Answers
The rate of emptying the lake is -1/8.
The rate of filling the lake is 1/15
Let t be the time in weeks to empty the lake,
Now, add the given rate to get the total rate of emptying of -1/t.
[tex]\begin{gathered} \frac{-1}{8}+\frac{1}{15}=-\frac{1}{t} \\ \frac{-15+8}{120}=-\frac{1}{t} \\ -7\times t=-120 \\ t=\frac{120}{7} \end{gathered}[/tex]Thus,
[tex]t=17\frac{1}{7}[/tex]Therefore, it will take 17 weeks and 1 day to empty the lake.
Related Questions
To which subset of the real numbers does 22‾√ belong?
Answers
Ok
Squared root of 2 is a irrational number because it can not be expressed as a fraction.
So the correct choice is Irrational, the last one.
A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts.One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.Write your answer as a fraction. I need help with this math problem
Answers
There is a total of 2 + 7 + 11 = 20 shirts
Given that events "A" and "B" are independent, P(A) = 0.80, and P(A and B) = 0.24, what is P(B)?
Answers
Answer:
P(B)=0.3
Explanation:
Given two independent events, A and B:
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Substitute the given values:
[tex]\begin{gathered} 0.24=0.8\times P(B) \\ \text{ Divide both sides by 0.8} \\ \frac{0.24}{0.8}=\frac{0.8\times P(B)}{0.8} \\ P(B)=0.3 \end{gathered}[/tex]The probability of event B is 0.3.
h e l p please. can't solve. picture explains, and i know the answer, but i cannot figure out how to make the equation to solve
Answers
We want to find how many miles Jodi traveled if her ride costed $12.50. We also know that a taxi ride has an initial fee of $3.75 plus $1.25 for every 1/2 mile traveled.
This means that for every mile, the fee will be:
[tex]2(1.25)=2.50[/tex]And the expression for the cost on terms of the miles traveled will be:
[tex]\begin{gathered} 3.75+2.50x \\ \text{where }x\text{ represents the number of miles traveled } \end{gathered}[/tex]As we know that Jodi spent $12.50 on a ride, we equal the value to the above expression:
[tex]3.75+2.50x=12.50[/tex]And we solve for x, as we want to know the number of miles:
[tex]\begin{gathered} 2.50x=12.50-3.75 \\ 2.50x=8.75 \\ x=\frac{8.75}{2.50}=3.5 \end{gathered}[/tex]This means that the number of miles that Jodi traveled was 3 and a half.
A travel agency polled its customers about their favorite kind of vacation. The results of the survey are shown in the given two-way frequency table.
Vacation Preferences
Seaside Mountain Historical Sightseeing Total
Female 38 36 32 17 123
Male 43 52 23 19 137
Total 81 88 55 36 260
What is the marginal relative frequency of customers who prefer sightseeing vacations?
A.
0.47
B.
0.21
C.
0.14
D.
0.89
Answers
The marginal relative frequency of customers who prefer sightseeing vacations is (C) 0.14
The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
[tex]Marginal relative frequency = \frac{sightseeing(total)}{Total}[/tex]
= 36/260
= 0.1385
≅ 0.14
Hence, marginal relative frequency of customers who prefer sightseeing vacations is 0.14.
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17. Felicia bought 5 pieces of candy for 75 cents. Write a proportion youcould solve to find out how much would 8 pieces cost? *
Answers
Given the information on the problem, we can write the 5 pieces of candy for 75 cents like this:
[tex]\frac{75\text{ cents}}{5\text{ pieces}}[/tex]then, for 8 pieces, we would have the following proportion:
[tex]\frac{x\text{ cents}}{8\text{ pieces}}[/tex]then, we can equate both proportions to get the following:
[tex]\begin{gathered} \frac{75\text{ cents}}{5\text{ pieces}}=\frac{x\text{ cents}}{8\text{ pieces}} \\ or \\ \frac{75}{5}=\frac{x}{8} \end{gathered}[/tex]thus, solving for x, we get:
[tex]\begin{gathered} \frac{x}{8}=\frac{75}{5} \\ \Rightarrow x=\frac{75}{5}\cdot8=120 \\ x=120\text{cents} \end{gathered}[/tex]therefore, 8 pieces cost $1.20
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Juan bought three and three-fourths pounds of pineapple and three and three-eighths pounds of strawberries for a fruit salad. After eating one and fifteen-sixteenths pounds of the fruit salad, how much was left?
five and three-sixteenths pounds
five and three-eighths pounds
five and nine-sixteenths pounds
seven and twenty-one sixteenths pounds
Answers
Salad was left (A) Five and three-sixteenths pounds.
