Answer:
No, q=15 is not a solution to the inequality.
Step-by-step explanation:
As given, q=15. So, substituting is the best way to solve this problem.
Step 1: Substitute
[tex]\frac{15}{5}=3[/tex]
[tex]15-20=-5[/tex]
Step 2: Substitute values into inequality
[tex]3 < -5[/tex]
Equation is false since 3 is a bigger value than -5.
Hope this helps ya!
Solve:
6n-5=-35
R=12=25
9x+3=21
Answer:
6n - 5 = -35
Adding 5 on both sides, we get
6n = -30
Dividing by 6 on both sides, we get
n = -5
R/12 = 25
Multiplying both sides by 12, we get
R = 300
9x + 3 = 21
Subtracting 3 from both sides, we get
9x = 18
Dividing by 9 on both sides, we get
x = 2
find the solution of the system of equations 2x + 6y = -16 -6x - 3y = -27 i need a answer neoowww
The solution of the system of equations are (7,-5).
Define about the system of equations?A set or group of equations that you solve all at once is referred to as a "system" of equations. The fundamental linear system comprises two equations as well as two variables. Linear equations (those that graph simply straight lines) are easier to understand than non-linear ones.The system of equations:
2x + 6y = -16 and -6x - 3y = -27
2x + 6y = -16
Divide by 2
x + 3y = -8 ..eq 1
-6x - 3y = -27 ..eq 2
Use elimination method.
Add eq 1 from 2
x + 3y -6x -3y = -8 - 27
-5x = -35
x = 7
3y = -8 - 7
y = -15/3
y = -5
Thus, the solution of the system of equations are (7, -5).
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two cyclists, 48 mi apart, start riding towards each other at the same time. one cycles twice as fast as the other. if they meet 1 hr later, at what average speed is each cyclist traveling?
The slower cyclist travels at a speed of 16 miles per hour, while the faster cyclist travels at twice the speed, which is 32 miles per hour.
Let's assume that the slower cyclist's speed is x mi/h, then the faster cyclist's speed is 2x mi/h.
Since they are riding towards each other, their relative speed is the sum of their speeds, which is 3x mi/h.
They travel a total distance of 48 mi in 1 hour, so we can use the formula:
distance = rate x time
48 = 3x x 1
Solving for x, we get:
x = 16
Therefore, the slower cyclist's speed is 16 mi/h and the faster cyclist's speed is 32 mi/h.
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HELP NOW!
Without graphing, identify the key features of the given function.
-vertex
-axis of symmetry
-direction of opening
-number of x-intercepts
-compression/expansion
[tex]f(x)=2(x-3)^2+5[/tex]
Explain your answers on how you found each answer.
The key features of the given function include the following:
Vertex = (3, 5)
Axis of symmetry = 3.
Direction of opening: upward.
Number of x-intercepts = 0.
Expansion.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that its vertex can be determined as follows:
y = a(x - h)² + k
f(x) = 2(x - 3)² + 5
Vertex, (h, k) = (3, 5)
Axis of symmetry, Xmax = -b/2a = -(-6)/2(1) = 6/2 = 3.
In conclusion, the function does not have an x-intercept and it represents an expansion because the scale factor is greater than one (1) i.e k = 2.
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Benzoic acid is used to determine the heat capacity of bomb calorimeters because it can be obtained in pure form and its energy of combustion is known very accurately (-26.43 kJ/g).
Determine the calorimeter constant of the calorimeter that had a temperature increase of 9.199 degrees Celsius when 3.500 g of benzoic acid was used.
Benzoic acid is used to determine the heat capacity of bomb calorimeters because it can be obtained in pure form and its energy of combustion is known very accurately (-26.43 kJ/g).
The calorimeter constant is -2873.5.
Determine the calorimeter constant of the calorimeter that had a temperature increase of 9.199 degrees Celsius when 3.500 g of benzoic acid was used.To determine the calorimeter constant, follow these steps:
Explanation:
1. Calculate the energy released by the benzoic acid combustion: Multiply the mass of benzoic acid by its energy of combustion.
