You spin the spinner twice.6789What is the probability of landing on a 6 and then landing on a prime number?Simplify your answer and write it as a fraction or whole number.
Answers
Given,
The number of section in the spinner is 4.
Required
The probability of landing on a 6 and then landing on a prime number.
The probability of spinner lands on 6 is,
[tex]\begin{gathered} P(6)=\frac{n(6)}{total\text{ section}} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of spinner lands on prime is,
[tex]\begin{gathered} P(prime)=\frac{n(prime)}{total\text{ section}} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of landing on a 6 and then landing on a prime number.
[tex][/tex]Related Questions
Lucy rides her bike at a constant speed of 12 km/h. How far can she travel in 235 minutes?
Answers
Answer:
47 km
Explanation:
• Lucy's constant speed = 12 km/h.
,• Time taken = 235 minutes
First, recall the formula below:
[tex]Distance=Speed\times Time[/tex]Next, note that the speed is given in km/hr, so we convert the given time to hours:
[tex]235\text{ minutes}=\frac{235}{60}\text{ hours}[/tex]Therefore:
[tex]Distance=12\times\frac{235}{60}=47\text{ km}[/tex]She can travel 47 km in 235 minutes.
Farmer buys a tractor for 159,000 and assumes the trade in value of 87,000 after 10 years . The farmer uses a constant rate of depreciation to determine the annual value of the tractor . Find the linear model
Answers
Hello there. To solve this question, we have to find the linear model of the annual value of the tractor.
In this case, we want to find a line equation as follows:
[tex]y=mt+b[/tex]Where m is the slope of the line, b is the y-intercept and t is the time in year.
We know the farmer bought a tractor for $159.000 and assumes the trade in value of $87.000 after 10 years.
Think of these values as points in a graph: (0, 159000) and (10, 87000)
Since the graph of this function is on the ty plane, we can use the slope formula to find the value of m:
[tex]m=\frac{87000-159000}{10-0}=-\frac{72000}{10}=-7200[/tex]Now, plugging in the value of m and any of the points in the equation of the line, we calculate the value of b:
[tex]\begin{gathered} 159000=-7200\cdot0+b \\ b=159000 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-7200t+159000[/tex]B) What is the depreciated value of the tractor after 6 years?
Plugging in t = 6, we get:
[tex]y=-7200\cdot6+159000=115800[/tex]C) When will the depreciated value fall below $80.000?
In this case, we solve for the inequality:
[tex]\begin{gathered} y<80000 \\ -7200t+159000<80000 \end{gathered}[/tex]Subtract 159000 on both sides of the inequality
[tex]-7200t<-79000[/tex]Divide both sides of the inequality by a factor of -7200. Remember this flips the inequality sign.
[tex]t>10.97\text{ years}[/tex]Since we need to round to the nearest integer:
The depreciated value will fall below $80.000 on the 11th year.
The graph will look like the following:
Out of scale. The correct option is indeed C.
Hi I need help with this question, please and thank you
Answers
ANSWER
Factoring Pattern: C. difference of Cubes
Factored Form: (x - y)(x^2 +xy + y^2)
EXPLANATION
Step 1:
If you observe the expression very well, both terms are Perfect Cubes;
Hence, Difference of Cubes formula would be applied to factorize the expression.
Step 2:
Difference of Cubes formula
[tex](a-b)(a^2+ab+b^2)[/tex]where a = x and b = y.
Step 3:
Rewriting the Expression
[tex]\begin{gathered} (x-y)(x^2+xy+y^2) \\ =x^3+x^2y+xy^2-x^2y-xy^2-y^3) \\ \text{ = x}^3-y^3 \end{gathered}[/tex]Hence, the Factored Form is (x - y)(x^2 +xy + y^2)
expand the following expresion 8 (3x + 10y)
Answers
Expand the expression.
[tex]\begin{gathered} 8(3x+10y)=8\cdot3x+8\cdot10y \\ =24x+80y \end{gathered}[/tex]Thus expression after expand is 24x + 80y.
A balloon with a snail leak loses 0.5% of its volume each day.If it originally contained 40 liters of gas,what is the volume of the gas after one week?
Answers
The initial volume is 40 liters.
The volume lost on first day is,
[tex]40\cdot\frac{0.5}{100}=40\cdot0.005[/tex]The volume left after first day leak is,
[tex]\begin{gathered} 40-40\cdot0.005=40(1-0.005) \\ =40(0.995) \end{gathered}[/tex]The volume leak on second day is,
[tex]40(0.995)\cdot\frac{0.5}{100}=40(0.995)\cdot0.005[/tex]The volume left after second day leak is,
[tex]\begin{gathered} 40(0.995)-40(0.995)(0.005)=40(0.995)(1-0.005) \\ =40(0.995)\cdot(0.995) \\ =40\cdot(0.995)^2 \end{gathered}[/tex]In same manner if volume decreases for seven days, then volume of gas is,
[tex]40\cdot(0.995)^7[/tex]Answer: Option D
The variable y varies directly as x, and y = 3 when x=10, Write an equation that relates x and y. Find у when x=-6. Equation: y= (A) When x=-6, y =(B)__
Answers
hello
x varies directly as y and this means that as x increase, y increases likewise when x decreases, y decreases
[tex]\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \\ \frac{x_1}{y_1}=\frac{x_2}{y_2}=\frac{x_3}{y_3}\ldots\frac{x_n}{y_n} \end{gathered}[/tex][tex]\begin{gathered} x_1=10 \\ y_1=3 \\ k=\text{?} \\ k=\frac{x}{y}=\frac{10}{3} \end{gathered}[/tex]now we can find y2 when x = - 6
[tex]\begin{gathered} k=\frac{x}{y} \\ k=\frac{10}{3} \\ \frac{10}{3}=\frac{-6}{y} \\ \text{cross multiply both sides and solve for y} \\ 10\times y=3\times-6 \\ 10y=-18 \\ y=-\frac{18}{10} \\ y=-\frac{9}{5} \end{gathered}[/tex]when x = -6, y = - 9/ 5
explain or show how you could find 5 / 1/2 1/3 I mean explain or show how you could find 1 / 1/3 by using the value of x 3 if needed use this diagram to support your reasoning
Answers
we can see that 5 divided by 1/3 can be pictured as a rectagule divided is 3 parts (red lines). This rectagle was previously divided in 5 parts (black lines). Hence,
[tex]\begin{gathered} 5\text{ divided by }\frac{1}{3}\text{ is equal to 15 parts. In other words} \\ \frac{5}{\frac{1}{3}}=\frac{\frac{5}{1}}{\frac{1}{3}}=\frac{5\cdot3}{1\cdot1}=\frac{15}{1}=15 \end{gathered}[/tex]In which we used the "sandwich law"
A video rental store charges a $20 membership fee and $2.50 for each video rented.1) Write and graph a linear equation (y=mx+b) to model this situation.2) If 15 videos are rented, what is the revenue?3) If a new member paid the store $67.50 in the last 3 months, how many videos were rented?
Answers
Given that the membership fee of $20 is constant, the amount of video rented is $2.50 per video.
It can be observed that the independent variable is the number of video rented at the rate of $2.50, which can also be regarded as the gradient. The membership fee is constant, while the revenue is the dependent variable that is determine based on varied number of video rented.
This information can modelled using the linear equation below
[tex]\begin{gathered} y=mx+b \\ m=2.5 \\ b=20 \\ y=\text{revenue} \\ x=number\text{ of video rented} \\ \text{The modelled equation would be} \\ y=2.5x+20 \end{gathered}[/tex]The graph of the modelled linear equation is as shown below
Hence, the linear equaton modelled is y = 2.5x + 20 and the graph is as shown above
2) If 5 videos are rented, the revenue is as calculated below:
[tex]\begin{gathered} y=2.5x+20 \\ x=15 \\ y=2.5(15)+20 \\ y=37.5+20 \\ y=57.5 \end{gathered}[/tex]Hence, the revenue when 15 videos were rented is $57.50
3) If a new member paid the store $67.50 in the last 3 months, the number of video rented would be
[tex]\begin{gathered} y=2.5x+20 \\ y=67.50 \\ 67.50=2.5x+20 \\ 67.50-20=2.5x \\ 47.50=2.5x \\ \text{LHS}=\text{RHS} \\ 2.5x=47.50 \end{gathered}[/tex][tex]\begin{gathered} \frac{2.5x}{2.5}=\frac{47.50}{2.5} \\ x=19 \end{gathered}[/tex]Hence, the number of videos rented when a new member paid $67.50 is 19
y - 2*x = 12; Solve for x = 3
Answers
ANSWER
y = 18
EXPLANATION
We are given that:
y - 2x = 3
We want to solve for x = 3.
To do this, we put the value of x as 3, that is:
y - 2(3) = 12
y - 6 = 12
Collect like terms:
y = 12 + 6
y = 18
That is the answer.
The price of a gallon of unleaded gas has dropped to $2.82 today. Yesterday's price was $2.87. Find the percentage decrease. Round your answer to the nearesttenth of a percent.__ %
Answers
Answer
1.7%
Step-by-step explanation
Percentage decrease is found as follows:
[tex]\text{ \% Decrease}=(-100)\times\frac{final\text{ - initial}}{initial}[/tex]In this case, the final value is $2.82 and the initial value is $2.87. Substituting these values into the formula, we get:
[tex]\begin{gathered} \text{ \% decrease}=(-100)\times\frac{2.82-2.87}{2.87} \\ \operatorname{\%}\text{ decrease }=(-100)\times\frac{-0.05}{2.87} \\ \operatorname{\%}\text{ decrease }=1.7\text{ \%} \end{gathered}[/tex]if f(x)=-5x+2 g(x)=2x-7 find (f/g) (x)
Answers
To solve this answer, we just have to divide the functions
[tex](\frac{f}{g})(x)=\frac{-5x+2}{2x-7}[/tex]Hence, the resulting function is[tex](\frac{f}{g})(x)=\frac{-5x+2}{2x-7}[/tex]Find an equation of the tangent line at the indicated point on the graph of the function.w = g(z) = 1 + square root of (6 - z), (z, w) = (5, 2)w = - (1/2)z + (9/2)w = (1/2)z - (9/2)w = (1/2)z + (9/2)w = - (1/2)z - (9/2)
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} w=g(z)=1+\sqrt{6-z} \\ (z,w)=(5,2) \end{gathered}[/tex]STEP 2: Explain Tangent line
Tangent Lines:
The tangent line to a function f(x) is a line that touches the graph of the function at one specific point of tangency where it has the same slope as the function at that point.
If x = a is the point of tangency, the tangent line can be written in slope-intercept form as:
[tex]\begin{gathered} y=mx+b \\ where\text{ }m=f^{\prime}(a)\text{ }and\text{ }y|_{x=a}=f(a) \end{gathered}[/tex]STEP 3: Find the tangent
We can first determine the slope of the tangent line by differentiating the function. Writing the function as:
[tex]g(z)=1+(6-z)^{\frac{1}{2}}[/tex]We find the derivative using the chain rule:
[tex]\begin{gathered} \mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g' \\ =\frac{d}{dz}\left(1\right)+\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right) \\ \frac{d}{dz}\left(1\right)=0,\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right)=-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ \\ =0-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ =-\frac{1}{2\left(-z+6\right)^{\frac{1}{2}}} \\ \\ =-\frac{1}{2}(6-z)^{-\frac{1}{2}} \end{gathered}[/tex]At the point of tangency, the slope is
[tex]\begin{gathered} g^{\prime}(5)=-\frac{1}{2}(6-5)^{-\frac{1}{2}} \\ g^{\prime}(5)=-\frac{1}{2} \end{gathered}[/tex]We can begin to write the equation of the tangent line in slope-intercept form
[tex]w=-\frac{1}{2}z+b[/tex]Substituting both coordinates of the point of tangency allows us to solve for the intercept:
[tex]\begin{gathered} 2=-\frac{1}{2}(5)+b \\ -\frac{1}{2}\left(5\right)+b=2 \\ -\frac{1}{2}\cdot \:5+b=2 \\ -\frac{5}{2}+b=2 \\ \frac{5}{2}+b+\frac{5}{2}=2+\frac{5}{2} \\ b=\frac{9}{2} \end{gathered}[/tex]The complete equation of the tangent line at (5,2) is then
[tex]w=-\frac{1}{2}z+(\frac{9}{2})[/tex]Solve the system by elimination. 2x+3y=06x+9y=8
Answers
Given:
The system of equations is,
2x+3y=0
6x+9y=8
Explanation:
Multiply the equation 2x+3y=0 by 3 and subtract from equation 6x+9y=8
.
[tex]\begin{gathered} 6x+9y-3(2x+3y)=8-3\cdot0 \\ 6x+9y-6x-9y=8-0 \\ 0=8 \end{gathered}[/tex]Since no variable left and left-hand side and right-hand side of the equation are unequal. So lines are parallel lines and there is no solution.
Answer: No solution
The average number of miles flown by a Boeing 777 which is operated by a commercial airline over its lifetime is 52,500,000 miles. Assume these mileage amounts have a normal probability distribution with a standard deviation of 2,975,000 miles, and find the mileage that eighty percent of the 777 fleet exceeds over the course of its lifetime in commercial aviation.
Answers
Solution:
Given:
[tex]\begin{gathered} \mu=52,500,000 \\ \sigma=2,975,000 \end{gathered}[/tex]From Z-score table, the Z-score of 80% is 0.842
Hence, using the Z-score formula,
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ 0.842=\frac{x-52,500,000}{2,975,000} \\ Cross\text{ multiplying;} \\ x-52,500,000=0.842\times2,975,000 \\ x-52,500,000=2,504,950 \\ x=2,504,950+52,500,000 \\ x=55,004,950miles \end{gathered}[/tex]Therefore, the mileage that eighty percent of the 777 fleet exceeds over the course of its lifetime in commercial aviation is 55,004,950 miles
A triangle has a base of 4 m and a height of 3 m.What is the area of the triangle?
Answers
Answer: 6m².
Explanation
Given
• Triangle
• Base: 4 m.
,• Height: 3 m.
Procedure
The area of a triangle (A) is given by the following formula:
[tex]A=\frac{1}{2}b\cdot h[/tex]where b represents the base and h the height.
In our problem, we are given that b = 4m and h = 3. Thus, we can replace the values in the formula:
[tex]A=\frac{1}{2}\cdot4\cdot3[/tex]Simplifying:
[tex]A=\frac{1}{2}\times12[/tex][tex]A=\frac{12}{2}[/tex][tex]A=6m^2[/tex]What percent of 65 is 0.39?
Answers
To find what percent of 65 is 0.39, divide 0.39 by 65 and multiply the fraction by 100:
[tex]\frac{0.39}{65}\times100=0.6[/tex]Therefore, 0.39 equals 0.6% of 65.
The answer is:
[tex]0.6\text{ \%}[/tex]Let cos(2x) - cos(x) = 0, where 0° sx s 180°. What are the possible values for x?O 60° onlyO 120° onlyO 0° or 120°O 60° or 180°
Answers
Given the equation:
[tex]\cos \mleft(2x\mright)-cos\mleft(x\mright)=0[/tex]First, we will express the cos (2x) in terms of cos (x) using the angle double rule:
[tex]\cos (2x)=2\cos ^2(x)-1[/tex]So, the given equation will be:
[tex]\begin{gathered} 2\cos ^2(x)-1-\cos (x)=0 \\ 2\cos ^2(x)-\cos (x)-1=0 \end{gathered}[/tex]The last equation has the form of the quadratic equation, so we will factor the equation:
[tex]\begin{gathered} (2\cos +1)(\cos x-1)=0 \\ 2\cos x+1=0\rightarrow\cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})=120\degree \\ \cos x-1=0\rightarrow\cos x=1\rightarrow x=\cos ^{-1}(1)=0\degree \end{gathered}[/tex]So, the answer will be option 3) x = 0° or 120°
Name the number of degrees in the monomial.8a%b8c4d18 degress0 19 degreesO 8 degreesO O degree
Answers
Answer:
19 degrees
Step by step explanation:
The degree of a monomial is the sum of the exponents of all its variables.
In this case.
[tex]a^6=6[/tex][tex]b^8=\text{ 8}[/tex][tex]c^4=\text{ 4}[/tex][tex]d\text{ = 1}[/tex][tex]degrees\text{ = 6+8+4+1}=\text{ 19}[/tex]please help me to do this problem please. Quadratic Formula
Answers
Applying the quadractic formula:
[tex]m=\frac{5\pm\sqrt[]{25-(4)(1)(-14)}}{2}=\frac{5\pm9}{2}[/tex]then the solutions will be m=7 and m=-2[tex]2x + 39 - 21 {}^{2} [/tex]factor everything
Answers
Hello there. To solve this question, we'll calculate the square, add the values and factor out the terms
Given
2x + 39 - 21²
We calculate the square
21² = 441
2x + 39 - 441
Add the values
2x - 402
Factor the equation by a factor of 2
2(x - 201)
This is 8th grade math, Would you please clear up how to do it on my own?
