Answers
Let x represent the number of days
Let f(x) represent water depth
We can see that the water depth is a function of the number of days.
Water depth, f(x) is the dependent variable and number of days, x is the independent variable.
As the days go by, the water depth changes.
The function is therefore:
[tex]f(x)=54-0.5x[/tex]The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.
[tex]0\le x\le108[/tex]Because at 0 days,
[tex]f(x)=54-0.5(0)=54^{\doubleprime}[/tex]And at 108 days,
[tex]f\mleft(x\mright)=54-0.5\mleft(108\mright)=0[/tex]Related Questions
Can someone help me with this question.
A line passes through the point (-4,-9) and has a slope -5/4 using the Ax+By=C form!!!
Answers
The equation of the line passing through point (-4,-9) and has a slope -5/4 is 5x + 4y = 40
How to find the equation of the linegiven data
A line passes through the point (-4,-9)
slope = -5/4
Ax + By= C
slope = ( y - y1 ) / ( x - x1 )
-5/4 = ( y - 9 ) / ( x - -4 )
-5/4 ( x + 4 ) = ( y - 9 )
-5( x + 4 ) = 4( y - 9 )
-5x + 4 = 4y -36
4 + 36 = 4y + 5x
40 = 4y + 5x
rearranging to suit Ax + By = C
5x + 4y = 40
5x + 4y = 40 is the required equation of the line
Read more on equation of line here: https://brainly.com/question/13763238
#SPJ1
The students in Mr. Kim's class are discussing how to apply the properties of equality. Juan started with the equation 4 +5 = 9. He multiplied the left side by 3. He said that he could divide the right side by another
Answers
B. 3
1) Let's examine Juan's work
4+5 = 9 Multiplying the left side
(4+5)*3 =9
27 = 9 Divide only the right side by 3
9 = 3 False!
2) Then we can state that
B.
The only way Juan can maintain equality is by multiplying the right side by
3
27= 9
27 = 9 x 3
27 = 27 True!
3) The answer is B and 3.
What is the initial value and what does it represent?The table shows the total cost of purchasing x same-priced items and a catalog.Total CostNumber of Items Total Cost(x)1$102$143$184$22O $4, the cost per itemO $4, the cost of the catalog$6, the cost per item$6, the cost of the catalogMy
Answers
Duck if the cost of 1 item and the catalog is $ 10 and onwards, the cost for every additional item is $ 4, then:
• The cost per item is $ 4
,• The cost of the catalog is $ 6
I know you are able to select the correct choices.
Thanks for coming, Duck!
Answer:
Step-by-step explanation:
6$ cost of the catalog
An experimental calculation of the boiling point of olive oil yields 550°F the actual boiling point of olive oil is 570°F use the values in the box below to set a proportion which can be used to find the percent of error in the experimental calculation.
Answers
To calculate the percentage error, the following formula would be applied;
[tex]\begin{gathered} \text{Percentage error}=\frac{|approximate\text{ value-exact value|}}{exact\text{ value}}\times\frac{100}{1} \\ \text{Percentage error}=\frac{|550-570|}{570}\times100 \\ \text{Percentage error}=\frac{20}{570}\times\frac{100}{} \\ \text{Percentage error}=3.50877192 \\ \text{Percentage error}\approx3.5\text{ (nearest tenth of a percent)} \end{gathered}[/tex]ANSWER:
The percentage error, as shown in the calculations above is 3.5 % (to the nearest tenth of a percent)
Mr. Clayton is contemplating which chauffeured car service to take to the airport. The first costs $5 up front and $4 per kilometer. The second costs $15 plus $3 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? Write a system of equations, graph them, and type the solution.______ kilometers
Answers
Given in the question:
a.) The first costs $5 upfront and $4 per kilometer.
b.) The second costs $15 plus $3 per kilometer.
Let's generate the equation of each of the car service charges,
Let,
y = total cost of service
x = distance traveled
a.) The first costs $5 upfront and $4 per kilometer.
[tex]\text{ y = 5 + 4x}[/tex]b.) The second costs $15 plus $3 per kilometer.
[tex]\text{ y = 15 + 3x}[/tex]Let's determine the driving distance when the two companies charge the same.
We get,
[tex]y_{1st\text{ Company}}=y_{2nd\text{ Company}}_{}[/tex][tex]\text{ 5 + 4x = 15 + 3x}[/tex][tex]\text{ 4x - 3x = 15 - 5}[/tex][tex]\text{ x = 10}[/tex]Therefore, the two companies charge the same at a driving distance of 10 kilometers.
