Determine whether the given value of the variable is a solution of the inequality.
Answers
Answer:
Yes, \(\frac{3}{4}\) is a solution of the inequality.
Step-by-step explanation:
Solution of an inequality is given by the values of the variable t ≥ \(\frac{2}{3}\)
Or t ≥ 0.67
If a solution of this inequality is t = \(\frac{3}{4}\)
Or t = 0.75
Since, on a number line 0.75 > 0.67
Therefore, \(\frac{3}{4}\) will be a solution of the inequality.
Related Questions
A^3=5 b^3=4 Find value of (ab^2)^-3
Answers
Answer:
1/80
Step-by-step explanation:
(ab²)^-3 = (a^-3)(b^-6) = \(\frac{1}{5}\)b^6
\(\frac{1}{5}\)b^6 = 1 /[5(b³)²] = 1 / (5·4²) = 1/80
The function f(1) = 60,000(2)
00(2) 410 gives the number
of bacteria in a population & minutes after an initial
observation. How much time, in minutes, does it
take for the number of bacteria in the population to
double?
Answers
It takes 10 minutes for the number of bacteria in the population to double.
To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.
The given function is f(t) = 60,000 * 2^(t/10).
To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:
120,000 = 60,000 * 2^(t/10).
Next, we can simplify the equation by dividing both sides by 60,000:
2 = 2^(t/10).
Since both sides of the equation have the same base (2), we can equate the exponents:
t/10 = 1.
To solve for t, we multiply both sides by 10:
t = 10.
Therefore, it takes 10 minutes for the number of bacteria in the population to double.
This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.
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Swornima is an unmarried nurse in a
hospital. Her monthly basic salary is Rs
48,000. She has to pay 1% social
security tax on her income up to Rs
5,00,000 and 10% income tax on Rs
5,00,001 to Rs 7,00.000. She gets 1
months' salary as the Dashain
allowance. She deposits 10% of her
basic salary in Citizen Investment Trust
(CIT) and gets 10% rebate on her
income tax. Answer the following
questions. (i) What is her annual
income? How much tax is rebated to
her? (iii) How much annual income tax
should she pay?
Answers
To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:
Monthly basic salary: Rs 48,000
Social security tax rate: 1%
Income tax rate on income up to Rs 5,00,000: 0% (no tax)
Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%
Dashain allowance: 1 month's salary
Deposit in Citizen Investment Trust (CIT): 10%
Rebate on income tax: 10%
(i) Annual Income:
Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:
Annual Basic Salary = Monthly Basic Salary x 12
= Rs 48,000 x 12
= Rs 5,76,000
Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:
Annual Income = Annual Basic Salary + Dashain Allowance
= Rs 5,76,000 + Rs 48,000
= Rs 6,24,000
Swornima's annual income is Rs 6,24,000.
(ii) Tax Rebate:
Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.
(iii) Annual Income Tax:
First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.
Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000
= Rs 1,24,000
Income Tax in this range = Taxable Income x Tax Rate
= Rs 1,24,000 x 0.1
= Rs 12,400
Now, let's calculate the total annual income tax:
Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000
= Rs 12,400
Next, we calculate the rebate on income tax:
Tax Rebate = Total Annual Income Tax x Rebate Rate
= Rs 12,400 x 0.1
= Rs 1,240
Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.
To summarize:
(i) Swornima's annual income is Rs 6,24,000.
(ii) Swornima's tax rebate is Rs 1,240.
(iii) Swornima should pay an annual income tax of R
Find the area of each sector. Round your answers to the nearest tenth.
Answers
Answer:
Area of the given sector = 130.9 cm²
Step-by-step explanation:
Area of a sector is given by the formula,
Area of the sector = \(\frac{\theta}{2\pi }\times (\pi r^{2})\)
Area of the sector of the circle given in the picture = \(\frac{\frac{5\pi }{6} }{2\pi }[\pi (10)^{2}]\)
= \(\frac{5}{12}(100\pi )\)
= 130.8996
≈ 130.9 cm²
PLEASE HELP!!! PLATO ALGEBRA 2
Answers
Answer:
(gof) (4) = 9
Hence, option A is true.
Step-by-step explanation:
f(x)=-x³
g(x)=|1/8x -1|
(gof) (4) = g{f(4)}
First wee need to determine f(4)
f(4)=-(4)³
= -64
so
(gof) (4) = g{f(4)} = g(-64)
= \(\left|\frac{1}{8}\left(-64\right)-1\right|\)
\(=\left|-\frac{1}{8}\cdot \:64-1\right|\)
\(=\left|-8-1\right|\)
\(=\left|-9\right|\)
\(\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a\)
\(=9\)
Thus,
(gof) (4) = 9
Hence, option A is true.
I need help with this
Answers
The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3
For the equation to be true, two scenarios need to be considered:
When the expression 6x-3 is positive and equals 3:
6x-3 = 3
When the expression 6x-3 is negative and equals -3:
6x-3 = -3
By solving these two equations, we can find the equivalent statement:
Solving 6x-3 = 3:
Adding 3 to both sides gives us:
6x = 6
Dividing both sides by 6:
x = 1
Solving 6x-3 = -3:
Adding 3 to both sides gives us:
6x = 0
Dividing both sides by 6:
x = 0
Therefore, the equivalent statement to |6x-3|=3 is:
6x-3=3 or 6x-3=-3, which can be further simplified to:
6x-3=3 or 6x-3=-3
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When Mr. Stanley's gas tank is full holds 15 gallons Mr. Stanley put 12 gallons of gas into the tank which filled it up how far was the gas tank before Mr. Stanley put 12 gallons in
Answers
O y=
y = cos(x + 1)
O y = cos(x+ 2x)
y-con~+5 )
Oy= cos(x+8)
©
Answers
Option C - y = cos(x + 5π) is the equation that most closely represents the graph. See attached graph.
What is an equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.
The graph of y = cos(x + 5π) is a cosine function that is shifted horizontally 5 units to the left compared to the standard cosine function.
The function is a periodic function that oscillates between -1 and 1, with each cycle shifted 5 units to the left compared to the standard cosine function.
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What is the y intercept?
Look at the picture.
Answers
Answer:
-1
Step-by-step explanation:
It hits the y-axis at -1, so the answer is -1.
Y=-3 Y=Ax2+4x-4 In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A) -4
B) -2
C) 2
D) 4
Answers
For constant A to be -4 (option 1) the system of equations have exactly one real solution.
NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?
We have given, y=-3
y= Ax^2+4x-4
Therefore, -3= Ax^2+4x-4
or, Ax^2+4x-1=0
For second order equation of ax^2+bx+c=0 have a solution for
x= [-b± (√b^2-4ac)]/2a] [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]
For single solution b^2-4ac=0
here, Ax^2+4x-1=0
4^2 - 4a(-1)=0
16+4a=0
a= -(16)/4
a= -4
option A is correct .
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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.
B) -2
The given system of equations can be written as:
Y = A*x^2 + 4*x - 4
We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:
x = [-b +/- sqrt(b^2-4ac)]/2a
where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.
Substituting these values into the equation, we get:
x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A
Simplifying this, we get:
x = [-4 +/- sqrt(16 + 16A)]/2A
For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.
This is only true when A is equal to -2. Therefore, the correct answer is B) -2.
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Solve -2x+4=7 by using a graph
Answers
The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (U.S. Department of Energy website, February 22, 2008). A portion of the data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car; Compact, Midsize, or Large. The column labeled Displacement shows the engine's displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled HwyMPG shows the fuel efficiency rating for highway driving in terms of miles per gallon.
a) Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement.
Let x represent the engine's displacement.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x
b) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?: ____%
c) Consider the addition of the dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize and the value of ClassLarge are both 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement and the dummy variables ClassMidsize and ClassLarge. Let x1 represent engine's displacement. Let x2 represent variable ClassMidsize. Let x3 represent variable ClassLarge.If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3
d) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %
e) Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. Let x1 represents engine's displacement. Let x2 represents variable ClassMidsize. Let x3 represents variable ClassLarge. Let x4 represents variable FuelPremium. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3 + ___x4
f) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %
Answers
a) Y=38.6594-5.4198x; b) 39.1% explained variation; c) Y=44.9379-5.9522x1-1.2758x2-2.0102x3; d) 49.9% explained variation; e) Y=45.2478-6.1081x1-0.9945x2-2.5692x3+0.9963x4; f) 53.1% .
a) The estimated regression equation for predicting fuel efficiency for highway driving is Y = 38.6594 - 5.4198x, where x represents the engine's displacement in liters.
b) The estimated regression equation explains 39.1% of the variation in the sample values of HwyMPG.
c) The estimated regression equation that includes the dummy variables ClassMidsize and ClassLarge is Y = 44.9379 - 5.9522x1 - 1.2758x2 - 2.0102x3, where x1 represents engine's displacement, x2 represents variable ClassMidsize, and x3 represents variable ClassLarge.
d) The estimated regression equation with the added dummy variables explains 49.9% of the variation in the sample values of HwyMPG.
e) The estimated regression equation that includes the dummy variable FuelPremium is Y = 45.2478 - 6.1081x1 - 0.9945x2 - 2.5692x3 + 0.9963x4, where x1 represents engine's displacement, x2 represents variable ClassMidsize, x3 represents variable ClassLarge, and x4 represents variable FuelPremium.
f) The estimated regression equation with all three dummy variables explains 53.1% of the variation in the sample values of HwyMPG.
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The revenue, in thousands of dollars, of a new flavor of liquor is given below as function of the number of gallons (in hundreds), x, sold:
\(r(x) = 50x - {x}^{2} \)
What is the maximum revenue? Use units
Answers
Answer:
$625,000
Step-by-step explanation:
The maximum revenue will be found where the derivative of the revenue function is zero.
r'(x) = 50 -2x = 0
50 = 2x
x = 25
When 2500 gallons are sold, the revenue is ...
r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands
The maximum revenue is $625,000.
B) What is the cost of making 35 items?
And c. The domain
Answers
The cost of making 35 items is 1100 and the domain is (-∞,∞)
The cost of making 35 items :
x = 35plug the value into the cost equation
C(35) = 10(35) + 800
C(35) = 350 + 800
C(35) = 1100
Hence, cost of making 35 items is 1100
The domain of the functionSince the value of X can be any real number, we can plug in any real number for x and get a real number output.
Hence, the domain = (-∞,∞)
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Alesha went to the movies. A popcorn is $3 more than a soda. She purchased 1 popcorn and 2 sodas. She spent $21. How much is a popcorn?
Answers
Answer: a popcorn is $9
Step-by-step explanation:
soda is $6
What is the distance from(-3,10) to (-3 ,-9) on a coordinate plane?? (30 PIONT)
-1 unit
-19 units
1 unit
19 units
I'll give brainlyest !!!
Answers
Answer:
The distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units
Step-by-step explanation:
The distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units[1].
To find the distance between two points on a coordinate plane, we use the distance formula based on the Pythagorean theorem. The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of the two points are (-3,10) and (-3,-9). Substituting these values into the distance formula, we get:
d = sqrt((-3 - (-3))^2 + (-9 - 10)^2)
= sqrt(0^2 + (-19)^2)
= sqrt(361)
= 19
Therefore, the distance from (-3,10) to (-3,-9) on a coordinate plane is 19 units.
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An engineer believes that there is a linear relationship between the thickness of an air filter in the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer test many filters of different thicknesses and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot?
Answers
Answer:
There should be a negative, linear association in the residual plot.
Step-by-step explanation:
Answer:
There should be no pattern in the residual plot ( I just took the quiz)
Step-by-step explanation:
Consider the triangle.
Which statement is true about the lengths of the sides?
45°
Each side has a different length.
OTwo sides have the same length, which is less than
the length of the third side.
O The three sides have the same length.
O The sum of the lengths of two sides is equal to the
length of the third side.
45
Answers
Answer:
two sides have the same length which is less than the length of third side
Step-by-step explanation:
The sum of the lengths of the two sides is equal to the length of the third side.
Option D is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
In a triangle,
The side opposite to the equal angle are equal.
Now,
We have two 45 angles.
This means,
The sides opposite to the 45 angles will be congruent.
And,
The other angle is 90 degrees.
Which is a right triangle
Thus,
The sum of the lengths of the two sides is equal to the length of the third side.
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A radio station claims that the amount of advertising per hour of broadcast time has an average of 13 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the z-score for this amount of advertising time.
Answers
Answer:
\(Z = 3.33\)
Step-by-step explanation:
Z-score:
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
\(\mu = 13, \sigma = 1.2\)
You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the z-score for this amount of advertising time.
We have to find Z when X = 17. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{17 - 13}{1.2}\)
\(Z = 3.33\)
Given that €1 = £0.72
a) How much is €410 in £?
b) What is the £ to € exchange rate?
Answers
362.67Step-by-step explanation:
Answer:
€410 = 0.72 x 410 = £295.2
thus, £295.2 is €410.
to determine the exchange rate from £ to €:
€1 = £0.72
Divide both sides by 0.72 which gives us
£1 = €1.389
What is the answer....................................................
Answers
Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.
Step-by-step explanation:
The following are the ages of 12 history teachers In a school district 29,30,32,32,39,41,46,49,50,51,52,53 minimum lower quartile median upper quartile maximum and interquartile range
Answers
The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
How does interquartile range work?Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.
According to the given information:To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.
Step 1: Find the median (Q2)
When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:
Median (Q2) = (41 + 46)/2 = 43.5
Step 2: Find the lower quartile (Q1)
The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:
Q1 = (32 + 32)/2 = 32
Step 3: Find the upper quartile (Q3)
The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:
Q3 = (50 + 51)/2 = 50.5
Now we have all the information we need to construct the five-number summary and interquartile range:
Minimum: 29
Lower quartile (Q1): 32
Median (Q2): 43.5
Upper quartile (Q3): 50.5
Maximum: 53
Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5
the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
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Maisie has saved up $50 to buy concert tickets, but the tickets cost $125. She is able to earn $15 per day by walking her neighbor’s dogs. How many days will Maisie have to walk the dogs to earn enough money to buy the tickets? Let d = the number of days worked.
Answers
Subtract 50 from 125
75
Divide by 15 (number of dollars per day)
5
If Maisie walks her neighbors dogs for 5 days, she will save up to a total of 125
Hope this helps :)
Answer:
✔ 50 + 15d = 125
What equivalent equation can you write after combining like terms?
✔ 15d = 75
How many days will Maisie have to walk the dogs?
✔ 5 days
Step-by-step explanation:
took. test.
In August Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8. how many short sleeve shirts were sold
Answers
The number of short sleeves that Maria sold is 819.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8.
The number of short sleeves will be:
= Ratio for short sleeve / Total ratio × Total number of clothes
= 9 / (8 + 9) × 1547
= 9/17 × 1547
= 819
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The difference of the present ages of the two brothers is 5 years . 6 years ago , if the product of their ages was 696, find the ratio of present age of elder brother and the younger brother.
Answers
The present age of the elder brother is in a ratio of 23 to the present age of the younger brother, which can be simplified to a ratio of 5 to 4.
Let's assume the present age of the elder brother is E years, and the present age of the younger brother is Y years. According to the given information, the difference in their ages is 5 years, which can be expressed as E - Y = 5.
Six years ago, the elder brother's age was E - 6, and the younger brother's age was Y - 6. According to the second given condition, the product of their ages at that time was 696, which can be expressed as (E - 6)(Y - 6) = 696.
To find the ratio of their present ages, we need to solve the two equations simultaneously. We can start by expanding the second equation:
(E - 6)(Y - 6) = 696
EY - 6E - 6Y + 36 = 696
EY - 6E - 6Y = 660
Now we can substitute the value of E - Y from the first equation into the second equation:
(E - Y) - 6E - 6Y = 660
5 - 6E - 6Y = 660
-6E - 6Y = 655
Simplifying the equation:
6E + 6Y = -655
Now we have a system of linear equations:
E - Y = 5
6E + 6Y = -655
Solving these equations, we find that the present age of the elder brother (E) is 23 years and the present age of the younger brother (Y) is 18 years.
Therefore, the ratio of the present age of the elder brother to the younger brother is 23:18, which can be simplified to 5:4.
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The average wingspan of monarch butterflies at a butterfly preserve is 8.5 centimeters with a stan deviation of 0.4 centimeter. If the wingspans are normally distributed, what is the probability, to t nearest hundredth, that monarch butterflies have a wingspan longer than 8.8 centimeters?
Answers
If the average wingspan of monarch butterflies at a butterfly preserve is 8.5. the probability, to t nearest hundredth, that monarch butterflies have a wingspan longer than 8.8 centimeters is : 0.23.
How to find the probability?First step is to standardize the value of 8.8 centimeters using the z- score formula:
z = (x - mu) / sigma
where:
x = wingspan
mu = mean wingspan
sigma= standard deviation
z standardized score
Substituting the given values
z = (8.8 - 8.5) / 0.4
z = 0.75
So,
P(z > 0.75) = 1 - P(z <= 0.75)
Using a standard normal distribution table P(z <= 0.75) = 0.7734
P(z > 0.75) = 1 - P(z <= 0.75)
= 1 - 0.7734
= 0.2266
= 0.23 ( Approximately)
Therefore the probability is 0.23.
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Fast help pls
13¢ per mile. Company B charges $50.50 and 8€ per mile. How much more does Company A
charge for x miles than Company B?
Answers
it might be 5 if you subtract 13 from 8
Help me out with this please!
No links to websites other than Brainly.
Answers
Problem 1
Answers:
It costs 1.72 dollars to send a letter that is 1.5 ounces
It costs 1.72 dollars to send a letter that is 2 ounces
In short, both answers are 1.72 dollars
--------------------------------
Explanation:
The piecewise function may seem really ugly and complicated, and I can understand why many don't like them, but they aren't too bad once you get used to it.
