Ry=1 means a reflection in the y axis, so we have to change the sign of the y coordinate so the answer is:
[tex](3,4)\to(3,-4)[/tex]So is option (A)
set amount of carbon dioxide in moles produced in a chemical reaction is given by the function f(t) = 0.02t^2 and t is in seconds find the rate of production of carbon dioxide after two seconds
We have the following function for the amount of carbon dioxide in moles produced in a chemical reaction:
[tex]f(t)=0.02t^2[/tex]And we also have that it is a function of time (t), and we need to find the rate of production of carbon dioxide after two seconds.
1. To find the rate of production, we need to find the derivative for the function since it will give us the instant rate of change for the chemical reaction. Then we have:
[tex]\frac{df(t)}{dt}=\frac{d}{dt}(0.02t^2)[/tex]2. And now, applying the derivative rules for a constant, and for a power, we have:
[tex]\begin{gathered} \frac{d}{dt}(0.02t^2)=0.02*\frac{d}{dt}(t^2)=0.02*2*t=0.04*t \\ \\ \text{ Therefore, the derivative is:} \\ \\ 0.04*t \end{gathered}[/tex]3. Then after 2 seconds, we have that the rate of production of carbon dioxide is:
[tex]0.04(2)=0.08\frac{\text{ mol}}{s}[/tex]Therefore, in summary, the rate of production of carbon dioxide after two seconds is 0.08 mol/s (option c).
A baseball field is a square with sides of length 90 feet. What is theshortest distance between first base and third base?
127.3 ft
Explanation
Step 1
Diagram
as the field is a square ,we know each angle is 90 °, hence, the triangle formed by , the first base, the third base and the second baseis a rigth triangleb
so, we can use the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse:
so
Let
[tex]\begin{gathered} side1=\text{ side2= 90 ft} \\ hypotenuse=h \end{gathered}[/tex]hence
[tex]\begin{gathered} 90^2+90^2=h^2 \\ 8100+8100=h^2 \\ 16200=h^2 \\ h=\sqrt{16200} \\ h=127.279 \\ \end{gathered}[/tex]therefore, the answer is
127.3 ft
I hope this helps you
Suppose potato chips cost 24.5 cents per ounce. If a bag costs $3.23, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
one bag of chips costs $3.23
one once of chips costs 24.5 cents = $0.245
therefore, there are the following number of ounces inside the bag:
[tex]\frac{3.23}{0.245}=13.18[/tex]So, the answer is 13.18 ounces
water flows out of pipe a at a constant rate pipe a can feel three buckets of the same size and 14 minutes write a linear equation that represents the situation
Notice that the rate at which the water flows is constant. Let;s call such R.
Then, the equation that represents the number of buckets as a function of time must include this info:
Number of buckets = Rate * time (in minutes)
3 = R * 14
Then R = 3 buckets over 14 minutes.
Number of buckets = 3/14 * time
This is the linear equation that represents the number of buckets filled as a function of the time elapsed (in minutes).
of girls make up 3/5 of a class.and there are 24 girls.How many total people are in the class?
If the girls make up 3/5 of the class, then girls are 60% of the class.
Then, we can use the formula for percents:
[tex]\text{Total}\cdot\frac{\text{percent}}{100}=\text{Equivalent number to the percent}[/tex]Substitute, percent and the equivalent number to the percent and we can solve for the variable ''Total'':
[tex]\begin{gathered} \text{Total}\cdot\frac{60}{100}=24 \\ \text{Total}=\frac{24\cdot100}{60} \\ \text{Total}=40 \end{gathered}[/tex]There are 40 students in the class.
A) draw a graph, and label and scale both axes. Plot the points (-2, 3) and (1, -5), clearly labeling them.B) connect the dots plotted above and find the slope of that line
Below is the grapph of the plotted points
A)
B) Below is the graph of the plotted points as the dots has been connected
We can now go ahead to find the slope
The formula for calculating slope is given by;
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]From the two points;
x₁=-2
y₁=3
x₂=1
y₂=-5
substitute the values in the formula
[tex]\text{slope}=\frac{-5-3}{1+2}[/tex][tex]=\frac{-8}{3}[/tex][tex]=-2.67[/tex]A pool holds 8.1 × 10⁹ liters of water. The pool is being filled by a hose at rate of 3×10⁷ liters per hour. How many hours will it take to fill the pool?
We are given that the rate of volume per time is 3×10⁷liters per hour and that we need to fill a volume of 8.1 × 10⁹ liters, we are asked how many hours will it take to fill the given volume. To do that, we need to remember the formula for the rate of change of volume with time, that is:
[tex]Q=\frac{V}{t}[/tex]Where Q is the rate of change of the volume. Solving for time "t", we get:
[tex]t=\frac{V}{Q}[/tex]Replacing the known values we get:
[tex]t=\frac{8.1\times10^9L}{3\times10^7\frac{L}{h}}[/tex]Solving the operation, we get:
[tex]t=270h[/tex]Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 22,16,10
From the question we are given the sequence
[tex]22,16,10[/tex]We are to determine if the sequence is arithmetic or geometric
This will be done by find checking if the sequence has a common ratio or a common difference
Hence, from the sequence we can deduce that
[tex]16-22=10-16=-6[/tex]Therefore the common difference = -6
But
[tex]\frac{16}{22}\ne\frac{10}{16}[/tex]Hence the sequence does not have a common ratio
Finally
The sequnce has a common difference of -6 hence it ia an arithmetic sequence
i have other question but i need help with this one
Answer:
[tex]10x+2y[/tex]Explanation:
Given the below expression;
[tex]3x+4y-2y+7x[/tex]Let's go ahead and combine terms with x and terms with y together;
[tex]3x+7x+4y-2y=10x+2y[/tex]Johnny started working at the local grocery store this year and earns $9.75 for every hour he works. There is a proportional relationship between the number of hours Johnny works and the amount of money he earns. Complete the table. Hours Worked Amount Earned ($) 2.