Summary:
1. The system of equations.
y = 5 + 4x
y = 15 + 3x
2. The solution.
x = 10
3. Graphing the system of equations.
The equation to find the constant of proportionality or k is?
2K = Y + X
Y = 2K + X
None of the above
K = Y / X
Answers
The equation to find the constant of proportionality or k is K=Y/X.
The value of the ratio between two proportional quantities, known as the constant of proportionality, is constant. When the product or ratio of two changing amounts gives a constant, that relationship is said to be proportionate. Depending on the kind of proportion between the two specified quantities—direct variation or inverse variation—the proportionality constant's value will vary.
When two variables are proportional to one another either directly or indirectly, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. This k is referred to as the proportionality constant.
Hence the equation to find the constant of proportionality or k is
K = Y/X
Learn more about Proportionality here:
brainly.com/question/24868934
#SPJ1
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answers
Answer:
Step-by-step explanation:
here are is answer and the steps it's in the pic below go check it out sorry if it's wrong have a nice day:)
A student downloaded a new game on her phone that was recommended by her friend. Shewanted to show her friend how good she was doing, so she wrote down all her scores on thegame. Her first five scores on the game were 432,543, 348, 788, and 823. On the twoquestions below, round to the nearest whole number when relevant.a. What is her mean, or average, score on the game?b. What is her median score on the game?
Answers
a) mean = (432 + 543 + 348 + 788 + 823) / 5
= 586.8
rounded = 587
b) median = 348, 432, 543, 788, 823
Median = 543
The expression 1.04 (0.9x) + 50 represents the total cost of a catered meal at a conference.The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event. Sales tax wascharged on the reduction price The organizers were also charged a set-up fee. The variable x represents the price of catered mealbefore the reduction.
Answers
Answer:
- The set-up fee is $50 ---- True
- The organizers were given a 10% discount on the catered meal. ---- True
Explanation:
Given that the expression that represent the total cost of a catered meal at a conference is;
[tex]1.04(0.9x)+50[/tex]The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event.
let a represent the percentage discount;
[tex](1-\frac{a}{100})x[/tex]Sales tax was charged on the reduction price;
let b represent the sales tax;
[tex](1+\frac{b}{100})(1-\frac{a}{100})x[/tex]The organizers were also charged a set-up fee.
Let c represent the set-up fee;
[tex](1+\frac{b}{100})(1-\frac{a}{100})x+c[/tex]Comparing to the given equation;
[tex]\begin{gathered} c=\text{ \$50} \\ (1-\frac{a}{100})=0.9 \\ a=10\text{\%} \\ (1+\frac{b}{100})=1.04 \\ b=4\text{\%} \end{gathered}[/tex]So,
discount = 10%
sales tax = 4%
set up fee = $50.
Now let us determine which of the given options are true;
- The cost of the catered meal was less than the set-up fee -- Not enough information, Probably false.
- The sales tax rate was 10% -- false ( sales tax rate is 4%)
- The set-up fee is $50 ---- True
- The organizers were given a 10% discount on the catered meal. ---- True
how do I solve x+6y=36
Answers
Answer:
If you're solving for x and y, the answers are there!
Step-by-step explanation:
Hope this helps!
What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169
Answers
Answer:
Step-by-step explanation:
What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169Question
What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169
At take-off, an airplane weighs 220000 pounds. Convert the weight to tons.
Answers
220000 pounds.
[tex][/tex]The final answer
[tex]110[/tex]4x^2-36 is divided by x+3
Answers
[tex] \frac{4 {x}^{2} - 36 }{x + 3} \\ = \frac{4( {x}^{2} - 9)}{x + 3} \\ = \frac{4(x + 3)(x - 3)}{x + 3} \\ = 4(x - 3) \\ = 4x - 12[/tex]
NOTE THE x+3 in the numerator cancels with the x+3 in the denominator.
Find three rational numbers between (-6) and (-7)
Answers
Answer: Option (b) 21:18, option(c) 42:36, option(d) 63:54, option(e) 84:62 are equivalent ratios of 7:6
Step-by-step explanation: Hope this helped
Answer: -6 1/4, -6 9/10, -6 11/20
Step-by-step explanation: You find any number in decimals between them, then you covert into fractions if needed.
The ages of people who attend a local church are normally distributed . The mean age is 39.5 , and the standard deviation is 18. First sketch a normal curve. Then find the probability that that a person chosen at random from this church is ages 21.5 or younger
Answers
Given:
The ages of people who attend a local church are normally distributed.