Fraction is the comparison between numbers or mathematical quantities.
Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds
Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds
So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds
Juan eats = (1+15/16) = 31/16 pounds
Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds
Hence the correct option is (A).
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On average, there are six pages in every chapter of a Rodriguez Hernandez novel. Each book has Approximately 73 chapters. Rodriguez Hernandez has published 54 books. Approximately how many pages has Rodriguez Hernandez written?
Answers
Given:
There are given that 6 pages in every chapter and each book have 73 chapters.
Explanation:
According to the question:
We need to find the pages for 54 books.
So,
First, we need to find that 73 chapters mean one book.
Then,
[tex]\begin{gathered} 1ch\rightarrow6pages \\ 76ch\rightarrow6\times76 \\ =456pages \end{gathered}[/tex]Now,
We need to find the pages for 54 books:
So,
[tex][/tex]Analyze the diagram below and complete the instructions that follow./Find sinA.1/3B.5/14C.4/5D.12/13
Answers
As given by the question
There are given that the triangle.
[tex]\begin{gathered} OM^2=3^2+4^2 \\ OM=5 \end{gathered}[/tex][tex]undefined[/tex]in rst the measure of ∠J=90° the measure of ∠H=69° and Hl=88 feet. find the length of JH to the nearest tenth of a foot
Answers
From the information provided, we can construct the following triangle;
The measure of angle J is 90 degrees, the measure of angle H is 69 degrees and line HI measures 88 feet. Therefore to calculate line JH;
[tex]\begin{gathered} \cos \theta=\frac{adj}{hyp} \\ \cos 69=\frac{JH}{88} \\ \text{Cross multiply and you'll have;} \\ 88\times\cos 69=JH \\ 88\times0.35836794\ldots=JH \\ 31.5363\ldots=JH \\ JH\approx31.5ft \end{gathered}[/tex]The answer is 31.5 feet (rounded to the nearest tenth of a foot
Question 60 state wether the triangle is an isosceles triangle,right triangle, neither of these or both.
Answers
Given:
The points of the triangle:
[tex]P_1=(7,2);P_2=(-4,0);P_3=(4,6)[/tex]Required:
To find out if the given triangle is an equilateral triangle or an isosceles triangle or both or none of these.
Explanation:
To find if the triangle is an equilateral triangle or an isosceles triangle we will have to first find the length of the sides by distance formula.
Distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)_^2+(y_2-y_1)^2}[/tex]So applying the distance formula on side P₁P₂
Substituting the value of P₁ and P₂ in the distance formula we get
[tex]P₁P₂=\sqrt{(-4-7)^2+(0-2)^2}=\sqrt{(-11)^2+(-2)^2}=\sqrt{121+4}=\sqrt{125}=5\sqrt{5}[/tex]Now lets find the length of P₂P₃
Substituting the value of P₂ and P₃ in the distance formula we get
[tex]P₂P₃=\sqrt{(4-(-4))^2+(6-0)^2}=\sqrt{(4+4)^2+6^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]Now lets find the length of P₁P₃
Substituting the value of P₁ and P₃ in the distance formula we get
[tex]P₁P₃=\sqrt{(4-7)^2+(6-2)^2}=\sqrt{(-3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]S now we have the length of all three sides, that is
[tex]\begin{gathered} l(P₁P₂)=5\sqrt{5} \\ \\ l(P_2P_3)=10 \\ \\ l(P₁P_3)=5 \end{gathered}[/tex]If we add any two sides of triangle then it is greater than the third side so it is a triangle.
