By working with percentages, we will see that there are 10 gallons of ethanol in the mixture.
How many gallons of ethanol are in the mixture?We know that we have a mixture with a volume of 100 gallons, and 10% of that mixture is ethanol, so we just need to find the 10% of 100 gallons.
To work with percentages, we will use the equation:
Volume of ethanol = total volume*ratio of ethanol.
V = 100gal*(10%/100%)
V = 100gal*0.10 = 10 gal
There are 10 gallons in the mixture.
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Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)
Answer:
0
Explanation:
Let us call
[tex]f(x)=\frac{\sqrt[]{x}}{\csc x}[/tex]The function is continuous on the interval [0, 2pi]; therefore,
[tex]\lim _{x\to\pi^+}f(x)=\lim _{x\to\pi^-}f(x)[/tex]To evaluate the limit itself, we use L'Hopital's rule which says
[tex]\lim _{x\to c}\frac{a(x)}{b(x)}=\lim _{x\to c}\frac{a^{\prime}(x)}{b^{\prime}(x)}[/tex]Now in our case, we have
[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{\frac{d\sqrt[]{x}}{dx}}{\frac{d \csc x}{dx}}[/tex][tex]=\lim _{n\to\pi}\frac{d\sqrt[]{x}}{dx}\div\frac{d\csc x}{dx}[/tex][tex]=\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex]since
[tex]\frac{d\csc x}{dx}=-\frac{\cos x}{\sin^2x}[/tex]Therefore, we have
[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex][tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}[/tex]Putting in x = π into the above expression gives
[tex]-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}\Rightarrow-\frac{1}{2\sqrt[]{\pi}}\times\frac{\sin^2\pi}{\cos\pi}[/tex][tex]=0[/tex]Hence,
[tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}=0[/tex]Therefore, we conclude that
[tex]\boxed{\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=0.}[/tex]which is our answer!
25 men volunteered to lay 1450 pieces of sod around a new church building if each man was given an equal number of pieces how many pieces would each man get
The number of pieces of sod to lay around the church is 1450 and 25 men volunteered to lay it.
If sod is equally distributed among the men, then each man get sod is equal to number of sod divided by number of men. So,
[tex]\frac{1450}{25}=58[/tex]So each man get 58 number of sod.
Answer: 58
Find the volume of the composite figure.First, find the volume of the cylinder.Use 3.14 for it.CylinderVolume = [?] cm9 cm9 cmCube6 cmVolume = [ ]cm4 cmTotal Volume ofComposite Figure = [] cm3=9 cm
Solution
- The question gives us a composite figure made up of a cylinder and a cube.
- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.
- The formulas needed for this calculation are:
[tex]\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\ \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\ \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\ \end{gathered}[/tex]- With the information above, we can proceed to solve the question
Volume of the Cylinder:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{ \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\ \\ \therefore V=\pi\times3^2\times4 \\ \\ V=36\pi cm^3 \end{gathered}[/tex]Volume of Cube:
[tex]\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}[/tex]Volume of Composite Figure:
[tex]\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\ \\ V=36\left(3.14\right)+729 \\ \\ V=842.04cm^3 \end{gathered}[/tex]Final Answer
The volume of the composite shape is 842.04 cm³
x³=yis this a linear or nonlinear equation
ANSWER:
No, it is not a linear equation
Explanation:
Given:
x³=y
Equations are categorized base on the highest exponent of their variables.
An equation with an exponent less rthan equal to 1 is a linear equation, am equation with an exponent of 3 is a cubic equation
This equation x³=y is a non linear equation. It can also be called a cubic equation because x has an exponent of 3.
Also the satndard form of a linear equation is:
y = mx + b
In this case, x³=y is not in that form, so it is not a linear equatio.
y = x³
I need help please there are two parts when we are done with part one the next part shows :) now can I get help
The months in which the income was greater than the expenses are:
June, July and August
For each situation, an inequality is written. Which one has an incorrect inequality?АThree less than a number is greater than negative four and less than negative one; - 4 75DAll real numbers that are greater than or equal to - 7 1/2or less than or equal to zerox < 0 or x>-7 1/2
Option D has an incorrect inequality.
Since option D Says:
"All real numbers that are greater than or equal to - 7 1/2 or less than or equal to zero"
Greater than or equal is represented with the symbol ≤ or ≥.
So the correct inequality is for this statement is:
x ≤0 or x>-7 1/2
Not
x < 0 or x>-7 1/2
Note that the x and 0 part doesn't have an equal sign.
at what rate is the depth of the pool water increasing?
Given:
Find-:
Rate is the depth of the pool water increasing
Explanation-:
The rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two points is:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ \\ (x_2,y_2)=(4,2) \end{gathered}[/tex]So, the rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{4-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]So, 1/2 ft per hour
What are the coordinates of the four vertices and the two foci?
Consider the following expression-x + 8x2 - 9x?Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.
Solution
For this case we have the following polynomial:
[tex]-x+8x^2-9x[/tex]For this case the higher degree is 2 then the answer is:
Degree= 2
Leading Coefficient of the polynomial: 8
I need helps this is an assignment dealing with kites
In a kite, there is one pair of congurent angles. So
[tex]3x-22=x+52[/tex]Solve the equation for x.
[tex]\begin{gathered} 3x-22=x+52 \\ 3x-x=52+22 \\ x=\frac{74}{2} \\ =37 \end{gathered}[/tex]So value of x is 37.
Answer: 37
Can you help me with #7? X^3-2x^2+3x-6 = 0Please follow prompt b
Given:
The polynomial is given as,
[tex]x^3-2x^2+3x-6=0[/tex]The objective is to factor the polynomial completely.
Explanation:
Consider x = 2 in the given equation.
[tex]\begin{gathered} f(2)=2^3-2(2)^2+3(2)-6 \\ =8-8+6-6 \\ =0 \end{gathered}[/tex]Thus, (x -2) is a factor of the polynomial.
Now, using synthetic division,
Thus, the polynomial equation will be,
[tex]x^2+3=0\text{ . . . . .(1)}[/tex]On factorizing the equation (1),
[tex]\begin{gathered} x^2=-3 \\ x=\pm\sqrt[]{-3} \\ x=\pm i\sqrt[]{3} \\ x=i\sqrt[]{3},-i\sqrt[]{3} \end{gathered}[/tex]Hence, the factors of the polynomial are (x-2), (x+i√3), (x-i√3).
Determine if the proportion is true 1/6= 3/18 Proportion is not true Proportion is true
Question: Determine if the proportion is true 1/6= 3/18
Solution:
we have the following equation that it may be true or false:
[tex]\frac{1}{6}\text{ = }\frac{3}{18}[/tex]But, the above equation is equivalent to:
[tex]1\text{ x 18 = 3 x 6}[/tex]But 1x 18 = 18, and 3x 6 = 18 so the above equation is equivalent to
[tex]18\text{ = 18}[/tex]The above equality always is true, so we can conclude that the proportion is true.
you can help me ??? only 24, 26 and 27
Answer:
∠VYZ = 65
∠VXY = 75
∠WZY = 50
∠XWZ = 80
∠WXY = 150
Explanation:
The angle ∠VYZ and the angle ∠VZY are complementary , meaning they add up to 90 degrees. Since ∠VZY = 25 we have
[tex]undefined[/tex]Let x(t) = t - sin(t) and y(t) = 1 - cos(t)
Explanation:
The functions are given below as
[tex]\begin{gathered} x(t)=t-sin(t) \\ y(t)=1-cos(t) \end{gathered}[/tex]Part 1:
To find the value of x(t), we will put t=2
[tex][/tex]Find the value when x = 2 and y = 3.x ^-3y^ -3A. 54B. 216C. 1/216
Explanation:
x ^-3y^ -3
Two companies provide service in a community.• The total cost of a service call for x hours of labor at company A is modeled byy = 28x+ 32.5.• The initial charge for a service call at company B is $3 less than at company A, but their hourly rate is 25% greater.What is the expected total cost of a service call for 6 hours of labor at company B?
Answer:
The expected total cost of a service call for 6 hours of labor at company B is $239.5
Step-by-step explanation:
To solve this, we'll find the expression that models the cost at company B.
First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:
This way,
[tex]\begin{gathered} x=28\times\frac{125}{100} \\ \\ \Rightarrow x=35 \end{gathered}[/tex]Therefore, we'll have that the hourly rate for company B is $35.
Now, we know that the charge for service is $3 less than at company A. This way,
[tex]32.5-3=29.5[/tex]We can conclude that the charge for service at company B is $29.5
Using this data, we'll have that the expression that models the cost for company B is:
[tex]y=35x+29.5[/tex]Using x = 6 (six hours of labor),
[tex]\begin{gathered} y=35(6)+29.5 \\ \\ \Rightarrow y=239.5 \end{gathered}[/tex]Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5
gabriella bought two hoodies that were $15 each. The store was having a sale, everything in the store 15% off. If the sales tax on the purchase was 8%, what was the final cost of the hoodie?
Given:
The cost of each hoodie is, C = $15.
The discount percentage is, d = 15%.
The tax percentage on purchase is t = 8%.
The objective is to find the final cost of the hoodie.
The selling price of one hooie can be calculated as,
[tex]\begin{gathered} SP=c-d \\ =15-(\frac{15}{100}\times15) \\ =15-2.25 \\ =12.75 \end{gathered}[/tex]Now, by adding sales tax to the selling price the final cost will be,
[tex]\begin{gathered} FC=SP+t \\ =12.75+(\frac{8}{100}\times12.75) \\ =12.75+1.02 \\ =13.77 \end{gathered}[/tex]Cost of two hoodie can be calculated as,
[tex]\begin{gathered} C(\text{two)}=2\times13.77 \\ =27.54 \end{gathered}[/tex]Hence, the final cost of one hoodie is $13.77 and final cost of two hoodie is $27.54.
TASK 2: Awards DinnerTran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family membersto sit around for dinner. Below is the floor plan that she drew for the event.StageCLUE Illuminate EducationIncSign out11US 01:09hp
According to the image each table has an amount of 8 seats, and there are
Can anyone help me with this I’m stuck and this is pretty difficult.
Answer:
x=-1
Explanation:
Given the equation:
[tex]$$ 24=4(x-7)+8(1-6 x) $$[/tex]First, expand the brackets:
[tex]24=4x-28+8-48x[/tex]Next, collect like terms and simplify:
[tex]\begin{gathered} 24=4x-48x-28+8 \\ 24=-20-44x \\ \text{ Add 20 to both sides} \\ 24+20=-44x \\ 44=-44x \\ \text{ Divide both sides by -44} \\ \frac{44}{-44}=\frac{-44x}{-44} \\ x=-1 \end{gathered}[/tex]The solution to the equation is -1.
If the distance from the too of the building to the tip of its shadow is 150ft, what is the length of the buildings shadow
In order to know the length of the shadow, we will use a trigonometric function in this case for the data given and the distance we want to find we will use the sine
[tex]\sin (75)=\frac{S}{150}[/tex]we isolate S
[tex]S=\sin (75)\cdot150=144.89[/tex]the length of the shadow is 144.89ft
in a game a player starts with 100 points each question has two parts and a incorrect answer for both parts result in a loss of one point the student loses one half of a point for getting only one part of the question correct at the end of 25 question round the player has 82.5 points what to equations and solutions represent X Missed points
Answer:
10 questions with an incorrect answer for both parts
15 questions with a correct answer in only one part
Explanation:
Let's call x the number of questions with an incorrect answer for both parts and y the number of questions with only one part of the question correct.
So, the equation that gives us the number of points after 25 rounds is:
100 - x - 0.5y = 82.5
Where: x + y = 25
So, solving for y, we get:
y = 25 - x
Replacing this on the initial equation and solving for x, we get:
[tex]\begin{gathered} 100-x-0.5y=82.5 \\ 100-x-0.5(25-x)=82.5 \\ 100-x-12.5+0.5x=82.5 \\ 87.5-0.5x=82.5 \\ 87.5-82.5=0.5x \\ 5=0.5x \\ \frac{5}{0.5}=x \\ 10=x \end{gathered}[/tex]Then, the value of y is:
[tex]\begin{gathered} y=25-x \\ y=25-10 \\ y=15 \end{gathered}[/tex]Therefore, the player gets 10 questions with an incorrect answer for both parts and 15 questions with a correct answer in only one part.
an airliner travels 30 miles in 4 minutes. what is its speed in miles per hour?
We need to convert minutes to hours. We know that 1 hour is 60 minutes so we can use the conversion factor of 1 hour = 60 minutes. We make sure the minutes cancel in the top and bottom leaving
30 miles 60 minutes
------------- * --------------
4 minutes 1 hour
30 miles * 60
--------------------
1 hour
180 miles
--------------
hour
A rectangle is placed around a semicircle as shown below. The width of the rectangle is . Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Solution
Step 1
Write the given data:
Radius r of the semi-circle = 4 yd
Width of the rectanhle = 4 yd
Length of the rectangle = 2 x 4 = 8 yd
Step 2
Write the formula for the area of the shaded region:
[tex]\begin{gathered} Area\text{ of the shaded region} \\ =\text{ Area of a rectangle - Area of the semi-circl} \\ =\text{ W }\times\text{ L - }\frac{\pi r^2}{2} \\ =\text{ 4}\times\text{ 8 - }\frac{3.14\times4^2}{2} \\ =\text{ 32 - 25.12} \\ =\text{ 6.88 yd}^2 \end{gathered}[/tex]Final answer
6.88
←
In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
Given,
In a sex selection technique,
The number of female babies in the result = 284
The number of male babies in the result = 15
Total children = 284 + 15 = 299
We have to find the probability of being a girl child;
Probability;
Probability refers to potential. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.
Here,
The probability of being a girl child, P = 284/299 = 0.9498
That is,
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
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Find the volume of the cylinder and round to the nearest hundreth. Use 3.14 for pi
Volume of a cylinder: pi * r^2 * h
Where:
pi = 3.14
r= radius = 8km
h= heigth = 7km
Replacing:
V = 3.14 * (8)^2 * 7 = 1,406.72 km3
Jenelle invests $8,000 at 3% simple interest for 48 years. How much is in the account at the end ofthe 48 year period? Round your answer to the nearest cent.Answer: $Submit Question
Given
Principal = $8,000
Rate = 3%
Time = 48 years
Find
Amount at the end of the 48 years
Explanation
Amount = Simple interest + Principal
Simple Interest is given by
[tex]S.I=\frac{P\times R\times T}{100}[/tex]now substitute the values ,
[tex]\begin{gathered} S.I=\frac{8000\times3\times48}{100} \\ \\ S.I=11520 \end{gathered}[/tex]amount = 11,520 + 8000 = $19,520.00
Final Answer
Therefore , the amount at the end of the 48 years will be $19,520.00
Drag the tiles to the boxes to form correct pairs.Match each set of vertices to the triangle they form.acute equilateralright isoscelesacute isoscelesA(3,5),B(3,4),C(5,4)A(2,4), B(4,5), C(3,6)A(3,5),B(5,6),C(3,0)A(2,4),B(3,5), C(2,6)obtuse scaleneright scalene
Step 1
Plot the triangles
let
A)
we can see that angle in B is 90 ° and length AB is different to BC, When one of the three angles measure 90 degrees and the angles or lengths of other two sides are not congruent, then the scalene triangle is called right scalene triangle
right scalene
Step 2
triangle 2
[tex]A(2,4)\text{ B\lparen4,5\rparen c\lparen3,6\rparen}[/tex]in this case, we have that length AC equlas AB,also we can see that angle A is smaller than 90 ° ,an acute angle measure less than 90 degrees,so
so
[tex]AC=AB[/tex]a triangle in which two sides have the same length is called acute isosceles
Step 3
A(3,5),B(5,6),C(3,0)
an obtuse scalene triangle can be defined as a triangle whose one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. All three sides and angles are different in measurement.so this is an
obtuse scalene
Step 4
finally, A(2,4),B(3,5), C(2,6)
An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.
we can see that
[tex]\begin{gathered} m\angle B=90 \\ AB=BC \end{gathered}[/tex]therefore, this is an
rigth isosceles
I hope this helps you
Answer:(3,5) (4,5) (3,6)
acute isosceles
Step-by-step explanation:
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.y²-3y - 18/y²-9y + 18Rational expression in lowest terms:Variable restrictions for the original expression: y
Given: The expression below
[tex]\frac{y^2-3y-18}{y^2-9y+18}[/tex]To Determine: The lowest term of the given rational fraction
Solution
Let simplify both the numerator and the denominator
[tex]\begin{gathered} Numerator:y^2-3y-18 \\ y^2-3y-18=y^2-6y+3y-18 \\ y^2-3y-18=y(y-6)+3(y-6) \\ y^2-3y-18=(y-6)(y+3) \end{gathered}[/tex][tex]\begin{gathered} Denominator:y^2-9y+18 \\ y^2-9y+18=y^2-3y-6y+18 \\ y^2-9y+18=y(y-3)-6(y-3) \\ y^2-9y+18=(y-3)(y-6) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} \frac{y^2-3y-18}{y^2-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y-6-is\text{ common} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{y+3}{y-3} \end{gathered}[/tex]Hence, the rational expression in its lowest term is
[tex]\frac{y+3}{y-3}[/tex]The variable for the original expression is as given as
[tex]\begin{gathered} \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y\ne3,y\ne6 \end{gathered}[/tex]The length of a wire was measured using two different rulers. How many significant figures are in each measurement?
We will have the following
In the first image we can see that the maximum you will measure with a good degree of certainty is the unit, and in the next one we wil have that is the unit and a fraction of it, so:
Top: 1 significative figure.
Bottom: 2 significative figures.
9=3(x+2) simplified
x=1
Explanation
Step 1
[tex]9=3(x+2)[/tex]apply distributive property
[tex]\begin{gathered} 9=3(x+2) \\ 9=3x+6 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} 9=3x+6 \\ \text{subtract 6 in both sides} \\ 9-6=3x+6-6 \\ 3=3x \end{gathered}[/tex]Step 3
finally, divide both sides by 3
[tex]\begin{gathered} 3=3x \\ \frac{3}{3}=\frac{3x}{3} \\ 1=x \end{gathered}[/tex]so, the answer is x=1
I hope this helps you