Interpreting the parameters of a linear function that models a real-world situation
Answers
SOLUTION
The equation relating x and y is
\(\begin{gathered} y=27x+600 \\ \text{Where } \\ x=\text{Total number of minutes } \\ y=\text{Total amount of water in the pond} \end{gathered}\)The equation connecting x and y is an equation of the form
\(\begin{gathered} y=mx+c \\ \text{Where m is the slope or chnages betwe}enx\&y\text{ } \\ \end{gathered}\)Since slope is also refers to as changes between two variables,
Hence
Cmparing with the equation given,
\(\begin{gathered} m=27 \\ \text{Slope}=27 \end{gathered}\)Therefore,
The change per minute in the total amount of water in the pond is 27 litres
The starting amount ot water is when the time is at 0 minutes .
Hence, substite x=0 into the equation given and obtain the value of y which stands for the amount of water at the begining.
\(\begin{gathered} y=27x+600 \\ \text{put x=0} \\ y=27(0)+600 \\ y=0+600 \\ \text{Then } \\ y=600 \end{gathered}\)Therefore,
The starting amount of water is 600 litres
Answer: A) 27 litres B). 600 litres
Related Questions
do similar triangles always have equal lengths of corresponding sides?
Answers
Answer:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
Answer:
No. Similar triangles only have equivalent angles. Congruent triangles have equal side lengths.
Step-by-step explanation:
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5. Calculate the probability of getting at least 4 calls between eight and nine in the morning.
Answers
Answer:
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Step-by-step explanation:
We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\mu\) is the mean in the given interval.
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.
This means that \(\mu = 5\)
Calculate the probability of getting at least 4 calls between eight and nine in the morning.
This is:
\(P(X \geq 4) = 1 - P(X < 4)\)
In which
\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)
So
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067\)
\(P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337\)
\(P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842\)
\(P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404\)
Then
\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265\)
\(P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735\)
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
(-14) + 22 + 8 + (-16)
Answers
Answer:
0
Step-by-step explanation:
-14+22=8
8+-16=-8
-8+8=0
Answer:
0
Step-by-step explanation:
(-14) + 22 + 8 + (-16)
0
So 0is the answer
What will be the new position of the given point (3, 5) after translation of 2 units left and 3 units up?
Answers
Answer:5 8
Step-by-step explanation:left 2 up 3
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 10 17 39
Female 2 19 3 24
Total 14 29 20 63
If one student was chosen at random,
find the probability that the student got a B.
Answers
So we can simply take the total number of students that got B and the total number of students overall. That will be 29/63.
29 divided by 63 is 0.46. Multiply that by 100 and you’ll convert that to a percentage, which is 46%.
If one student was chosen at random, the probability that the student got a B is 46%.
Hope this helped!
3/8 of the plants neede3/8 of the plants needed water. 63 plants need water. How many plants are there total?d water. 63 plants need water. How many plants are there total?
Answers
The total number of plants is given as follows:
168 plants.
How to obtain the total number of plants?The total number of plants is obtained applying the proportions in the context of this problem.
The variable that represents the total number of plants is given as follows:
n.
The fraction of the number of plants that needed water is given as follows:
3/8.
The fraction 3/8 of n is equivalent to an amount of 63, hence the total amount of plants is obtained as follows:
3n/8 = 63
3n = 63 x 8
n = 21 x 8(simplifying by 3).
n = 168 plants.
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a rectangle with a width of 30 centimeters has a perimiter of 100 centimeters to 160 centimeters graph a compound inequality
Answers
Answer:
5 ≤ L ≤ 35
Step-by-step explanation:
Let w represent the width of the rectangle.
The perimeter (P) of the rectangle is given by:
P = 2w + 2L
Where L is the length of the rectangle.
We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:
100 ≤ 2(30) + 2L ≤ 160
100 ≤ 90 + 2L ≤ 160
10 ≤ 2L ≤ 70
We can now divide both sides by 2 to solve for L:
5 ≤ L ≤ 35
Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is: 5 ≤ L ≤ 35
how many pairs of matching surfaces does a cereal box have
Answers
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
Find 133.5% of 413. Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Determine the two consecutive multiples of 10 that bracket 551
551 is between 550 and 560
555 is the midpoint between 550 and 560
As illustrated on the number line, 551 is less than the midpoint (555)
Therefore, 551 rounded to the nearest ten = 550
551 rounded to the nearest ten with a number line
Answer: 551.36
Step-by-step explanation:
“Of” means you have to multiply so multiply 133.5 and 413 and you will get 55,135.5 then you move the decimal point to the right 2 times and that will be 551.355, then since there is a five you change the other five to a 6 (5 or more raise the score 4 or less let it rest) and that will be 551.36.
A coin is tossed twice. Let
E
be the event "the first toss shows heads" and
F
the event "the second toss shows heads".
(a) Are the events
E
and
F
independent?
Input Yes or No:
(b) Find the probability of showing heads on both tosses. Write your answer as a reduced fraction.