Answers
From the graph, we can recognize two functions:
From the graph, we have that the blue graph is the absolute value function:
[tex]y(x)=|x+3|[/tex]We can take the coordinates of the points:
(-7, 3) and (-3, 0)
(5, 6) and (-3, 0)
The slope for the first case is -3/4 and the second case is 3/4. Then the lines are from this function.
In the second case, we have a parabola if we connect the points from the graph. We can see from the coordinates that the vertex is in x = 5, and y = -6. And the graph can be described by the function:
[tex]y(x)=(x-5)^2-6[/tex]Since the x is shifted five units to the right (x-axis) and 6 units below in the y-axis.
Here we have two functions. If we have these two functions at the same time, we will end with two ranges, and to be a function one needs the function will have only one range. Therefore, this graph does not represent a function (in fact it represents two functions).
What is the equation written in point slope form given (2,5) and (5,9)? y-y1=m(x-x1) (fill in the blanks y- = (x-)
Answers
(2,5) ==> x1 = 2, y1 = 5
(5,9) ==> x2 = 5, y2 = 9
slope m = (y2 - y1)/(x2 - x1) = (9 - 5)/(5 - 2) = 4/3
The slope form equation is:
y - y1 = m(x - 1)
If we use the values for this exercise:
y - 5 = (4/3)(x - 2)
Answer:
y - 5 = (4/3)(x - 2)
A lock has a 3-number code made up of 24 numbers. If none of the numbers areallowed to repeat, how many different ways can you choose three different numbersin order for a unique code?
Answers
Hello! Let's solve the exercise:
The lock has a 3-number code, and we have 24 numbers which can be a possible solution. We also know that the numbers aren't allowed to repeat. So, how many ways we can select three numbers for the code?
Let's think:
For the first password, we can choose any of the 24 numbers that are able, right? So for the first, we have 24 possible options.
For the second, we have 24 possible options minus 1 option which is already in use in the first password, so we have 24 -1 = 23 possible options here.
For the third, we also have 24 options, but we have to consider 2 unavailable options (1 in the first and 1 in the second), so we have 24 -2 = 22 options.
To finish it, we just have to multiply the possibilities of each lock:
24 * 23 * 22 = 12144 possible options to a unique code.
Evaluate the expression when x=5 and y=-4. -x+6y
Answers
We will investigate how to evaluate the expression given in terms of variables as follows:
[tex]-x\text{ + 6y}[/tex]The above expression is dependent on two variables namely ( x and y ). To evaluate the above expression we need the values of the two variables given as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 5 , y = -4}}[/tex]The only step involved in the basic evaluation of expression is to " substitute " the values of respective variables as follows:
[tex]-(\text{ 5 ) + 6}\cdot(\text{ -4 )}[/tex]Then use the basic methematical operation keeping in mind the rule of "PEMDAS" when applying each parameter. We will solve the respective parentheis as follows:
[tex]-5\text{ - 24}[/tex]Apply the basic mathematical operaiton of " subtracttion " as follows:
[tex]\textcolor{#FF7968}{-29}[/tex]how to find value of coordinates when only angle degrees are give
Answers
We just need to apply some trigonometric identities:
[tex]\sin (45)=\frac{s}{13\sqrt[]{2}}\Rightarrow s=13\sqrt[]{2}\sin (45)=13=w[/tex][tex]\cos (45)=\frac{x}{13\sqrt[]{2}}\Rightarrow x=13\sqrt[]{2}\cos (45)=13=v[/tex]Then we have until now s=w=x=v=13, lets continue now with the other ones
[tex]20-w=y-s\Rightarrow20-13=y-13\Rightarrow y=20[/tex]Finally, to find z we apply the tangent identity:
[tex]\tan (30)=\frac{13}{z-20}\Rightarrow z=\frac{13}{\tan (30)}+20=20+13\sqrt[]{3}[/tex]then z=42.5166605 aproximately
If the expression is written in rational exponent notation, rewrite notation, rewrite it in radical notation. If the the expression is written in radical notation, rewrite it in rational exponent notation.