Energy released = mass × energy of combustion
Energy released = 3.500 g × -26.43 kJ/g = -92.505 kJ
2. Convert the temperature increase to a change in energy: Multiply the temperature increase by the mass of benzoic acid.
ΔEnergy = temperature increase × mass of benzoic acid
ΔEnergy = 9.199°C × 3.500 g = 32.1965 J
3. Determine the calorimeter constant: Divide the energy released by the change in energy.
Calorimeter constant = Energy released / ΔEnergy
Calorimeter constant = -92.505 kJ / 32.1965 J
Note: We need to convert the units to be consistent, either to J or kJ.
1 kJ = 1000 J, so -92.505 kJ = -92505 J.
Calorimeter constant = -92505 J / 32.1965 J = -2873.5
The calorimeter constant is -2873.5.
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WILL GIVE BRIANLIST TO BEST ASNWWR
Richard buys a new car for $28,000. The car depreciates in value by 9% each year. Which of the following uses the variable y to represent the value of the car after t years in an exponential model to represent the situation?
y=28,000(1.09)
y=28,000(91)
y-28,000(-9)
y=28,000(0.09)
The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.
The formula for the exponential model is what?A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.
The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t
Where:
Y is equal to the car's value after t years.
In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.
t equals the amount of years
The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t
By condensing the formula, we obtain the following result: y = 28,000(0.91)t
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A ball is thrown from an initial height of 3 meters with an initial upward velocity of 30(m)/(s). The ball's height h (in meters) after t seconds is given by the following.
h=3+30t-5t^(2)
Find all values of t for which the ball's height is 13 meters.
Answer: -451
Step-by-step explanation:
so, the height we are trying to find is 13 meters.
13=3+30t-5t^2
so, we can go ahead and pull that number in.
now we have to subtract the 3 to try and get as much as possible over on the other side to find t.
10=30t-5t^2
Step-by-step explanation:
h(t) = 3 + 30t - 5t²
the height is set to 13 meters.
since the ball will go up and then come back down again, we expect 2 points of time, when the ball is at 13 meters high. if any at all, by the way (keep that in mind for similar questions, the object might not even reach a certain height).
13 = 3 + 30t - 5t²
10 = 30t - 5t²
2 = 6t - t²
0 = -t² + 6t - 2
the general solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ±sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -1
b = 6
c = -2
t = (-6 ±sqrt(6² - 4×-1×-2))/(2×-1) =
= (-6 ±sqrt(36 - 8))/-2 = (-6 ±sqrt(28))/-2 =
= (-6 ±sqrt(4×7))/-2 = (-6 ±2×sqrt(7))/-2 =
= 3 ± sqrt(7)
t1 = 3 + sqrt(7) = 5.645751311... seconds
t2 = 3 - sqrt(7) = 0.354248689... seconds
on its way up the ball will pass the mark of 13 meters after about 0.35 seconds, and on its way back down it will pass the mark of 13 meters again after about 5.65 seconds.
Shapera has three sources of income. she earns $15 for each lawn she mows. She earns $7 per hour working part-time at a pet store. She earns $20 each day she delivers newspapers.
Part A: Write an expression that represents her total earnings.
Part B: In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the computer? Explain your answer
(Please answer as fast as possible!!)
Answer:
Step-by-step explanation:
Mowed lawns 15 times 7 = 105 Working at pet store 7 times 36 = 252 Delivers newspapers 20 times 7 = 140 105+252+140= 497The pseudoinverse of the null (all zero) vector is the transposed null vector. The pseudoinverse of a non-nullvector is the conjugate transposed vector divided by its squared magnitude:x+ = { 0,. if x = 0;x-1 otherwise.
What is a pseudoinverse?
The pseudoinverse of the null (all zero) vector is indeed the transposed null vector. This is because the null vector has no direction or magnitude, so when we calculate its pseudoinverse, we are essentially looking for a vector that when multiplied with the null vector gives us the identity matrix. Since there is no such vector, the pseudoinverse is simply the transposed null vector. This is denoted by x+ and is defined as follows:
x+ = {0, if x = 0; x*-/(||x||^2), otherwise.
Here, x* denotes the conjugate transpose of x, and ||x||^2 represents the squared magnitude of x. Essentially, we are finding a vector that when multiplied with x gives us the identity matrix (or as close to it as possible). This vector is the pseudoinverse, and it is computed using the formula above.
So in summary, the pseudoinverse of the null vector is the transposed null vector, while the pseudoinverse of a non-null vector is the conjugate transposed vector divided by its squared magnitude.
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What is the value of 2(÷)3+if x = 72, y = 24, and z=12?
the value of the expression 2 ÷ 3 + (x / y) - z, where x = 72, y = 24, and
z = 12, is approximately -8.33.
However, assuming that the intended expression is 2 ÷ 3, we can evaluate it using the rules of arithmetic. Division is performed before addition, so the expression can be rewritten as:
2 ÷ 3 + (x / y) - z
Substituting the given values of x, y, and z, we get:
2 ÷ 3 + (72 / 24) - 12
To evaluate this expression, we need to perform the division first:
2 ÷ 3 + 3 - 12
Next, we can simplify by combining like terms:
2 ÷ 3 - 9
To evaluate this expression, we need to perform the division first:
0.666666... - 9
Finally, we can simplify by subtracting:
-8.333333...
Therefore, the value of the expression 2 ÷ 3 + (x / y) - z, where x = 72, y = 24, and z = 12, is approximately -8.33.
It's important to note that if the intended expression was not 2 ÷ 3, the answer may be different. Additionally, it's important to be clear and precise when writing mathematical expressions to avoid ambiguity and confusion.
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There are 35 counters in a bag the ratio of red to blue counters is 2:5 there are 9 more blue counters the rest are green how many green counters are there?
there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information. The given information provides us with the ratio of red to blue counters in a bag, which is 2:5. This means that for every 2 red counters in the bag, there are 5 blue counters.
Let the number of red counters in the bag be 2x, where x is a constant. Then, the number of blue counters in the bag is 5x. We are also given that there are 9 more blue counters than before, so the new number of blue counters is 5x + 9.
We know that there are 35 counters in total, so we can write an equation based on this information:
2x + 5x + 5x + 9 = 35
Simplifying this equation, we get:
12x + 9 = 35
Subtracting 9 from both sides, we get:
12x = 26
Dividing both sides by 12, we get:
x = 2.1667
Since we cannot have a fraction of a counter, we can round x up to 3.
Therefore, the number of red counters in the bag is 2x = 2(3) = 6, and the number of blue counters in the bag is 5x + 9 = 5(3) + 9 = 24.
Finally, we can find the number of green counters in the bag by subtracting the number of red and blue counters from the total number of counters:
35 - 6 - 24 = 5
So there are 5 green counters in the bag.
In summary, there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.
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Find the area of the following shapes. Please help
A=?cm2
The shape is an identical parallelogram and the area is equal to 30 square centimeters.
Area of parallelogramIn calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.
we shall calculate for the area of the shape by evaluating the area of the one parallelogram and then multiply the result by two as follows:
area of one identical parallelogram = 5 cm × 3 cm
area of one identical parallelogram = 15 cm²
area of identical parallelogram shape = 2 × 15 cm²
area of identical parallelogram shape = 30 cm²
Therefore, the area for the identical parallelogram shape is equal to 30 square centimetres.
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the probability that no cars will pass by a section in an hour is 0.4 (modelled as a poisson process. further, no car passed by in the last 2 hours. what is the probability that you have to wait at least 1 more hour (after the 2 hours) for the next car?
The probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.
