By using the given dimensions and volume of water, we will see that the height of the tank is 36.6cm
How to find the height of the tank?We know that 27,238 cm³ is the volume of water on the tank, and this is equal to 2/3 of the volume of the tank.
So we can write:
27,238 cm³ = (2/3)*V
Then the volume of the tank is:
V = (3/2)*27,238 cm³ = 40,992 cm³
The base of the tank measures 40cm by 28cm, then:
B = 40cm*28cm = 1,120 cm²
Then the height H is such that:
H*1,120 cm² = 40,992 cm³
Solving for H:
H = (40,992 cm³)/(1,120 cm²) = 36.6cm
The height of the tank is 36.6 centimeters.
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Solve the following quadratic equation 5x^2+18x+9=0
Answer:
[tex]x = -3~\text{and}~ x = -\dfrac 35[/tex]
Step-by-step explanation:
[tex]~~~~~~5x^2 +18x +9=0\\\\\implies 5x^2 +15x +3x +9 = 0\\\\\implies 5x(x+3) +3(x+3) = 0\\\\\implies (x+3)(5x+3) = 0\\\\\implies x = -3,~ x = -\dfrac 35[/tex]
Answer:
x = -3
OR
x = -(3/5)
Step by step explanation:
Given:
5x^2+18x+9=0To Find:
xSoln:
Use quadratic formulae:
Here I typed Quadratic formula as x[tex] \rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}[/tex]
According to the question,on the formula,
a = 5b = 18c = 9So substitute them on the formula:
THEN solve for x.
[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{18 {}^{2} - 4(5 \times 9) }}{2 \times 5} [/tex]
[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 20 \times 9) }}{10} [/tex]
[tex]\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10} [/tex]
[tex] \rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10} [/tex]
[tex] \rm \implies \: x = \cfrac{ - 18 \pm12}{10}[/tex]
[tex] \rm \implies \: x = \cfrac{9 \pm 6}{5} [/tex]
Final solution will after adding first(9+6),then secondly subtracting both 9-6
[tex] \rm \implies \boxed{x = - \cfrac{3 }{5} }[/tex]
[tex] \implies \boxed{\rm x = - 3}[/tex]
So there'll be two possible answers.
Integrate h(x,y)=(x y)i (y2−x)j over the closed curve that begins at (−7,0), goes along the x-axis to (7,0), and returns to (−7,0) by the upper part of the circle x2 y2=49
Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C.
What is Green's Theorem?Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C. It is a two-dimensional variant of Stokes' theorem.
The path of the particle is positively oriented so we can use Green's theorem to find the work done in moving particle along C.
The work done is given by [tex]\oint_{c}\vec F \cdot \vec{dr}[/tex]
Here, [tex]\vec F[/tex](x,y)=<x+y, y²-x>
Then [tex]\oint_{c}\vec F \cdot \vec{dr} = \oint_{c}(x+y)dx+(y^2-x)dy[/tex]
In comparison with [tex]\oint_{c}Pdx+Qdy[/tex] what we have,
P= x+y and Q=y²-x
Then [tex]\dfrac{\partial P}{\partial y} = 1[/tex] and [tex]\dfrac{\partial Q}{\partial x} =-1[/tex]
Using the Green's Theorem,
[tex]\oint_{c}Pdx+Qdy = \iint_{D} \left ( \dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}\right )dA[/tex]
Here D in polar Co-ordinates is given by,
D={(r,θ) : 0 ≤ r ≤ 7, 0 ≤ θ ≤ π}
Then
[tex]\oint_{c}(x+y)dx+(y^2-x)dy\\\\=-\iint_D 2dA\\\\=-\int_{\pi}^{0}\int_{0}^7 2r drd\theta\\\\=-49\pi[/tex]
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Solve the compound inequality y + 7 ≥ –1 and y∕4 + 3 ≤ 5
A)
6 < y ≤ 32
B)
–8 < y ≤ 8
C)
–8 ≤ y ≤ 8
D)
6 ≤ y ≤ 32
what is the volume of a cube if the diagonal of one side is 5sqrt(2)
Must include diagram
The what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units
What is a square?A square is a shape with 4 sides
Let the side of the square be x units. If the length of the diagonal is 5√2, the value of x can be expressed using the pythagoras theorem as shown;
x² + x² = (5√2)²
2x² = 25(2)
x² = 25
x = 5 units
Determine the volume
V = x³
V = 5³
V = 125 cubic units
Hence the what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units
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PLEASE HELP ILL MAKE YOU THE BRAINIEST
Find the value of x
Answer:
12.04
Step-by-step explanation:
add 8 and 9 by the power of two: 8^2+9^2
that equals to 145
find the square root of 145 and that equals to 12.04
1. Find the area of the shaded area of this figure:
Write 0.15 as a fraction in the simplest form.