Answers
The expressions can be rewritten using the rule of exponent:
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]QUESTION A
[tex]\sqrt[3]{12}[/tex]In rational exponent form, we have the expression to be:
[tex]\Rightarrow12^{\frac{1}{3}}[/tex]QUESTION B
[tex]\sqrt[4]{10^7}[/tex]In rational exponent form, the expression will be:
[tex]\Rightarrow10^{\frac{7}{4}}[/tex]QUESTION C
[tex]14^{\frac{2}{5}}[/tex]In radical form, the expression will be:
[tex]\Rightarrow\sqrt[5]{14^2}[/tex]QUESTION D
[tex]\sqrt[8]{15^3}[/tex]In rational exponent form, the expression will be:
[tex]\Rightarrow15^{\frac{3}{8}}[/tex]QUESTION E
[tex]21^{\frac{9}{4}}[/tex]In radical form, the expression will be:
[tex]\Rightarrow\sqrt[4]{21^9}[/tex]what is 14 over 50 simplified
Answers
A fraction, by definition, has the following form:
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator. Both are Integers.
In this case you have the following fraction given in the exercise:
[tex]\frac{14}{50}[/tex]You can identify that the given fraction can be simplified by dividing the numerator and the denominator by 2. Then:
[tex]=\frac{14\div2}{50\div2}=\frac{7}{25}[/tex]Since the numetaror and the denominator cannot be divided by the same number, you can determine that the answer is:
[tex]\frac{7}{25}[/tex]Answer:
2
Step-by-step explanation:
14 ÷2
50 ÷ 2
Therefore, 14/50 simplified to the lowest terms is 7/25.
Mais family drinks a total of 10 gallons of milk every 6 weeks. How many weeks does it take the family to consume 1 gallon of milk?
Answers
Given:
Mais family drinks a total of 10 gallons of milk every six weeks.
The proportion per week is,
[tex]\frac{10}{6}=\frac{5}{3}[/tex]The number of weeks required for a family to consume 1 gallon of the milk is,
[tex]\frac{6}{10}=\frac{3}{5}=0.6[/tex]Answer: the family will need 0.6 weeks to consume 1 gallon of milk.
Find the surface area and the volume of the figure shown. Note that the figure may not be drawn to scale.7d2 yd9 ydThe surface area of the figure isM (Simplify your answer.)The volume of the figure isV (Simplify your answer.)
Answers
In order to find the surface area we need to calculate the area of each face
We have two faces with his shape
[tex]A_1=(2\cdot9)+(3\cdot2)=24yd^2[/tex]then we have rectangles in the other faces the formula of the area of a rectangle is l times w where l is the length and w is the width
where A2 is the bottom face and A7 is the lateral face that we can't see in the image but we know they exist
[tex]A_2=9\cdot12=108yd^2[/tex][tex]A_3=12\cdot2=24yd^2[/tex][tex]A_4=7\cdot12=84yd^2[/tex][tex]A_5=3\cdot12=36yd^2[/tex][tex]A_6=2\cdot12=24yd^2[/tex][tex]A_7=5\cdot12=60yd^2_{}[/tex]In order to calculate the surface area we sum all the areas we found remember we have 2 faces with the A1
[tex]\begin{gathered} SA=2A_1+A_2+A_3+A_4+A_5+A_6+A_7_{} \\ \end{gathered}[/tex]we substitute the values
[tex]SA=2(24)+108+24+84+3624+60=384yd^2[/tex]The surface area of the figure is 384 yd^2
Then for the volume, we have the next formula
[tex]V=A_1\cdot w[/tex]where
A1=24yd^2
w=12yd
we substitute the values
[tex]V=24\cdot12=288yd^3[/tex]the volume of the figure is 288yd^3
HUHS is looking to buy more sports equipment for the upcoming school year. The function C(x) = 314 - 7.7x models the cost of shipping the equipment, x, to the school. The function R(x) = 19.3x models the revenue the school earns from fundraising for the equipment, x, they want to buy. Which function, P9x), models the profit that the school earns if they fundraise for the equipment? (Profit = Revenue - Cost)
Answers
According to the information the function for the profit p(x) is obtained by substracting the revenue and the costs.
[tex]p(x)=R(x)-C(x)[/tex]replace the functions into the equation
[tex]p(x)=19.3x-(314-7.7x)[/tex]distribute the negative sign
[tex]p(x)=19.3x-314+7.7x[/tex]simplify the equation
[tex]p(x)=27x-314[/tex]