The given problem can be solved using the Poisson distribution. Let [tex]$\lambda$[/tex] be the average rate of cars passing through the section per hour. Then, since the probability of no cars passing in one hour is 0.4, we have:
[tex]$P(X=0)=\frac{\lambda^0e^{-\lambda}}{0!}=0.4$[/tex]Solving for [tex]$\lambda$[/tex], we get [tex]$\lambda= -ln(0.4) \approx 0.916$[/tex]. Therefore, the probability of no cars passing in three hours (two hours have already passed) is:
[tex]$P(X=0 \text{ in } 3 \text{ hours})=\frac{(0.916\cdot3)^0e^{-0.916\cdot3}}{0!} \approx 0.148$[/tex]The probability of waiting at least 1 more hour for the next car is the same as the probability of having no cars pass in the next hour, given that no cars have passed in the last 2 hours. This can be calculated using the conditional Poisson distribution:
[tex]$P(X=0 \text{ in } 1 \text{ hour} | X=0 \text{ in } 3 \text{ hours}) = \frac{P(X=0 \text{ in } 1 \text{ hour and } X=0 \text{ in } 3 \text{ hours})}{P(X=0 \text{ in } 3 \text{ hours})}$[/tex][tex]$= \frac{\frac{(0.916\cdot1)^0e^{-0.916\cdot1}}{0!}\cdot \frac{(0.916\cdot2)^0e^{-0.916\cdot2}}{0!}}{0.148} \approx 0.631$[/tex]
Therefore, the probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.
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the sides of a square are growing at a rate of 3 inches per minute. how fast is the area increasing when each side is 5 inches long?
24 centimeters. Hope this helped!
eighteen more than 7 times a number is -12
The solution x = -30/7 is the value of the unknown number that satisfies the statement "eighteen more than 7 times a number is -12".
This question is incomplete, the complete question is:
Eighteen more than 7 times a number is -12, find the unknown number.
What is the value of the unknown number?Given that, eighteen more than 7 times a number is -12.
Let's use "x" to represent the unknown number.
From the given information, we can use algebra to translate this sentence into an equation.
We start by using "7x" to represent the product of 7 times "x", and adding 18 to it:
7x + 18
Then, we set this expression equal to -12, since that's what the sentence told us the expression is equal to:
7x + 18 = -12
To solve for "x", we can first subtract 18 from both sides:
7x + 18 - 18 = -12 - 18
7x = -30
Then, we can isolate "x" by dividing both sides by 7:
7x/7 = -30/7
x = -30/7
Therefore, the value of the unknown number is x = -30/7.
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When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because
When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because they have better knowledge and understanding about the pet food, and they have established trust with their customers.
What is pet food?
Pet food is a nutrient-rich food specially designed for domestic animals, like dogs, cats, and other pets. It is made from various animal and plant-based sources, such as beef, fish, and corn. Since pet food is designed to meet the nutritional needs of the pets, it must be balanced and complete to provide them with the necessary nutrients they need to be healthy and active.
Why veterinary practice is at an advantage over feed stores and grocery stores?Veterinarians are at an advantage over feed stores and grocery stores when it comes to the sale of pet food because they have the knowledge and expertise about the pet food. They are aware of the specific nutritional requirements of the pets and the various pet food brands available in the market. They can provide advice and recommendations to pet owners on what type of pet food is best suited for their pets based on their age, breed, and health conditions.
Moreover, veterinary practices have established trust with their customers. When customers know they can rely on a particular veterinary practice for quality products and trustworthy advice, they are more likely to shop there repeatedly.