The mean age = μ = 39.5
And the standard deviation = σ = 18
The sketch of the normal curve will be as follows:
As shown the peak of the curve at the mean value = 39.5
and the distance between the consecutive numbers = 18
now, we will find the probability that a person chosen at random from this church is ages 21.5 or younger
So, we will find P( x < 21.5)
As shown, from the graph:
The answer will be = 0.1587
7) 5x² - y² +41x-3y + 24 = 0
3x-y=-4
A) (7,0), (6,0)
B) No solution.
C) (1,7), (7,0)
D) (1,7)
Answers
Answer:
D (1, 7)
Step-by-step explanation:
From equation 2
y = (-4 + y)/3
Plug this value into the first equation which will give an equation involving only y. Solve for y which should give y = 7
Plug this value of y = 7 into 3x -y = -4
=> 3x - 7 = -4
=> 3x = 3
x = 1
So solution is x =1, y = 7 which can be represented as (1, 7)
help meeeeeeeeee pleaseee !!!!!
Answers
For the functions f(x) and g(x), the two compositions are:
(f o g)(x) = 9x² + 5(g o f)(x) = 3x² + 15How to find the two compositions?Here we have the next two functions:
f(x) = x² + 5
g(x) = 3x
The compositions are:
(f o g)(x) = f( g(x))
So we need to evaluate the function f(x) in g(x), this will give:
(f o g)(x) = f( g(x)) = g(x)² + 5
(f o g)(x) = (3x)² + 5
(f o g)(x) = 9x² + 5
The other composition is:
(g o f)(x) = g( f(x)) = 3*f(x)
(g o f)(x) = 3*(x² + 5)
(g o f)(x) = 3x² + 15
Learn more about compositions:
https://brainly.com/question/10687170
#SPJ1
Find m BDC. B C (-3x + 20° { (-2x + 55) ° D А a. 290 b. 61° c. 25° d. 759
Answers
Let's begin by listing out the information given to us:
We will observe that these two angles are complementary (they sum up to 90 degrees)
[tex]\begin{gathered} m\angle BDC=-3x+20 \\ m\angle CDA=-2x+55 \\ m\angle BDC+m\angle CDA=90^{\circ} \\ -3x+20+(-2x+55)=90 \\ \text{Put like term}s\text{ together, we have:} \\ -3x-2x+20+55=90 \\ -5x+75=90 \\ Subtract\text{ 75 from both sides, we have:} \\ -5x+75-75=90-75 \\ -5x=15 \\ \frac{-5x}{-5}=\frac{15}{-5} \\ x=-3 \\ \\ m\angle BDC=-3x+20=-3(-3)+20 \\ m\angle BDC=9+20=29 \\ \therefore m\angle BDC=29^{\circ} \end{gathered}[/tex]Hence, option A is the correct answer
Find the simple interest.Principal: $6000 Rate: 4% Time in months: 3
Answers
Given:
Principal, P = 6000
Rate, r = 4%
Time, t = 3 months
To find:
The simple interest
Explanation:
Using the simple interest formula,
[tex]SI=P\times\frac{r}{100}\times\frac{t}{12}[/tex]Where t represents the number of months.
On substitution, we get
[tex]\begin{gathered} SI=6000\times\frac{4}{100}\times\frac{3}{12} \\ SI=\text{ \$}60 \end{gathered}[/tex]Final answer:
The simple interest is $60.
The volleyball team is selling snack bags to raise money for new uniforms. The table shows the percent of the total bags sold for each type of snack bag. If they sold 210 bags of pretzels and cheese puffs, how many snack bags did they sell in all? If each snack bags costs $1.75, how much money did they raise?
Snack
Percent
Cheese Puffs
10
Corn Chips
15
Popcorn
25
Potato Chips
30
Pretzels
20
Answers
The total amount that was raised by the volleyball team is $1,225.
What is the total amount raised?
Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %.
The first step is to determine the total number of snacks sold.
Total number of snacks sold = number of pretzels and cheese puffs sold / percentage representing pretzels and cheese puffs
210 / (10% + 20%)
210 / 30%
210 / 0.30 = 700
The second step is to multiply the total number of snacks by the cost per snack
Total cost of the snacks = cost per snack x total number of snacks
700 x $1.75 = $1,225
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
after how many minutes m Novak have eaten more hot dogs than Roger?
Answers
Data input
After 2 min
Roger 8 hot dogs
Novak 7 hot dos
Then,
Roger 3 hot dogs each minute
Novak 4 hot dogs each minute
Equation:
Roger < Novak
8+3m < 7+4m
The answer would be option B. 8 + 3m < 7 + 4m
I was going back over this and saw i got it wrong what was the right awnser
Answers
ANSWER
E. None of these
EXPLANATION
We want to find the converse of the statement.
A statement is made up of an hypothesis, then a conclusion.