Answer:
3/20
Step-by-step explanation:
0.15 = 15/100
This is not simplified though :
15/100 ÷ 5/5 = 3/20
This is simplified
Hope this helped and brainliest please.
answer this now for 10
Answer:
15
Step-by-step explanation:
First lets simplify the left side :
5/12 + 5/12 + 5/12 = 15/12
15/12
To make the right side into 15/12 we must multiply it by 15:
15 × 1/12 = 15/12
So the blank is 15
Hope this helped and brainliest please.
Answer:
15/1
Step-by-step explanation:
you simply add the 5's only not the 12. when u multiply 1 and 12 u get 12 and when you multiply 15 and 1 you get 15
What is another name for an X-Value
9TH GRADE ALGEBRA 1
A-output values
B- range
C- domain
D- function
Answer:
see explanation
Step-by-step explanation:
the set of x- values ( the input ) are called the domain
Answer:
domain
Step-by-step explanation:
as the y values is the range
Hypothesis Test for the Population Mean (II)
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
You are to write this code block yourself.
Use Step 3 to help you write this code block. Here is some information that will help you write this code block. Reach out to your instructor if you need help.
The dataframe for your team is called your_team_df.
The variable 'pts' represents the points scored by your team.
Calculate and print the mean points scored by your team during the years you picked.
Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it. (Hint: this is given in the problem statement)
Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
Calculate and print the test statistic rounded to two decimal places.
Calculate and print the P-value rounded to four decimal places.
The test statistic is -0.46 and the p-value is gotten as 0.3340
How to Calculate the P-value?The question is not complete because the data from the sample is 105, 107, 117, 106, 110.
Mean of sample is;
Mean = (105 + 107 + 117 + 106 + 110)/5
Mean; x' = 109
From online standard deviation calculator, the standard deviation of the sample is; S = 4.848
Now, the claim is that your team scored an average significantly less than 110 points. Thus, let's define the hypothesis as;
Null Hypothesis; μ = 110
Alternative Hypothesis; μ < 110
standard error of the mean; S_m = S/√n
S_m = 4.848/5
S_m = 2.17
Thus, the t-statistic is;
t = (x' - μ)/S_m
t = (109 - 110)/2.17
t = -0.46
Degree of freedom for this sample size is;
D.F = N - 1 =5 - 1 = 4
From online p-value from t-score calculator, we have;
p-value = 0.3340
The p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
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Represent each cylinder as a net. Find the surface area of each cylinder.
Answer:
113.04m^2
Step-by-step explanation:
Surface area for Base and top
[tex]2*\pi d=2*3.14*4=25.12[/tex]
Surface area for the other part
[tex]\pi d*h = 12.56*7 = 87.92[/tex]
you will get
113.04m^2
In each problem below, find the total area of the shaded regions.
Thanks!
The area of the shaded region = area of semicircle - area of triangle ACB = 11.32 cm².
What is the Area of a Semi-circle and Triangle?Area of a triangle = 1/2(base)(height).
Area of a semi-circle = 1/2(πr²).
m∠ACB is a right triangle based on the central angle theorem. Therefore, ΔACB is a right triangle.
Radius of circle = OC = 4 cm
CB = 4 cm
Diameter AB = 2(4) = 8 cm
Using the Pythagorean theorem, find AC in ΔACB:
AC = √(AB² - CB²)
AC = √(8² - 4²)
AC ≈ 6.9 cm
Area of ΔACB = 1/2(CB)(AC)
Area of ΔACB = 1/2(4)(6.9)
Area of ΔACB ≈ 13.8 cm²
Area of semicircle = 1/2(πr²) = 1/2(π)(4²)
Area of semicircle ≈ 25.12 cm²
Area of the shaded region = area of semicircle - area of triangle ACB = 25.12 - 13.8
Area of the shaded region = 11.32 cm²
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PLEASE HELP ME!!! It’s High School Math. Algebra 2 and it’s on Big Ideas Math.
Answer:
hope this will help you
[tex]let \: the \: angle \: be \: \alpha \\ \cos( \alpha ) = \frac{b}{h} \\ \cos(60) = \frac{x}{9} \\ \frac{1}{2} = \frac{x}{9} \\ x = \frac{9}{2} \\ x = 4.5[/tex]
What kind of relationship is expressed below?
5x+3=7
a. equation
b. function
c. inequality
Answer:
a. equation
Step-by-step explanation:
The LHS is equal to the RHS
Two or more expressions with an Equal sign is called as Equation. Hence Equation is the relationship of 5x+3=7.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given is 5x+3=7
It is a equation because the left hand side is equal to the RHS side
It has a equal sign.
Where as in expressions there will be no equal sign.
Expression has only numbers, operators and variables.
5x+3=7 is not a function as it has no y variable or other variable.
Hence equation is the relationship of 5x+3=7.
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(Will mark Brainliest)Function g can be thought of as translated(shifted)version of f(x)=x²
Write The equation for g(x)
g(x)=__?__
Answer:
g(x) = (x + 2)² + 1
Explanation:
Given parent function: f(x) = x²
If the function translates two units right
g(x) = (x + 2)²If the function translates one units up
g(x) = (x + 2)² + 1 ← final function.What is x in the figure?
im not sure I'd need to see the figure
Find CE. pleaseee help
Answer:
Radius = 20+5 = 25
We can find CE with the pythagorean theorem
20^2 + CE^2 = 25^2
CE = 15
can someone help me with this question? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
The given expression is :
[tex]\qquad \sf \dashrightarrow \:4x + 8[/tex]
plug the value of x as 3
[tex]\qquad \sf \dashrightarrow \:4(3) + 8[/tex]
[tex]\qquad \sf \dashrightarrow \:12 + 8[/tex]
[tex]\qquad \sf \dashrightarrow \:20[/tex]
Therefore, the required value is 20
Working alone, steve can complete a task in 6 hours. working simultaneously at their respective constant rates, he and mike can complete the same task in 4 hours. how long will it take mike working alone to complete the task
Answer:
It would take him 4 hrs.
Step-by-step explanation:
Hope this helps!
Time taken by mike alone to finish the Task is 12 hours.
steve can complete a task in 6 hours.
he and mike can complete the same task in 4 hours.
What is rate of change?
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
Rate of steve finishing task per hour = 1/6
Rate at which both finishes the task per hour = 1/4
Rate at which mike finishes the task per hour = M
now
M = 1/4-1/6
M = 3-2/12
M = 1/12
here, mike finishes his task at 12 hours
Thus, Time taken by mike alone to finish the Task is 12 hours.
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Simplify the expression to yield a quadratic trinomial in standard form.
6x(x-4)-(3x− 2)
Step-by-step explanation:
6x² - 24x - 3x + 2
6x² - 27x + 2
Can someone help me with this please
Answer:
D
Step-by-step explanation:
A function input can only have ONE output value
so the number 5 can't output two different numbers
What is the probability of a flowering plant bearing flowers in january if it is a tulip? a. 68% b. 72% c. 76% d. insufficient data
The probability of a flowering plant bearing flowers in January if it is a tulip is 68%.
How to find the Probability?
From the attached table, we see the respective probabilities of each flower bearing flowers in January as;
Tulip = 68%
Anemon = 81%
Manzanita = 77%
Peony = 70%
Fuschia Flowering currant = 74%
Total = 76%
Thus, it is clear that the probability of a flowering plant bearing flowers in January if it is a tulip is 68%.
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Answer: insufficient data
Step-by-step explanation: Plato 100% right
What is the value of log 256/ log 1024
Answer:
0.8
Step-by-step explanation:
The change of base formula for logarithms can be used to find this value exactly. (Your calculator can also tell you.)
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]
__
Using this relation with the given numbers, we have ...