Answer:
Answers
Answer:
(a) Yes, E and F are independent events.
(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4
how much work is done when a girl pushes a lunch cart 15m across the cafeteria with a force of 3N
Answers
Answer:
45 J
Step-by-step explanation:
Just plugged into the work force formula got 45 jules
I NEED HELP SOLVING THESE THREE QUESTIONS
(WILL MARK BRAINIEST)
Answers
Answer: D, C, 18
Step-by-step explanation:
The first one is trigonometry. It takes a long time to calculate, but sin20 degrees=0.342, and 15/43.8 is about 0.342
From that, we get the answer as D.
The second one is a bit of guesswork and logic
Notice that the angle on the left is 24
The angle on the right is 45
24 is about one-half of 45
51/3=17
So the triangle on the left has sides x, 24, and approx. 17.
17^2=289 and 24^2=576
576-289 is about 17, but using our eyes, we see that it's clearly not the same, so we round to 21.9 or C (risky, but don't know how to solve, sorry)
Last one:
Form a triangle using the start of the zipline, the end of the zipline, and the balance point. This forms a right triangle with angles 72, 90, and (2)
The triangles angle add up to 180, and 180-90=90 and 90-72=18 so (2)=18.
We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Answers
Answer: The answer to your question is C. Brainliest?
Step-by-step explanation:
For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:
2/12 = (2 x 5) / (12 x 5) = 10/60
For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:
2/15 = (2 x 4) / (15 x 4) = 8/60
Now, we can add the two fractions:
10/60 + 8/60 = 18/60
Simplifying this fraction by dividing both numerator and denominator by 6, we get:
18/60 = 3/10
Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.
The answer is C. 0.3.
Which equation can be used to represent three minus the difference of a number and one equals one-haf of the
difference of three times the same number and four?
e (1-0) -3 4 -32)
e 3-1-n) = 4-3)
O (2-1)-3= {(3m-4
O 3-(1-1)=(37-4
Answers
Answer:
3-(1-1)=(37-4
Step-by-step explanation:
Answer:
3-(1-1)=(37-4)
Step-by-step explanation:
step by step explanation
Which trigonometric function can equal or be
greater than 1.000?
Answers
Answer:
option c tangent is equal to 1 at 45°
and greater than 1 at 60° .
The number of letters received in the mail over the past week is recorded.2355515Which value appears to be an outlier?2153 5
Answers
hello
This question is from statistics and we can difine an outliner as a data point that is different from the other set of data observed. It usually occurs due to
Identify the algebraic rule that would translate a figure 3 units left and 2 units up.
Answers
The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). Option B.
To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.
When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.
Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.
Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.
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How do I find the possible degree(s) of a function from the graph alone?
Answers
Answer:
To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:
Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.
Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.
Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.
Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
Answers
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
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Find the product of -5.3(-0.5)
A. 4.1
B. 2.65
C. 2.75
D. 3.45
Answers
Answer: is B 2.65
Step-by-step explanation:
What restrictions are there on the range of the function H(w) below?
H(w)
(5.0, 20.00)
A. H(w) = 1
B. H(w) > 0
C. H(w) = 1
D. H(w) < 0
Answers
Answer:H(w) > 0
Step-by-step explanation:
The restrictions are there on the range of the function H(w) is H(w) > 0.
The answer is H(w) > 0, this is the option B.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given function
H(w) = (5.0, 20.00)
The function, named H(w) is defined by a graph that is a descendant line, that belongs only to the first quadrant. As w approaches to 0 by the right, the function approaches to + infinity. It never touches the vertical axis, decreases and approaches to 0 when w approaches to infinity. The graph never touches the horizontal - axis.
Then, the function is defined only for positive values of w and H(w) is always positive.
Then, the answer is H(w) > 0, this is the option B.
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Please help! ((I did the first part one))
Part 1:
Before school began, Mrs. Weeks bought a total of 86 balls. use the information below to help you write a numerical expression for the number of each type of ball.
footballs - there are 8
basketballs - Two more than twice the number of footballs are basketballs.
Baseballs - Four less than 5 times the number of footballs are baseballs.
Softballs - Six more than half of the baseballs and softballs.
type balls;; football
numerical Expression for the Numbers of balls;; ((given))
Total Number of Each type of ball;; 8
Basketballs
2 x 8 = 2. 16 + 2
35
Baseballs
5 x 8 - 4
40- 4
softballs
1/2 x 36 + 61. 8 + 6
24
______________
Part 2::
Use the space below to show your work. Check your work very carefully because you will need it to complete part 2
_______________
Use the information you found in part 1 to help you find answer part 2
Types of ball
football
basketball
baseball
softball.
Cost pre Ball;;
$8.00 ((footballs)), $9.00 ((basketballs)), $7.00 ((baseballs)), and $5.00 ((softballs)).
Total Number of Balls ((from part 1)).
_________________________
1. When Mrs. Weeks bought all of the baseballs and softballs, she paid for them using $100.00 bills. how much change did she receive?
2. Write expressions that include parentheses and order of operations to show how you got the answer. Show your work.
3. After School began, Mrs. Weeks realized that she needed more basketballs and footballs. If she spent $135.00 on basketballs and $48.00 on footballs, how many more balls did she purchase?
4. Write expressions that include parentheses and order of operations to show how you got the answer. Show your work.
________________________
Part 3:
At the end of the year, Mrs. Weeks bought an assortment of new balls to replace some of the old ones. She had $150.00 to spend. Describe two different ways that Mrs. Weeks could spend her money if she bought at least two of each bills.
Answers
Answer:
75
Step-by-step explanation:
ok for part 3 the answer is 75 I think
A square has a a side lenght of 5 feet what is its area?
Answers
Answer:
25 sq feet
Step-by-step explanation:
Length = 5 feet
Area = (Length)²
= 5²
= 25 sq feet
Since my uncles farmyeard apperas to be overrun with gos and chickens i asked him hom many of each did he have he responded that his dog and chicked had a total of 148 legs and 60 heads. hime mmay of each does he have
Answers
There are 14 dogs and 46 chickens in the farmyard.
The supposition that there are d dogs and c chickens.
Each chicken has two legs, but each dog has four.
Consequently, the total number of legs may be written as follows:
4d + 2c
Since we are aware that there are 148 legs in total, we can construct the following equation:
4d + 2c = 148
We may create another equation since we know that there are a total of 60 heads (dogs and chickens):
d + c = 60
Now that we have two equations with two variables, we may answer them both at the same time.
2d + 2c = 120 is the result of multiplying the second equation by two.
When we deduct this from the first equation, we obtain 2d = 28.
So, d = 14.
Reintroducing this into the second equation, we get:
14 + c = 60
So, c = 46.
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What is the slope and y-intercept of this line?
y=−12x+7
slope: 12, y-intercept: −7
slope: −7, y-intercept: −12
slope: −12, y-intercept: 7
slope: 7, y-intercept: −12
Answers
Answer:
(c) slope: -12, y-intercept: 7
Step-by-step explanation:
The given equation is in the slope-intercept form:
y = mx +b
In this form, m is the slope, and b is the y-intercept.
__
Comparing the given equation to the form, we see ...
y = mx +b
y = -12x +7 ⇒ m = -12, b = 7
The slope is -12; the y-intercept is 7.
The increased availability of light materials with high strength has revolutionized the design and manufacture of golf clubs, particularly drivers. One measure of drivers that result in much longer tee shots is known as the coefficient of restitution of the club. An experiment was performed in which 15 drivers produced by a particular club maker were selected at random and their coefficients of restitution measured. It is of interest to determine if there is evidence to support a claim that the mean coefficient of restitution exceeds 0.82. Assume values to be normally distributed. The following observations were obtained for the 15 drivers:
0.8411 0.8191 0.8182 0.8125 0.8750
0.8580 0.8532 0.8483 0.8272 0.7983
0.8042 0.8730 0.8282 0.8359 0.8660
Conduct the test using a significance level of 0.05.
Answers
Answer:
WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82
Step-by-step explanation:
This is a one sample t test :
The hypothesis :
H0 : μ = 0.82
H0 : μ > 0.82
Given the sample data:
0.8411 0.8191 0.8182 0.8125 0.8750
0.8580 0.8532 0.8483 0.8272 0.7983
0.8042 0.8730 0.8282 0.8359 0.8660
Sample size, n = 15
Sample mean = ΣX / n = 0.837
Sample standard deviation, s = 0.0246 (from calculator)
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (0.837 - 0.82) ÷ (0.0246/√(15))
T = 2.676
The critical value at α = 0.05
df = n - 1 ; 15 - 1 = 14
Tcritical(0.05, 14) = 1.761
Reject H0 if Test statistic > Tcritical
Since, 2.676 > 1.761 ; WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82
HELP NOWWWWW PLEASEEE
Answers
Answer:
D. 69.2
Step-by-step explanation:
v= 3.14 ×2.1^2 × 5
v = 69.237
when you round it, it is
69.2 cubic cm
Answer:
(c) 69.2 cm³
formula: v=πr²h
here, r = 2.1cm , h = 5cm
How do I convert 10.8 mg to ml
Answers
Answer:
10.8mg to ml
Step-by-step explanation:
If you want to convert mg to ml of water you use
1ml=1000mg,then convert the units
1ml=1000mg, then what is the ml of 10.8mg? by using crisscross, let unknown value is B
= 1ml=1000mg
B=10.8mg
=1ml*10.8mg
1000mg
=0.0108ml-9 (-2) please answer
Answers
Answer:
18
Step-by-step explanation:
You can multiply 9 x 2 like normal to get 18. Then you look at the signs. They are both negative, meaning their product is positive, making the answer 18.
When you multiply two negative numbers, the product is positive.
A 6-pack of ice cream sandwiches costs $3.86. What is the unit price, rounded to the nearest cent?
Answers
Answer: so either .64 or , .66,
Step-by-step explanation:
divide 3.86 by 6