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HELP 20 POINTS
NO WRONG ANSWERS OF LINKS THEY WILL GET REPORTED
Answer:
The second one, (x+1)(3x+2)
The answer is (x+1)(3x+2)
hope it helps
how could you lower the fat content of the following sandwich? 2 slices of white bread 2 ounces of sliced turkey 1 slice of provolone cheese 1 tablespoon of mayonnaise 1 leaf of lettuce 1 slice of tomato
1. Replace the white bread with whole grain bread
2. Replace the turkey with a leaner meat, such as chicken or turkey bacon
3. Replace the mayonnaise with low-fat Greek yogurt
4. Replace the provolone cheese with a lower-fat cheese such as mozzarella
5. Reduce the amount of lettuce used
6. Replace the tomato slice with tomato slices or tomato paste.
To lower the fat content of the sandwich, you can make these changes:
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in a recent survey of 619 salinas residents, 437 stated they experienced significant traffic delays within the last month. if one of the 619 residents is selected at random, what is the probability they have experienced delays?
If one of the 619 residents is selected at random, the probability they have experienced delays is 70.6%.
To find the probability that a randomly selected Salinas resident has experienced significant traffic delays within the last month, we need to use the formula for probability:
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the favorable outcome is the number of residents who have experienced significant traffic delays, which is 437. The total number of outcomes is the total number of residents surveyed, which is 619. Therefore, the probability is:
Probability = 437 / 619 ≈ 0.706
This means that there is a 70.6% chance that a randomly selected Salinas resident has experienced significant traffic delays within the last month, based on the given survey results.
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10. Which graph shows the solution to the inequality <-6?
How will the product of 7 x
Choose 1 answer:
64
5
compare to 7, and why?
It will be less because we are multiplying 7 by a fraction that is less
than 1.
It will be equal because we are multiplying 7 by a fraction that is
equal to 1.
It will be greater because we are multiplying 7 by a fraction that is
greater than 1.
According to the question the product of 7 x 5 will be greater than 7 from multiplication.
Explain Multiplication?Multiplication in mathematics is the addition of equal groups. As we proliferate, the quantity of items in the group increases. The product as well as the two elements are part of a multiplication issue. 6 and 9 are factors in the multiplication equation 6 9 = 54, and 54 is the result.
The product of 7 x 5 by multiplying with each other we can get 35
The number being multiplied with 7 is greater than 1 so the product will also be greater than 7.
The product of 7 x 5 will be greater than 7 because we are multiplying 7 by a number greater than 1.
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How do I solve this?
Answer:
150 handshakes
Step-by-step explanation:
50+50=100 Since the girls shook ONCE to a boy and a girl, we would multiply 100 twice, then add another 50.
The value of y varies directly with x
The calculated value of y when x is -4 is -10 given that the variation is a direct variation
Calculating the value of y when x is -4Direct variation is a mathematical concept that describes the relationship between two variables that change in proportion to each other.
More formally, two variables x and y are said to vary directly if their ratio is constant. This can be expressed mathematically as:
y = kx
So, we have
20 = -8k
This gives
k = -2.5
This means that
y = -2.5x
When the value of x is -4 we have
y = -2.5 * -4
Evaluate
y = 10
Hence, the value of y when x is -4 is -10
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use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge to this sum?
7−14z+28z2−56z3+⋯
sum =
domain =
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region x<−1 and 2
a) The sum of the given series is 7 / (1 + 2z)
b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).
The given series can be expressed as
7 – 14z + 28z^2 - 56z^3 + ...
This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is
sum = a / (1 - r)
Substituting the values of a and r, we get
sum = 7 / (1 + 2z)
So, the sum of the given series is 7 / (1 + 2z).
For the series to converge, the absolute value of the common ratio must be less than 1. That is,
|r| = |−2z| < 1
Simplifying this inequality, we get
1/2 < |z|
So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).
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What is √45 rounded to the nearest whole number
Answer:
3√5
Step-by-step explanation:
If g(x) = 1 – 2x + 3x2, find the average rate of change of the function as x varies from 2 to 5
The average rate of change of the function as x varies from 2 to 5 is 22.
Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]
To find the average rate of change of the function as x varies from 2 to 5.
Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]
The average rate of change of the function as x varies from a to b is given by:
Average rate of change = f(b) - f(a) / b - a
Let a = 2 and b = 5
We have to find the average rate of change of g(x) as x varies from 2 to 5.