[tex]\dfrac{\log(256)}{\log(1024)}=\dfrac{\log(2^8)}{\log(2^{10})}=\dfrac{8\cdot\log(2)}{10\cdot\log(2)}=\dfrac{8}{10}\\\\\boxed{\dfrac{\log(256)}{\log(1024)}=0.8}[/tex]
Jamie had seven posters, but only three could fit on his closet door. How many different ways can he arrange the three posters out of the seven on his closet door?
A. 52.5
B. 210
C. 1260
D. 5,040
Explanation:
Jamie has 7 choices for the first slot, then 6 choices for the next, and 5 choices for the final slot. Order matters. He has 7*6*5 = 210 permutations.
Alternatively you can use the nPr permutation formula with n = 7 and r = 3.
That formula is
[tex]nPr = \frac{n!}{(n-r)!}[/tex]
The exclamation marks indicate factorials. For instance, 4! = 4*3*2*1 = 24.
Answer:
B. 210 is correct!
Step-by-step explanation:
I got it correct on the quiz.
heyyy.... can someone pls help asap. Rearrange the formula to write r in terms of P and pi.
[tex]p = 2r + \pi \: r[/tex]
Step-by-step explanation:
p = 2r + pi×r
p = r(2 + pi)
r = p/(2 + pi)
Answer:
r = [tex]\frac{p}{2+\pi }[/tex]
Step-by-step explanation:
p = 2r + πr ← factor out r from each term
p = r(2 + π) ← divide both sides by (2 + π )
[tex]\frac{p}{2+\pi }[/tex] = r
Which statement best describes the function? Help. Please
The correct answer is option c. Which is the function is increasing when x is greater than zero.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
In the graph, we can see that at the origin the graph becomes zero. When the graph proceeds rightwards the value of the function is increasing as the value of x is increasing.
Therefore the correct answer is option c. Which is the function is increasing when x is greater than zero.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function . f(x) = ln x
Answer:
Behold! Try using Desmos or something
#PlatoAccuracyMatters
#WhaddyaMeanPlatoLives?
Step-by-step explanation:
The functions and their matching properties are:
[tex]h(x) = f(x - \frac{1}{2}) \to[/tex] x-intercept at (1.5,0)[tex]j(x) = f(x) - \frac{1}{2} \to[/tex] vertical asymptote x = 0[tex]g(x) = -\frac 12f(x - 2) \to[/tex] function decreases as x increasesHow to match the functions with their properties?To do this, we start by plotting the graphs of the functions h(x), j(x) and g(x)
Next, we list out the properties from the graphs
From the graphs of the functions (see attachment), we have the following highlights:
[tex]h(x) = f(x - \frac{1}{2})[/tex] has an x-intercept of (1.5,0)[tex]j(x) = f(x) - \frac{1}{2}[/tex] has a vertical asymptote of x = 0The function [tex]g(x) = -\frac 12f(x - 2)[/tex] decreases as x increasesRead more about functions at:
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Solve the system of equations using subtraction.
4x - 2y = 10
4x + y = 19
Answer:
y=3 x=4
Step-by-step explanation:
4x - 2y = 10
4x + y = 19
-3y=-9
the 4x canceled out.
y=3
plug in y into one of the equations
4x + 3 = 19
4x=16
x=4
Hope this helps!
If not, I am sorry.
Answer:
(4, 3 )
Step-by-step explanation:
4x - 2y = 10 → (1)
4x + y = 19 → (2)
subtract (1) from (2) term by term
(4x - 4x) +y - (- 2y) = 19 - 10
0 + y + 2y = 9
3y = 9 ( divide both sides by 3 )
y = 3
substitute y = 3 into either of the 2 equations and solve for x
substituting into (2)
4x + 3 = 19 ( subtract 3 from both sides )
4x = 16 ( divide both sides by 4 )
x = 4
solution is (4, 3 )
Which equation can be used to solve for x in the following diagram?
The equation we can use to find the value of x in the diagram given is: B. (5x + 30) + 5x = 90.
What are Complementary Angles?Angles that give a sum of 90 degrees when added are referred to as complementary angles.
The angles, (5x + 30) and 5x are complementary angles, since the sum of both gives a right angle (90 degrees).
Therefore, the equation that we can use to find x in the diagram is: B. (5x + 30) + 5x = 90.
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What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25
Answer:
C 17.25
Step-by-step explanation:
i think aanswer its c