SOLUTION
[tex]Volume\text{ }of\text{ }can=\pi r^2h[/tex][tex]Surface\text{ }area\text{ }of\text{ }can=2\pi r^2+2\pi rh[/tex]The ratio can be established as shown below
[tex]\begin{gathered} \frac{\pi r^2h}{2\pi r^2+2\pi rh} \\ \frac{\pi r^2h}{2\pi r(r+h)} \\ \frac{rh}{2(r+h)} \end{gathered}[/tex]The correct answer is OPTION D
Tank A contains a mixture of 10 gallons of water and 5 gallons of pure alcohol tank b has 12 gallons of what and 3 gallons of alcohol how many gallons should be taken from each tank and combiend in order to obtain 8 gallons of a solution countaning 25% alcohol
The volume from tanks A and B are taken as 3 and 5 gallons respectively.
Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B = 1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40 + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3
Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.
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Determine the shape when the following points are graphed one a coordinate plane. A(-3, 1), B(2, 1), C(2, 4), D(-3, 4)
The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).
The image below shows the figure formed by these points.
As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.
Therefore, the answer is "rectangle".Consider the two polynomials p(x), q(x) in Z[x] by p(x) = 1+2x+3x2, q(x) = 4+5x+7x3. Then p(x) + q(x) is
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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4. (A.20) Natasha and her friends go out for ice cream. They decide to create their own ice cream, which costs $1.60 plus 8 cents per topping. If x represents the number of toppings on the ice cream, then which'equation describes y, the total cost for the ice cream?A. y = 0.08 + 1.60)x B. y = .08 + 1.60x C. y = 1.60 +.08x D. y = 8x + 1.60
Answer:
C. y = 1.60 +.08x
Explanation:
The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x
So, the total cost for the ice cream is represented by the equation:
y = 1.60 +.08x
can you solve for x and y y=4x-11=x+13
x = 8, y = 21
Explanations:The given equation is:
y = 4x - 11 = x + 13
This can be splitted into two equations as:
y = 4x - 11..........(1)
y = x + 13..........(2)
Substitute equation (1) into equation (2)
4x - 11 = x + 13
4x - x = 13 + 11
3x = 24
x = 24/3
x = 8
Substitute the value of x into equation (1)
y = 4x - 11
y = 4(8) - 11
y = 32 - 11
y = 21
x = 8, y = 21
solve for x. z=5x-9y
ANSWER:
[tex]x=\frac{z+9y}{5}[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]z=5x-9y[/tex]We solve for x as follows:
[tex]\begin{gathered} z+9y=5x \\ 5x=z+9y \\ x=\frac{z+9y}{5} \end{gathered}[/tex]In the figure below, ZYZA and _YZX are right angles and _XYZ and ZAYZ arecongruent. Which of the following can be concluded about the distance frompoint A from point Z using Thales's method?O A. The distance between points A and Z is the same as the distancebetween points X and Z.B. The distance between points A and Z is the same as the distancebetween points A and Y.O C. The distance between points A and Z is the same as the distancebetween points Yand Z.D. The distance between points A and Z is the same as the distancebetween points X and Y.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} \angle YZA=90^{\circ} \\ \angle YZX=90^{\circ} \\ \angle XYZ\cong\angle AYZ \end{gathered}[/tex]Thale's method shows that angles in a triangle opposite two sides of equal length are equal
[tex]undefined[/tex]As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)
can anyone help me?
solve using system of linear equations using elimination
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
The values of the variables are x = 2, y = -2 and z =0
How to solve the system of equations?From the question, the system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Subtract the second equation from the third
This action will eliminate (y)
So, we have
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
Evaluate
-x + z = -2
Make x the subject
x = z + 2
Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Evaluate
-2z - y = 2
-z + 3y = -6
Double -z + 3y = -6
-2z + 6y = -12
Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z
7y = -14
Divide
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the solution is x = 2, y = -2 and z =0
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Simplify (v2 + 10v + 11)(v2 + 3v – 4) using the distributive property of multiplication ove addition(DPMA)
Given:
[tex](v^2+10v+11)(v^2+3v-4)[/tex]To find- the simplification.
Explanation-
We know that the distribution property of multiplication over addition says
[tex]a(b+c)=ab+ac[/tex]Use this property to simplify, and we get
[tex]\begin{gathered} =(v^2+10v+11)(v^2+3v-4) \\ =v^2(v^2+3v-4)+10v(v^2+3v-4)+11(v^2+3v-4) \end{gathered}[/tex]Multiply by opening the bracket, and we get
[tex]=(v^4+3v^3-4v^2)+(10v^3+30v^2-40v)+(11v^2+33v-44)[/tex]Now, open the bracket and combine the like terms.
[tex]\begin{gathered} =v^4+3v^3-4v^2+10v^3+30v^2-40v+11v^2+33v-44 \\ =v^4+(3v^3+10v^3)+(11v^2-4v^2+30v^2)-40v+33v-44 \end{gathered}[/tex]On further solving, we get
[tex]=v^4+13v^3+37v^2-7v-44[/tex]Thus, from the distributive property of multiplication over addition, we get v⁴+13v³+37v²-7v-44.
The answer is v⁴ + 13v³ + 37v² - 7v - 44.
a storage container for oil is in the shape of a cylinder with a diameter of 10ft and a height of 17ft. what is the volume if the storage container in cubic feet?
To calculate the volume, w will use the formula:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question,
diameter = 10
This implies that; r=d/2 = 10/2 = 5
h = 17
susbtitute the values into the formula
[tex]V=\pi\times5^2\times17[/tex][tex]=425\pi\text{ cubic feet}[/tex]If we substitute the value of pie= 22/7
[tex]V=\frac{22}{7}\times425[/tex][tex]\approx1335.71\text{ cubic f}eet[/tex]Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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Use a graph to predict the value of jewelry in 7 years.
Solution:
Given that the initial cost price of the jewelry is $2,200.
The rate at which it decreases each year is 12%.
Thus, the exponential decay function is;
[tex]\begin{gathered} y(t)=2200(1-0.12)^t \\ \\ \text{ Where }t\text{ is the time in years.} \end{gathered}[/tex]The graph of the function is;
From the graph;
CORRECT OPTION:
[tex]\approx899.09[/tex]of a sample of 200 students surveyed,38 students said the soccer was their favorite sport what percent of the students in the sample prefer soccer 19% 38%40%76%
Out of 200 students surveyed, 38 said that soccer was their favorite sport.
The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:
200 students____100%
38 students _____ x%
Both relationships are at the same ratio so that:
[tex]\frac{100}{200}=\frac{x}{38}[/tex]To determine the percentage multiply both sides by 38:
[tex]\begin{gathered} 38\cdot\frac{100}{200}=38\cdot\frac{x}{38} \\ 19=x \end{gathered}[/tex]The percentage of students surveyed that like soccer is 19%
Andrea invites 12 cousins 6 aunts 4 brothers 2 sisters what fraction of her party guests are cousins?
To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.
She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.
Then:
[tex]\frac{nº\text{cousins}}{\text{total guests}}=\frac{12}{24}[/tex]Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12
[tex]\frac{12\div12}{24\div12}=\frac{1}{2}[/tex]The fraction
what is the approximation of 3√200
Given the expression:
[tex]\text{ }\sqrt[3]{200}[/tex]Let's simplify the expression and convert its decimal form to get its approximation.
We get,
[tex]\text{ }\sqrt[3]{200}\text{ = }\sqrt[3]{8\text{ x 25}}[/tex][tex]\text{ =2 }\sqrt[3]{25}[/tex]In decimal form:
[tex]\text{ 2 }\sqrt[3]{25}\text{ = 2 x 2.92401773821 = 5.84803547643 }\approx\text{ 5.8}[/tex]Therefore, the approximate equivalent of 3√200 is 5.8.
Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20
SOLUTION
From
[tex]\begin{gathered} \cos 2x=\cos x \\ \cos ^2x-\sin ^2x=\cos x \\ \cos ^2x-(1-\cos ^2x)=\cos x \\ 2\cos ^2x-1=\cos x \\ 2\cos ^2x-\cos x-1=0 \\ \text{From the quadratic formula} \\ \cos x=\frac{1\pm\sqrt[]{1-(-8)}}{4} \\ \\ \cos x=\frac{1\pm3}{4} \\ \cos x=\text{ 1 or -}\frac{1}{2} \\ \text{Taking the cos}^{-1}of\text{ 1 and -}\frac{1}{2} \\ We\text{ have }\theta\text{ = 0, }\frac{2\pi}{3},\frac{4\pi}{3},\frac{8\pi}{3}\ldots\ldots\ldots2\pi \end{gathered}[/tex]So your answer is
[tex]0,\text{ }\frac{2\pi}{3},\text{ }\frac{4\pi}{3}[/tex]Solve.Draw a rectangular fraction model to explain yourthinking.Then, write a number sentence.1/3of3/7=
We are asked to find 1/3 of 3/7 using a rectangular fraction model.
Let us draw a rectangular fraction model.
1/3 means make 3 rows
3/7 means make 7 columns
[tex]\frac{1}{3}\times\frac{3}{7}=\frac{3}{21}[/tex]Three 3 filled boxes represent the numerator and the total 21 boxes represent the denominator.
Therefore, the result is 3/21
the lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams . how many calories would this be? if you don’t know , don’t respond
There would be 91.8 calories in 27 grams.
Define unitary method.The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.
Given,
Calories per serving = 25
Serving size = 85 grams
Calories per serving using unitary method:
Dividing,
[tex]\frac{85}{25}[/tex]
3.4
Calories per serving using unitary method is 3.4 calories.
Now, we have 27 grams,
Multiplying:
27 (3.4)
91.8
There would be 91.8 calories in 27 grams.
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discriminant for 2n^2+8n+1=-7
The given equation is
[tex]\begin{gathered} 2n^2+8n+1=-7 \\ 2n^2+8n+1+7=0 \\ 2n^2+8n+8=0 \end{gathered}[/tex]Where a = 2, b = 8, and c = 8.
The discriminant formula is
[tex]D=b^2-4ac[/tex]Let's replace the values
[tex]D=(8)^2-4(2)(8)=64-64=0[/tex]The equation has one real solution.the difference of four times a number and seven is 13
ExplanatIon
Step 1
let x represents the number
hence,
four times a number =4*x=4x
the difference of four times a number and seven=4x-7
is can be written as equal or "="",so
the difference of four times a number and seven is 13
[tex]4x-7=13[/tex]Step 2
solve for x
[tex]\begin{gathered} 4x-7=13 \\ \text{add 7 in both sides} \\ 4x-7+7=13+7 \\ 4x=20 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]so, the number is 5.
I hope this helps you
Find an equation for the line that passes through the points (2,2) and (-6,4)
Answer:
y=-1x/4+5/2
Step-by-step explanation:
use the slope formula
Reflect the following figure across the x-axis: S: (0, -3), T: (3, 1), U: (4, -3)
We are given the following coordinates.
[tex]\begin{gathered} S(0,-3) \\ T(3,1) \\ U(4,-3) \end{gathered}[/tex]We are asked to reflect them across the x-axis.
Recall that the rule for reflection across the x-axis is given by
[tex](x,y)\rightarrow(x,-y)[/tex]As you can see, the y-coordinate gets reversed.
Let us apply this rule on the given coordinates S, T, U
[tex]\begin{gathered} S(0,-3)\rightarrow U^{\prime}(0,3) \\ T(3,1)\rightarrow T^{\prime}(3,-1) \\ U(4,-3)\rightarrow U^{\prime}(4,3) \end{gathered}[/tex]Therefore, the above coordinates are reflected over the x-axis.
Need answer if you could show work would be nice
In the Polynomial function f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]
So all the zeros of f(x) algebraically
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].
Step: 1
Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]
[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]
Step: 2
Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]
[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]
Step: 3
so for finding zeros of
[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]
[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]
Explanation: Please refer to solution in this step.
Answer:
So required zeros of
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]
What is polynomial function?A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means term, and so when combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.
The polynomial function in standard form is:
f(x) = [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]
This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.
The three most common polynomials we usually encounter are
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sarah spent a total of 10 on oranges and apples at the supet market. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
Let's write 2 equations from the two statements given.
Sarah spent 10 dollars on both oranges and apples
Let the price of oranges be "x" and price of apples be "y", thus we can write:
[tex]x+y=10[/tex]Oranges cost 3 less than apples, thus we can say:
[tex]y-3=x[/tex]We can substitute this into the first equation and solve for y:
[tex]\begin{gathered} x+y=10 \\ y-3+y=10 \\ 2y=10+3 \\ 2y=13 \\ y=\frac{13}{2} \\ y=6.5 \end{gathered}[/tex]Thus, let's solve for x now,
[tex]\begin{gathered} x=y-3 \\ x=6.5-3 \\ x=3.5 \end{gathered}[/tex]We want the price of oranges (x), thus,
Price of Oranges = $3.50
I need help with my math homework question please. Plus it has a second part of the question
The given quadratic equation is
y = - x^2 + 25
a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.
Leading coefficient = - 1
Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is
Down
b) The standard form of a quadratic equation is
y = ax^2 + bx + c
By comparing both equations,
a = - 1
b = 0
c = 25
The formula for calculating the x coordinate of the vertex of the graph is
x = - b/2a
By substituting the given values,
x = - 0/2 * - 1 = 0
We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have
y = - 0^2 + 25
y = 25
The coordinate of the vertex is (0, 25)
c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have
- x^2 + 25 = 0
x^2 = 25
Taking the square root of both sides,
x = square root of 25
x = ± 5
Thus, the x intercepts are
(5, - 5)
d) The y intercept is the value of y when x = 0
Substituting x = 0 into the orignal equation,
y = - 0^2 + 25
y = 25
y intercept = (0, 25)
e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have
y = - (6)^2 + 25 = - 36 + 25
y = - 11
We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below
For a standard normal distribution,Find P(-1.21 < Z< 2.26)
Answer:
The range of z-score is given below as
[tex]P(-1.21Using a graphing calculator, we will have the image be[tex]\begin{gathered} P(z<-1.21)=0.11314 \\ P(z<2.26)=0.9881 \\ P(-1.21Hence,The final answer is
[tex]P(-1.21\lt z\lt2.26)=0.8750[/tex]Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
The number of people that can attend Jordan's party would be; 50 people.
What is equation?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation will be;
The Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
Now substitute;
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + 4p
$800 = $600 + 4p
$800 - $600 = 4p
$200 = 4p
p = $200 / $4
p = 50 people
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Jan draws a card from the set below, replaces it and then draws another card. Which of the following tree diagrams correctly shows the sample space?
Given the word problem, we can deduce the following information:
1. Jan draws a card from the set below, replaces it and then draws another card.
Based on the given information, there is a replacement happening. It means that Jan put a card back in the set before selecting another card. So the tree diagram that shows all the possible outcomes is Diagram A.
Therefore, the answer is A.
You need a quarter of a pumpkin
to make a pie. How many pies
can you make with three and a
half pumpkins?
Answer: 14
Step-by-step explanation:
1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.
1 pumpkin = 4/4
3.5 pumpkins = 14/4
If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.
Jenny wants to earn $1,300by the end of the summer. How much more will she need to earn to meet her goal?
The most appropriate choice for subtraction of natural numbers will be given by-
Jenny needs $1172.95 to earn her goal.
What is subtraction?
At first, it is important to know about natural numbers.
Natural numbers are integers which are greater than or equal to 1
One of the operations on natural number is subtraction
The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.
Amount of money Jennyy had before = $127.05
Amount of money Jenny wants to earn = $1300
Amount of money Jenny needs to earn her goal = $(1300 - 127.05)
= $1172.95
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Complete Question
Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?
(Jenny had $127.05 before.)