A piecewise function is simply a collection of many functions glued together. Instead of listing four different functions, your teacher has combined them all into one super function of sorts.
Here are the rules for this function
If \(0 < w \le 1\), then F(w) = 1.15If \(1 < w \le 2\), then F(w) = 1.72If \(2 < w \le 3\), then F(w) = 2.29If \(3 < w \le 3.5\), then F(w) = 2.86As you can see, the definition of F(w) will change depending on what w is.
If the weight is w = 1.5 ounces, then we're on the interval \(1 < w \le 2\) since 1.5 is between 1 and 2. So we go for the second definition shown above and we conclude that it will cost $1.72 to send this 1.5 ounce letter.
If you wanted, you could rewrite those four bulleted points into this equivalent form
If \(0 < w \le 1\), then the cost is $1.15 to send the letterIf \(1 < w \le 2\), then the cost is $1.72 to send the letterIf \(2 < w \le 3\), then the cost is $2.29 to send the letterIf \(2 < w \le 3.5\), then the cost is $2.86 to send the letterwhich is a less mathematical way of stating it. It might also help to make it into a chart, which would help customers better who may not want to deal with math.
A letter that's 2 ounces will cost $1.72 as well since w = 2 makes \(1 < w \le 2\) true.
In short, both the 1.5 ounce and 2 ounce letters cost $1.72 each.
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Problem 2
Answer: The graph is shown below (attached image)
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Explanation:
We have what is called a step function, or a staircase function. Either name will work. The graph consists of the horizontal portion of the stairs, but the vertical parts of the stairs are not drawn (or else we wouldn't have a function due to the vertical line test).
Note the placement of the open and closed endpoints. An open endpoint excludes the value in question, while a closed endpoint includes the value.
For instance, we have an open endpoint at (1, 1.72) while there's a closed endpoint at (1, 1.15). Each closed endpoint is directly connected to the "or equal to" portion of the inequality sign, and each open endpoint does not have the "or equal to" portion.
As the graph shows, we basically have the a certain flat cost for the four different regions. This corresponds to the costs given in the piecewise function. Each height is drawn from the list {1.15, 1.72, 2.29, 2.86}
The point labels of A,B,C,D,E,F,G,H are optional. I only put them in there to help identify which endpoints are open or closed. Points on the left side of each segment, or horizontal stair component, are open endpoints. Points on the right side are closed endpoints.
What is the radius of a circle that has a circumference of 3.14 meters?
Answers
Answer:
0.5
Step-by-step explanation:
Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
A golfer aims for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point reaches 80 feet up in the air. Noemi’s team is working together to write the quadratic equation to model the path of the golf ball in graphing form. She calculated the value of a = - 1/90 . Is she correct?
Answers
Answer:
No she isn't. The value of \(a\) is \(a=-\frac{1}{45}\)
Step-by-step explanation:
We know that all quadratic equation can be written in the following way :
\(y=ax^{2}+bx+c\) (I)
Where \(a,b\) and \(c\) are real numbers.
I will attach a drawing with the quadratic graph to understand the situation.
We know by looking at the drawing and analyzing it that the parabola passes through the points : \((0,0) ; (60,80)\) and \((120,0)\)
\((0,0)\) because we put our coordinates origin there.
\((120,0)\) because that's where the golf hole is.
And \((60,80)\) because we know that its highest point reaches 80 feet up in the air at the middle of the distance between its roots (property of a negative parabola).
Finally, we work with the three points and the equation (I) in order to find the values of \(a,b\) and \(c\) ⇒
The parabola passes through \((0,0)\) ⇒
\(y=ax^{2}+bx+c\) ⇒
\(0=a(0)^{2}+b(0)+c\) ⇒ \(c=0\)
The parabola passes through \((60,80)\) ⇒
\(80=a(60)^{2}+b(60)\) ⇒
\(80=3600a+60b\) (II)
The parabola passes through \((120,0)\) ⇒
\(0=a(120)^{2}+b(120)\) ⇒
\(0=14400a+120b\)
\(120b=-14400a\)
\(b=-120a\) (III)
Now if we use (III) in (II) ⇒
\(80=3600a+60(-120a)\)
\(80=3600a-7200a\)
\(3600a=-80\)
\(a=-\frac{1}{45}\) ⇒ \(b=\frac{8}{3}\)
Finally the equation of the parabola is
\(y=-\frac{x^{2}}{45}+\frac{8}{3}x\)
Where the value of \(a\) is \(a=-\frac{1}{45}\)
