = $54,000
Now we can use the formula for compound interest to calculate the future value of the account:
FV = $0 * (1 + 0.07/6)^(645) + $54,000 * (1 + 0.07/6)^(645)
FV = $0 + $1,118,473.61
So, you can expect your savings account to be worth approximately $1,118,473.61 when you retire at 67 years old, assuming you make regular deposits of $200 every 2 months and earn an annual interest rate of 7%.
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Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2,400 bacteria selected from this population reached the size of 2,489 bacteria in one and a half hours. Find the hourly growth rate parameter.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
Answers
Hourly growth rate parameter is 1.97%
Given,
A sample of 2,400 bacteria selected from this population reached the size of 2,489 bacteria in one and a half hours.
Let,
y = population after given time x
x = time of passage in hours
p = size of initial population
k = constant for growth rate
[tex]y = pe^{kx}[/tex]
Substitute the values of variables,
2489 = 2400 e^1.5k
1.03 = e^1.5k
Take Ln on both sides to remove the exponent,
ln(1.03) = ln(e^1.5k)
0.029 = 1.5k
k = 0.029/1.5
k = 0.0197
k = 1.97%
Thus with the help of exponent the hourly growth rate parameter can be found out.
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PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
Answers
Answer:
[tex]y \leqslant x[/tex]
Given A(2, 4), what are the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin?
Answers
The coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).
To find the coordinates of A′, we need to apply the dilation formula:
A′ = (1.5)(A - O) + O
Where O is the center of dilation, which in this case is the origin (0, 0).
Substituting the values we have:
A′ = (1.5)(2, 4 - 0, 0) + (0, 0)
A′ = (3, 6) + (0, 0)
A′ = (3, 6)
Therefore, the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin are (3, 6).
To find the coordinates of A' for the dilation with a scale factor of 1.5 and center at the origin, follow these steps:
1. Identify the given point A(2, 4) and the scale factor 1.5.
2. The center of dilation is at the origin (0, 0).
3. Multiply the x-coordinate of point A by the scale factor: 2 * 1.5 = 3.
4. Multiply the y-coordinate of point A by the scale factor: 4 * 1.5 = 6.
5. The coordinates of A' after dilation are (3, 6).
So, the coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).
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What is the value of x?
URGENT
Answers
Answer:
14
Step-by-step explanation:
angle 90° is opposite the side x. angle 45° is opposite side 7√2.
x/sin 90 = (7√2)/sin 45
multiply both sides by sin 90 (sin 90 is = 1).
x = (7√2)/sin 45
= 14
I need 8 and 9 Please help
Answers
The measures of angles 8 and 9 are given as follows:
m < 8 = m < 9 = 28.5º.
How to obtain the angle measures?To obtain the angle measures, first we must consider that the sum of the measures of the internal angles of a triangle is of 180º.
Considering this, looking at the top triangle, we find the measure of angle 7 as follows:
m < 7 + 58 + 65 = 180
m < 7 = 180 - (58 + 65)
m < 7 = 57.
By the exterior angle theorem, an angle is supplementary with it's exterior angle, hence the measure of angle 6 is obtained as follows:
m < 6 = 180 - 57
m < 6 = 123º.
Triangle XWZ is an isosceles triangle, hence the measures of angles 8 and 9 are obtained as follows:
m < 8 + m < 9 + 123 = 180
m < 8 = m < 9 = (180 - 123)/2
m < 8 = m < 9 = 28.5º.
(isosceles triangle, these two angles have the same measure).
More can be learned about angle measures at brainly.com/question/25716982
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What is the equation of the straight line with gradient 5 that passes through
(3,9)?
Give your answer in the form y=mx+c, where m and c are integers or
fractions in their simplest forms.
Answers
Answer:
y = 5x - 6
Step-by-step explanation:
the equation of a line in gradient- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = 5 , then
y = 5x + c ← is the partial equation
to find c substitute (3, 9 ) into the partial equation
9 = 5(3) + c = 15 + c ( subtract 15 from both sides )
- 6 = c
y = 5x - 6 ← equation of line
The equation of the straight line with gradient 5 that passes through (3,9) is y = 5x - 6.
Explanation:To find the equation of a straight line with a given gradient, we can use the point-slope form of the equation: y - y1 = m(x - x1). In this case, the gradient is 5 and the given point is (3,9). Plugging in the values, we have:
y - 9 = 5(x - 3)
Expanding the equation, we get:
y - 9 = 5x - 15
Then, rearranging the equation to the form y = mx + c, we have
y = 5x - 6
Learn more about Equation of a straight line here:https://brainly.com/question/32765884
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Write a linear function representing Xavier’s gross income (earnings before taxes) in terms of the number of hours (x) he works.
3
Answers
Answer:
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
Step-by-step explanation:
To write a linear function representing Xavier's gross income in terms of the number of hours he works, we need the slope and the y-intercept.
Let's assume that Xavier earns a constant hourly rate of $3 per hour.
The slope of the linear function represents the rate at which Xavier's income increases per hour worked. In this case, the slope is $3, as his earnings increase by $3 for every hour worked.
The y-intercept represents Xavier's income when he hasn't worked any hours. Since he earns $0 when he hasn't worked any hours, the y-intercept is 0.
Therefore, the linear function representing Xavier's gross income (G) in terms of the number of hours (x) he works can be written as:
G = 3x
This equation shows that Xavier's gross income is equal to $3 multiplied by the number of hours he works.