[tex]\begin{gathered} 5\sqrt{5}+5>10 \\ 5+10>5\sqrt{5} \\ 5\sqrt{5}+10>5 \end{gathered}[/tex]So it is a valid triangle. But the length of all the sides of triangle are different.
In equilateral triangle all the sides are same.
In isosceles triangle any sides are same.
Since here none of the sides are same so it is neither an equilateral triangle nor an isosceles triangle. It is a Scalene triangle with all three sides different.
Final answer:
The answer is none of these.
Fill in the table using function rule
Y=6x+2
Answers
Using our equation y = 6x + 2, we were able to write out values for our table of function.
Function TableA function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.
Since we have our equation, we can proceed to find what values of y we would have when x is in a certain condition.
Using from -2 to + 5, we can have a good table of function.
When x = -2
y = 6x + 2
y = 6(-2) + 2 = -10
When x = -1
y = 6(-1) + 2 = -4
When x = 0
y = 6(0) + 2 = 2
When x = 1
y = 6(1) + 2 = 8
When x = 2
y = 6(2) + 2 = 14
When x = 3
y = 6(3) + 2 = 20
When x = 4
y = 6(4) + 2 = 26
When x = 5
y = 6(5) + 2 = 32
Using the values above, we have a good function table and can proceed to plot a graph if needed.
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I would like some help solving this step by step please
Answers
Combine like terms and write each expression in standard form
Answers
SOLUTION
From the expression
[tex]x^2-5+2x+x^2[/tex]combining like terms we have to bring the x-squares together, we have
[tex]\begin{gathered} x^2+x^2-5+2x \\ 2x^2-5+2x \end{gathered}[/tex]To write in standard form, the 2x should come before the -5, so we have
[tex]2x^2+2x-5[/tex]Hence the answer is
[tex]2x^2+2x-5[/tex]For each scenario below, choose the graph that gives the best representation.(A) Carlos is driving on the freeway at a constant speed. He then speeds up to pass a truck, After passing the truck, he exits the freeway and slows down.(B) Rachel is delivering a pizza to Mark's house. She drives at a constant speed toward the house until she hits a traffic jam and has to stop for severalminutes. After, she starts up again and drives at a faster speed than before.
Answers
Given:
Given the word problem, we can deduce the following information:
a)
1. Carlos is driving on the freeway at a constant speed.
2. He then speeds up, and exits the freeway and slows down.
Based on hte given information, the graph should have a constant or horizontal line at the first part, increases as he speeds up on the second part, and decreases as he slows down.
Thus the graph should be:
b)
1. Rachel is delivering at a constant speed toward the house until she hits a traffic jam and has to stop for several minutes.
2. She starts up again and drives at a faster speed than before.
So based on the given information, the graph should have a horizontal line at the first part since Rachel is driving at a constant speed. Next, the line should be increasing and higher than the horizontal line since Rachel is driving at a faster speed than before.
Therefore, the graph is:
Give an interval over which the function is increasing. Give an interval over which it is decreasing
Answers
one interval where the function is increasing is
(-3;1)
one interval where the function is decreasing is
(1;4)
Given the following frequency table of values, iIs the mean, median, or mode likely to be the best measure of the center for the data set? ValueFrequency211220230240250260270280290300310320330340352363371380392404413Select the correct answer below:ModeMeanMedian
Answers
Solution
In the dataset given. The distribution is skewed.
The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution)
Thus, the correct answer is median
How do you solve linear equations in algebra ?-3y>-3-4x
Answers
Given linear equations in algebra: -3y >-3-4x
The above is an inequality.
To solve linear equation with two variables we need two equations.
Only one equation is given. The only other explanation is to solve for any of the variables by making it the subject of formula.
50 points!