So the converese is found by switching the hypothesis and the conclusion.
The statement given is:
If it is raining then we will go to the beach
The converse of this statement will therefore be:
If we will go to the beach then it is raining
The answer is Option E since the converse is not among the other options.
When 3a^2-7a+6 subtracted from 4a^2-3a+4, the result is
Answers
The result when 4a² - 3a + 4 is subtracted from 3a² - 7a + 6 is
(-1)a² + (-4)a + 2.
What is subtraction?
The act of deleting items from a collection is represented by subtraction. The negative sign ("-") stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
Given, the minuend for the situation is= 3a² - 7a + 6
The subtrahend for the situation is= 4a² - 3a + 4
Therefore, the subtraction= Minuend - Subtrahend
= (3a² - 7a + 6) - (4a² - 3a + 4) = (-1)a² + (-4)a + 2
Thus, the result is (-1)a² + (-4)a + 2.
To learn more about this, tap on the link below:
https://brainly.com/question/1214333
#SPJ9
A junk drawer at home contains eight pens for of which work what is the probability that you randomly grab three pens from the drawer and don’t end up with a Penn that works express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answers
Given:
Total no of pens is 8.
No of pens that works =4
No of pens that don't work = 4
[tex]\text{Probability }of\text{ selecting 3 pens }from\text{ the drawer=}\frac{3}{8}[/tex][tex]\text{Probability of selecting }a\text{ pen thta don't work=}\frac{4}{8}[/tex][tex]\begin{gathered} \text{Probability of getting 3 pens from a drawer }and\text{ don't} \\ \text{ end up with a pen }that\text{ work is } \end{gathered}[/tex][tex]=\frac{3}{8}\times\frac{4}{8}[/tex][tex]=\frac{3}{16}[/tex][tex]=0.1875[/tex]The point A(7, -3) is reflected over the point (6, -5) and it's image is pointB. What are the coordinates of point B?
Answers
We have a point A=(7,-3) that is reflected over point C=(6,-5). This means that is refected in an axis that is perpendicular to the segment AC.
The image is point B, and we need to calculate its coordinates.
We can relocate the center of coordinates to point C, do the reflection and then relocate the original center of coordinates.
If now C became the center of coordinates A becomes:
[tex]A^{\prime}=A-C=(7-6,-3-(-5))=(1,2)[/tex]Now, we can reflect it as normal:
[tex]\begin{gathered} (x,y)\longrightarrow(-x,-y) \\ A^{\prime}=(1,2)\longrightarrow B^{\prime}=(-1,-2) \end{gathered}[/tex]Now, we convert this to the original coordinates as:
[tex]B^{\prime}=B-C\longrightarrow B=B^{\prime}+C=(-1+6,-2-5)=(5,-7)[/tex]The point B is (5,-7).
Describe how to find the anti logarithm of ln x= 2 to the nearest ten-thousandths
Answers
The expression is given as
lnx=2.
ExplanationTo find the antilogarithm of the expression,
To compute the antilogarithm of a natural logarithm, take e to that power.
[tex]lnx=2[/tex][tex]x=e^2[/tex][tex]x=7.389[/tex]AnswerHence the antilogarithm of lnx =2 to the nearest ten-thousandths is 7.3891.
explain the structure and creation of regular and semi-regular tessellations
Answers
A regular polygon is repeated to create a tessellation known as a normal tessellation. Recognize that the angles and sides of an ordinary polygon are the same. An equilateral triangle, a rectangular shape, or a hexagon can all be used to create regular tessellations.
Tessellations made from or larger than common polygons are known as semi-regular tessellations. Hexagons and equilateral triangles make up the semi-typical tessellation shown in the image. If we concentrate on the hexagons, we can see that the triangles are rotated around the hexagonal components to generate the pattern. It is a three.3.6 tessellation, as determined by our system for naming tessellations. The hexagon is represented by the six and the trees are the two triangles.
Regular polygons of the same size and shape make up regular tessellations. Multiple regular polygons combine to form semi-regular tessellations. There are only eight ways to arrange regular polygons to produce semi-regular tessellations.
Hence we derived the necessary information.
Learn more about Tassellations here:
brainly.com/question/11869345
#SPJ1
Find the slope of the line passing through the points (-6 ,2) and (2,2)
Answers
Answer: 8
Step-by-step explanation:
I need help on this question
Answers
Definition of segment bisector.
What question? It might just be a glitch for me, but I don't see any question. Maybe your forgot to add an image?
It takes 3/8 cup of sugar to make bread how much sugar do u need for 16 loaves
Answers
Answer:
6 cups
Step-by-step explanation:
