Answers
Given:
a.) After 2 minutes, the tank contains 400 gallons.
b.) After 5 minutes, the tank is full.
For us to be able to determine how many gallons of water does the full tank hold, let's first determine the discharge rate of the water filling in the tank.
We get,
[tex]\text{ Rate of discharge = }\frac{\text{ Volume}}{\text{ Time}}\text{ = }\frac{400\text{ Gallons}}{2\text{ Minutes}}[/tex][tex]\text{ Rate of discharge = 200 Gallons/Minute}[/tex]Since the tank is after 5 minutes of pumping water at a constant rate, we will just multiply the rate of discharge by the time it took for the tank to be full.
We get,
[tex]\text{Volume of the Tank = Time x Rate of Discharge = 5 (Minutes) x 200 Gallons/(Minute)}[/tex][tex]\text{ Volume of the Tank = 1000 Gallons}[/tex]Therefore the volume of the tank is 1000 Gallons
Related Questions
can someone please help me find the value of x to this equation
Answers
SOLUTION
This is a right-triangle problem.
We will use the SOHCAHTOA principle.
In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]The final answer is 73.87 degrees.
Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.
Answers
12x^3
Name: Monomial , because it has only 1 term
Degree: 3, exponent of the monomial
What mathematical symbol goes between the two parentheses to show that you will be using the distributive property?
8 x 57 = (8 x 50) _______ (8 x 7)
Answers
Answer: The Answer is the addition symbol
Step-by-step explanation:
8 x 50 = 400
8 x 7 = 56
400 + 56 = 456
8 x 57 = 456
you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?
Answers
Given data:
The given principal is P=$3,300.
The given rate of interest is r=3.3%.
The given time is t=20 years.
The expression for the final amount of money is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is 5,478.
a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?
Answers
the answer is 1 1/4 cups of vinegar
Step-by-step explanati
what is the median value?if another 5 is added, which statement must be true the mean would increase the mean would decrease the median would increaseboth the median and mean will stay the samehow many people made 3 or less trips to the movie
Answers
Solution
We have the following data:
0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
And the mean would be:
Mean = 2.958
And the median
Median = 4
Then if we add a 5 then the median would be the same 4
And the mean = 3.04
then the solution is:
The mean would increase
And for the other part of the question
we have:´
4+3+1+2 = 10 people made 3 or less trips to the movie
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answers
Answer:
I don't know if it is the answer
Find the length of the hypotenuse if the length of the legs are 6 inches and 9 inches. Round to two decimal places.The length of the hypotenuse is ___ inches.
Answers
The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ \text{Where AC is the hypotenuse, you now have;} \\ AC^2=6^2+9^2 \\ AC^2=36+81 \\ AC^2=117 \\ \text{Add the square root sign to both sides} \\ AC=\sqrt[]{117} \\ AC=10.8166 \\ AC=10.82\text{ (To 2 decimal places)} \end{gathered}[/tex]The answer is 10.82 inches, to 2 decimal places
A phone company offers two monthly plans. Plan A costs $19 plus an additional $0.07 Tor each minute of calls. Plan B costs $12 plus an additional $0.11 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? Х Submit AS
Answers
Explanation
Step 1
let x represents the number of minutes.
hence:
Plan A costs $19 plus an additional $0.07 for each minute of calls
[tex]A=19+0.07x[/tex]Plan B costs $12 plus an additional $0.11 for each minute of calls
[tex]B=12+0.11x[/tex]Step 2
there is a number of minutes x, such both plnas cost the same,so
[tex]undefined[/tex]There are 175 students enrolled in Blue Bear High School. Twenty-five students train in Karate (T) and 35 students compete with other schools in Karate (C). One hundred students practice martial arts, but not Karate. How many students qualify for a Karate tournament if they train and compete at Blue Bear High School? A. 0 B. 15 C. 60 D. 115
Answers
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
As given in the question,
Total number of students enrolled in Blue Bear High School =175
Number of students train in karate = 25
Number of students compete with other school in karate =35
Number of students practice martial arts but not karate=100
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School
= 25 + 35
= 60
Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
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Evaluate 14xy if x=−23 and y=35 . Write your answer as a fraction in simplest form.
Answers
Answer: -11270
Step-by-step explanation:
14xy = -11270 x=-23 y=35
14(-23)(35) = -11270
Find the missing value.Hint: Use the number line to find the missing value.-(-5) = -7A-15-10-5051015
Answers
Given:
The expression is ___-(-5) = -7.
The objective is to find the missing value using number line.
Consider the missing value as x.
Now, the expression can be rearranged as,
[tex]\begin{gathered} x-(-5)=-7 \\ x+5=-7 \\ x=-7-5 \end{gathered}[/tex]So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.
Hence, the missing value is -12.
A table is on sale for $589, which is 24% less than the regular price.
What is the regular price?
Answers
$589 + $141.36 = $730.36
Regular price was $730.36
Solve Step by step
8 = x/7 + 9
Answers
Answer:
[tex]x=\frac{-1}{7}[/tex]
Step-by-step explanation:
[tex]8=x/7+9\\[/tex]
Subtract 9 from both sides
[tex]-1=x/7[/tex]
Multiply both sides by 7
[tex]\frac{-1}{7} =x[/tex]
Swap the order because you're a smart person
[tex]x=\frac{-1}{7}[/tex]
The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.
Answers
SOLUTION:
Case: System of equations
Given: A table of value of snacks and drinks for Sidney and Erica
Required: Write a system of equations to determine the price of each candy and each drink.
Method:
Step 1: Assume the price of snacks be represented by s and drinks by d
Step 2: Equation for Sidney
[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica
[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]Final answer:
The system of equations is:
[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]Assessment
Time Remaining: 2:33:21 | Question 16
Charmaine spent $21 on fruit at the grocery store. She spent a total of $70 at the store. What percentage of the total did she spend on fruit?
%
Answers
Write the equation of the quadratic with a directrix of y=-5 and vertex of (-2,-3).
answer step by step, please
Answers
The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3
How to write the equation of parabola with directrix of y = -5 and vertex of (-2,-3)Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = -3
P in this problem, is the distance between the vertex and the directrix
P = -3 - -5 = -3 + 5 = 2
p = 2
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -2)² = 4 * 2 (y - -3)
(x + 2)² = 8 (y + 3)
rearranging the equation
8 (y + 3) = (x + 2)²
y + 3 = 1/8 (x + 2)²
y = 1/8 (x + 2)² - 3 (standard vertex form)
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24. Write the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5
Answers
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
[tex]y-y_1=m(x-x_1)[/tex]where m = slope.
[tex]\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}[/tex]Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Step-by-step explanation:
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)
where m = slope.
\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}
y−(−13)=
2
1
(x−0)
y+13=
2
1
(x)
y=
2
1
x−13
Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
In null hypothesis significance testing, if a result is unlikely under the hypothesis, then we infer
support for the _______ hypothesis.
Answers
Answer:
Step-by-step explanation:
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.
which expression would be easier to simplify if used the associative property to change the group.A.4+(1.2 +(-0.2)b. 85+(120+80)c. (2+3/7)+4/7d. [-40+(60)] +52
Answers
The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.
'The other expressions involve more steps.
Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?
Answers
The value of a nickel is 5 cents
The value of the quarter is 25 cents
Since Priam has a total of 9.30 dollars = 930 cents, then
[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5
[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then
[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)
[tex](3q-6)+5q=186[/tex]Add the like terms on the left side
[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides
[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8
[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24
Substitute q by 24 in equation 2 to find n
[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66
He has 66 nickels and 24 quarters
The mean height of women in a certain country ( ages 20 29) is 64.1 inches .A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches if the standard deviation is 2.52
Answers
The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches if the standard deviation is 2.52.