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6[tex]\sqrt{2}[/tex] ) can be [tex]x\sqrt{2}[/tex] while AB and CB are x. Because 6[tex]\sqrt{2}[/tex] is equal to [tex]x\sqrt{2}[/tex], you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = [tex]x\sqrt{3}[/tex]. CB is equal to 6 so 2x = 6, x = 3.
if a 3/4 of a cup serving of cereal provides your full daily value of vitamin B6 then what percentage of your daily value of vitamin B6 will you receive in 1/2 of a cup of your cereal
Answers
Given
3/4 cup serving of cereal provides 100% of vitamin B6 requirement
The percentage of daily value that would be available in 1/2 of a cup of cereal is:
[tex]\begin{gathered} \text{= }\frac{\frac{1}{2}}{\frac{3}{4}}\text{ }\times\text{ 100 \%} \\ =\text{ }\frac{1}{2}\times\frac{4}{3}\text{ }\times\text{ 100\%} \\ \text{= }\frac{4}{6}\text{ }\times\text{ 100\%} \\ =\text{ 66.67\%} \end{gathered}[/tex]Hence, the percentage of the daily value in 1/2 of a cup is 66.67%
zoo nutritionist orders 5 1/4 tons of apples and 7 2/4 tonsof bananas each year to feed theanimals. She orders 6 times as manytons of herbivore pellets than tons offruit. How many tons of herbivorepellets does the nutritionist order?
Answers
From the information provided, the zoo nutritionist orders the following quantity of fruits;
[tex]\begin{gathered} 5\frac{1}{4}\text{ tons of apples} \\ 7\frac{2}{4}\text{ tons of bananas} \\ \text{Total}=5\frac{1}{4}+7\frac{2}{4} \\ \text{Total}=\frac{21}{4}+\frac{30}{4} \\ \text{Total}=\frac{51}{4}\text{ tons} \\ \end{gathered}[/tex]Next, we are told that the nutritionist orders 6 times as many tons of pellets than tons of fruits.
This means for every ton of fruit ordered, there was 6 tons of pellets ordered.
Therefore;
[tex]\begin{gathered} \text{Fruits:Pellets}=1\colon6 \\ \text{When fruits are }\frac{51}{4}tons \\ \text{Pellets}=\frac{51}{4}\times6 \\ \text{Pellets}=\frac{306}{4} \\ \text{Pellets}=76\frac{1}{2}tons \end{gathered}[/tex]ANSWER:
[tex]\text{Pellets ordered}=76\frac{1}{2}tons[/tex]Find the prime factorization and match your result to the correct answer below 231.Select one:a. 21•11b. 2•3•7•11c. 3•7•11d. 3•77
Answers
Solution
Hence, the prime factorization of 231 is 3•7•11
Hence, the correct option is C.
The salaries of the employees at four companies are summarized below. Answer the question about them.
Answers
Given,
Company A: the range of the salaries is $60000 and the mean salary is $22000.
Company B: the range of the salaries is $58000 and the mean salary is $29000.
Company C: the range of the salaries is $67000 and the mean salary is $27000.
Company D: the range of the salaries is $63000 and the mean salary is $28000.
Required
The company have least average salary and least variability.
a) From the given data, it is clearly seen that the company that have the lowest salary is $22000.
Hence, the company that have the lowest salary is Company A.
b)From the given data, it is clearly seen that the company that have the least salary variability is $58000.
Hence, the company that have the least salary variability is Company B.
2x+y=21;y=-2x+21please hurry I need this straight away use any method
Answers
Answer:
(k, -2k+21) where k is any integer
Explanation:
Given the following simultaneous equation;
2x+y=21 ..... 1
y=-2x+21 ..... 2
Subtitute equation 2 into 1:
2x + (-2x+21) = 21
2x -2x+21 = 21
0x = 21-21
0x = 0
x = 0/0
Since the variables cannot be determined, we will subtitute x = k
Substitute x = k into equation 2;
From 2: y = -2x+21
y = -2k+21
Hence the solution to the system of equation is (k, -2k+21) where k is any integer
Find the median for the scores: 93,69,72,86,72,95,88,74,72,89,89,95,74,79
Answers
A set of data is given and it is required to find the median:
[tex]93,69,72,86,72,95,88,74,72,89,89,95,74,79[/tex]Recall that the Median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Hence, to find the median, rearrange the scores either in ascending or descending order.
[tex]69,72,72,72,74,74,79,86,88,89,89,93,95,95[/tex]Next, highlight the two middle numbers since the frequency of the scores is even (14):
[tex]69,72,72,72,74,74,\boxed{79,86},88,89,89,93,95,95[/tex]Find the mean of the two middle numbers to calculate the median for the scores:
[tex]\frac{79+86}{2}=\frac{165}{2}=82.5[/tex]Hence, the median score is 82.5.