So, the average rate of change of g(x) is given by:
Average rate of change = g(5) - g(2) / 5 - 2
= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3
= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22
Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.
An average rate of change is the amount that the function changes on average over a specified interval.
The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.
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Pls just say a b c or d
The prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.
What is PrοbabiIity?PrοbabiIity is a measure οf the IikeIihοοd οf an event οccurring, expressed as a number between 0 and 1. It is caIcuIated as the number οf favοrabIe οutcοmes divided by the tοtaI number οf pοssibIe οutcοmes.
The prοbabiIity οf the spinner stοpping at green is 1/3 since there are three equaI parts.
The prοbabiIity οf seIecting a yeIIοw card frοm the six cards is 1/6 since there is οne yeIIοw card οut οf six cards in tοtaI.
Tο find the prοbabiIity οf bοth events happening, we muItipIy the individuaI prοbabiIities:
P(green and yeIIοw) = P(green) * P(yeIIοw)
= (1/3) * (1/6)
= 1/18
Therefοre, the prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.
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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(-3) = -1
B. h(13) = 18
C. h(2) = 16
D. h(8) = 21
The statement that could be true for h for given function is Option C h(2) = 16 is correct.
What is Domain?The set of all potential values for the independent variable (typically designated as x) for which the function is specified is known as the domain of a function. In other terms, it refers to the entire set of input values for which a function returns a result.
We can state that for any value of x between -3 and 11, the corresponding value of h(x) will be between 1 and 25 because the function h has a domain of -3 x 11 and a range of 1 h(x) 25.
Indicates that the function h is not fixed and that its values change depending on the value of x.
Now, evaluate your options:
Option A h(-3) = -1 - This statement is false because the range of h(x) is stated to be between 1 and 25, so h(-3) cannot be less than 1.
OptionB h(13) = 18 - This statement cannot be true because h(x) is specified to have a range between -3 and 11, so h(13) is not defined.
OptionC h(2) = 16 - The statement may be accurate given that the value of h(x) for any x between -3 and 11 could range from 1 to 25, and there is no evidence to the contrary.
OptionD h(8) = 21 - Since we know that h(8) = 19, this assertion is false.
Therefore, the statement that could be true for h is: h(2) = 16
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Parker Paint has just created a new color, Sunset Orange, made by mixing 3 parts of Fire Red with 5 parts of Brilliant Yellow. A graph to help customers decide how much paint they need is hanging in the store. Use the point shown from the graph to help you decide how much Fire Red paint is needed to paint one 8 foot by 10 foot wall.
To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed.
Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed. Since we need to paint an 8 foot by 10 foot wall, we need 80 square feet of paint. To calculate how much Fire Red is needed, we can use the equation: 3 parts of Fire Red = 5 parts of Brilliant Yellow. We can rearrange this equation to read: 5 parts of Brilliant Yellow = 3 parts of Fire Red. To get the amount of Fire Red required to paint the wall, we can multiply 80 (the square footage of the wall) by 3 and divide it by 5, giving us a total of 48 parts of Fire Red.
To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.
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2. The function f gives the dollar value of a bond t years after the
bond was purchased. The graph of Jis shown.
What is f(0)? What does it mean in this situation?
b. What is f(4.5)? What does it mean in this situation?
c. When is f(t) = 1500? What does this mean in this
situation?
The function f a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year. b. f(4.5) represents the value of the bond 4.5 years later.
What does a mathematical function mean?A function in mathematics is a rule that designates a certain output value for each input value. Each input from the domain has precisely one output in the range, forming a relationship between two sets known as the domain and the range. The letter f(x), where x is the input variable and f(x) is the output variable, is a common way to represent a function. The output variable is specified by the function's rule, but the input variable can accept any value from the function's domain.
For the given graph of the function:
a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year.
b. f(4.5) represents the value of the bond 4.5 years later.
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