To proceed we, find the z-score of 65 in the distribution, we make use of the formula;
[tex]z=\frac{x-\mu}{(\frac{\sigma}{\sqrt[]{n}})}[/tex]x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.
inserting these values, we have;
[tex]\begin{gathered} z=\frac{65-64.1}{\frac{2.52}{\sqrt[]{70}}} \\ z=0.043 \end{gathered}[/tex]The problem now boils down to finding the probability of the z-score greater than 0.043
From z-score tables. the probability of the z-score greater than 0.043;
[tex]Pr(z>0.043)=0.48285[/tex]Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285
What is the probability that a card drawn randomly from a standard deck of 52 cards is a red four? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
We have a deck of 52 cards.
We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.
There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:
[tex]p=\frac{S}{N}=\frac{1}{52}[/tex]As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.
Answer: the probability is 1/52.
Explanation and answer for both Part A and B please
Answers
(2x - 21) + x = 90°
So after factorising:
(2x + x) -21 = 90°
And simplify:
3x -21 = 90°
Do some moving around:
3x = 90° + 21°
3x = 111°
Then divide by 3 on both sides:
x = 37°
Then, because we know what x is, we can substitute it into the formulas for each complimentary angle:
So:
(2x -21) = (2 times 37) - 21 = 53°
And:
x°= 37°
In the questions format:
∠SOT = 37 °
∠SOR = 53°
Hope this helps!
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Solve the system of equations below to find it's solution. List the x-coordinate and y-coordinate.y = 2x - 56x - 2y= 20
Answers
y = 2x - 5 Eq(1)
6x - 2y= 20 Eq(2)
We are going to use the elimination method to solve the system.
y-2x = -5 Transpose x to the othe side in Eq(1)
2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)
2y - 4x = -10
+ -2y +6x= 20
----------------------
2x = 10 Operating like terms
x= 10/2 Isolating x
x = 5
Replacing x in Eq(1)
y = 2*(5) -5
y= 10 - 5 = 5
The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).
The table below represents the total weight, in pounds, of a set ofstone blocks.<
Answers
k=12
1) Gathering the data, and setting this table:
Blocks | Pounds
5 60
6 72
7 84
8 96
2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx
Then we can write:
y =12x
3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.
5 x 12 = 60
6 x 12 =
The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x
2
+10x−5 is
Answers
The slope of the line passing through the y intercept and the vertex of the quadratic x²+10x-5 is 5.
The provided quadratic equation is,
y = x²+10x-5
The vertex of a quadratic equation,
(-b/2a, -D/4a)
Where,
a = 1,
b = 10,
c = -5,
D = (b²-4ac)
D = (10²-4(-5)(1))
D = 100+20
D = 120,
Putting all the values to find the vertex of the equation,
(-10/2,-120/4)
(-5,-30)
So, the vertex are now known,
To find the y intercept, putting x = 0 and solving the equation for y,
y = (0)²+10(0)-5
y = -5
The y intercept is,
(0,-5)
If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,
M = (d-b)/(c-a)
Now, we know two points,(-5,-30) and (0,-5).
We can now find the slope of line,
M = (-5+30)/(0+5)
M = 25/5
M = 5
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I need help on this also could you check if the first 3 questions are correct
Answers
We have two parallel lines intersected by other line.
We have to relate the angles.
We will take the angle with measure 17° as reference (red angle).
The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.
[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.
The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).
The relationship with the red angle is that they are alternate exterior angles.
Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.
Angle <4 and the red angle are corresponding angles.
They have the same measure, so they are congruent.
Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.
Angle <6 and the red angle are vertical angles, so they have the same measure.
Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.
Answer:
Angle <1:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <2:
Measure = 17°
Relationship: Alternate exterior and congruent.
Angle <3:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <4:
Measure = 17°
Relationship: Corresponding and congruent.
Angle <5:
Measure = 163°
Relationship: Linear pair and supplementary.
Angle <6:
Measure = 17°
Relationship: Vertical and congruent.
Angle <7:
Measure = 163°
Relationship: Linear pair and supplementary.
Can somebody please help me right now??? i’m stuck and i need help with this bad
Answers
Answer:
Step-by-step explanation:
The answer is B!
find the equation of the line that contains the point (6,4) and is perpendicular to the line y=3x-5
Answers
The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
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