The median score is 82.5.
Karen owns a seafood restaurant. She orders trout from an online retailer.Each pound of trout costs $30, and the company charges a $2 fee forshipping the order. However, if Karen orders 10 or more pounds, the troutcosts only $24 per pound, but the shipping fee is $6.Which piecewise function models the cost of x pounds of trout?○ A. f(x) = {={O B. f(x) ={O c. f(x) = -O D. f(x) =30x + 2, 0< x≤ 1024x+6, x 1024x+6, 0
Answers
The piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Let the number of pounds of trout is x and the price is C.
For, x < 10 :
From the question, we have
Each pound of trout costs $30
C = 30x + 2 ....1 )
For, x ≥ 10 :
Each pound of trout costs $24.
C = 24x + 6 ....2 )
Therefore, the piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Piecewise Function :
A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs. A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.
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6. Andre is drawing a triangle that is congruent to this one.He begins by constructing an angle congruent to angleLKJ. What is the least amount of additional informationthat Andre needs to construct a triangle congruent tothis one?
Answers
The measure of an angle
The measure of two legs
1) Andre can construct a congruent triangle using SAS congruence, knowing the angle congruent to LKJ and with a compass measure two legs of that triangle
2) Sketching out we have:
Notice that either with a protractor or with a compass we can measure congruent angles and based on SAS congruence we need two congruent legs to determine a SAS congruence.
3) Hence, Andre needs at least:
The measure of an angle
The measure of two legs
Without graphing, find the slope of the line that goes through each pair of coordinate points. (0,5) and (8,2 ) [Choose ] (2,-1) and (6, 1) [ Choose ] (-3,-2) and (- 1,-5) [ Choose]
Answers
Answers:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Explanation:
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, the slope of a line that goes through (0,5) and (8,2) is equal to:
[tex]m=\frac{2-0}{8-5}=\frac{2}{3}[/tex]The slope of a line that goes through (2, -1) and (6, 1) is:
[tex]m=\frac{1-(-1)}{6-2}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The slope of a line that goes through (-3, -2) and (-1, -5) is:
[tex]m=\frac{-5-(-2)}{-1-(-3)}=\frac{-5+2}{-1+3}=-\frac{3}{2}[/tex]Therefore, the answers are:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
N. Students wanted to determine theheight of the flagpole. They measuredits shadow as 27 ft and the shadow of a 6ft tall student as 2 ft. How tall is theflagpole? Use the digit in the ones placeof your answer for N.
Answers
Given:
Shadow of flagpole = 27 feet
Height of the tall student = 6 feet
Shadow of the tall student = 2 feet
Required:
the height of the pole
Explanation:
Both the triangles are similar so the ratio of their corresponding sides are equal
[tex]\frac{height\text{ }of\text{ }flagpole}{height\text{ }of\text{ }student}=\frac{shadow\text{ }of\text{ }flagpole}{shadow\text{ }of\text{ }student}[/tex]Substituting the given values we get
[tex]\begin{gathered} \frac{height\text{ }of\text{ }flagpole}{6}=\frac{27}{2} \\ \\ height\text{ }of\text{ }flagpole=\frac{27\times6}{2}=27\times3 \\ \\ height\text{ }of\text{ }flagpole=81\text{ }feet \end{gathered}[/tex]Final answer:
The height of the flagpole is 81 feet.
I’m not sure how to solve this I just know I have to get 5 with an exponent of 7 I think
Answers
this is an addition of powers .
on sunday , Margos dad gives 5c, we will represent it as 5^1
therefore: sunday 5^1
Monday 5^1 x ( 5^1)
because bases are the same , we add exponents
this means that 5^1(5^1) = 5^2
Tuesday 5^2(5^1) = 5^3
wednesday 5^3(5^1) = 5^4
thursday 5^4( 5^1)= 5^5
Friday 5^5(5^1)= 5^6
saturday 5^6 (5^1)= 5^7