Johnny works at the local grocery store and earns $9.75 per hour.
For 2 hours, he earns 2*$9.75 = $19.50
For 3 hours, he earns 3*$9.75 = $29.25
For 4 hours, he earns 4*$9.75 = $39.00
Now complete the table:
find three consecutive odd integers with the sum of 141 . translate each sentence into an equation and solve
Let's call x to the first odd integer. Then, three consecutive odd integers are:
x, x + 2 and x + 4.
The sum of them is equal to 141:
x + (x + 2) + (x + 4) = 141
olve the equation. If there is more than one solution, separate them with a comma.| 7x+2|=37
Given:
[tex]|7x+2\left|=37\right?[/tex]To find: The solutions
Explanation:
Since it is an absolute equation.
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
For the Positive case,
[tex]\begin{gathered} 7x+2=37 \\ 7x=35 \\ x=5 \end{gathered}[/tex]For the negative case,
[tex]\begin{gathered} -(7x+2)=37 \\ 7x+2=-37 \\ 7x=-39 \\ x=-\frac{39}{7} \end{gathered}[/tex]Final answers: The solutions are,
[tex]x=-\frac{39}{7},5[/tex]The function V(x)=x^3 may be used to find the volume of a cube with side of length x. Find the volume of a cube whose side is 22 inches.
The cube whose side length is 22 inches meaning for it x = 22 inches, and since the volume of a cube is given by
[tex]V(x)=x^3[/tex]For x = 22 this gives
[tex]V(22)=22^3[/tex][tex]\rightarrow V(22)=22\times22\times22=\textcolor{#FF7968}{10,648.}[/tex]Hence, the volume of a cube with side length of 22 inches is 10,648 cubic inches.
what does -3/4x+2>5 equal to?
Starting with the expression:
[tex]-\frac{3}{4}x+2>5[/tex]Notice that this is an inequality. We can solve this inequality for x by applying the properties of inequalities. Substract 2 from both sides:
[tex]-\frac{3}{4}x>3[/tex]Multiply both sides by 4/3:
[tex]-x>4[/tex]Multiply both sides by -1 swapping the inequality symbol:
[tex]x<-4[/tex]Triangle ABC has vertices A= (-1, 7), B = (1, 1) and C= (3, 8). Triangle A'B'C' is formed when Triangle ABC is translated right by 4 and up by 2. Which statement is true? Choose all that apply. O The angles of Triangle ABC and Triangle A'B'C' are the same. O Triangle A'B'C is located in Quadrant 1. The perimeter of Triangle ABC and Triangle A'B'C' are the same.
The coordinates of XYZ are given as follows;
[tex]\begin{gathered} X(-1,7),Y(1,1),Z(3,8) \\ \text{When the triangle is translated by 4 units to the right then we add 4 to the x coordinates} \\ \text{Also when its translated up by 2 units we add 2 to the y coordinates} \\ \text{Hence we now have;} \\ X\text{'(-1+4, 7+2)} \\ X^{\prime}(3,9) \\ Y^{\prime}(1+4,1+2) \\ Y^{\prime}(5,3) \\ Z^{\prime}(3+4,8+2) \\ Z^{\prime}(7,10) \end{gathered}[/tex]The correct answer therefore is option A
X' (3, 9)
Y' (5, 3)
Z' (7, 10)
Find the slope and y-intercept of the line represented by the table. X 0 3 6 9 12 у 4 19 34 49 64 The slope is m = , and the y-intercept is b =
The equation of line passes through the point (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substitute the coordinates of the points in the equation to obtain the equation of line.
[tex]\begin{gathered} y-4=\frac{19-4}{3-0}(x-0) \\ y-4=5x-5\cdot0 \\ y=5x+4 \end{gathered}[/tex]The general equation of line with slope m and y-intercept b is,
[tex]y=mx+b[/tex]On compare the general equation with y=5x+4, it can be observed that slope is m=5 and y intercept b is 4.
So answer is m=5 and b=4.
x = - 4y -14x - 3y =91 solve by substitution
We have a system of linear equations:
[tex]\begin{gathered} x=-4y-1 \\ 4x-3y=91 \end{gathered}[/tex]We have to solve it by substitution.
The first equation is giving us the equation to substitute x in the second equation and solve for y:
[tex]\begin{gathered} 4x-3y=91 \\ 4(-4y-1)-3y=91 \\ -16y-4-3y=91 \\ -19y=91+4 \\ -19y=95 \\ y=\frac{95}{-19} \\ y=-5 \end{gathered}[/tex]Now, we can use the first equation to solve for x:
[tex]\begin{gathered} x=-4y-1 \\ x=-4(-5)-1 \\ x=20-1 \\ x=19 \end{gathered}[/tex]Answer: x=19 and y=-5
What is the quotient of 7.584 x 10^6 and 7.9 x 10^2 expressed in scientific notation?
(7.584 x 10^6)/(7.9 x 10^2)
=0.96 x 10^6-2
= 0.96 x 10^4
=9.6 x 10^-1 x 10^4
= 9.6 x 10^-1+4
=9.6 x 10^3
Where are the minimum and maximum values for f(x) = 2 sin x - 1 on the interval [0, 2π]?A. min:z = 0, 2 max:z =OB. min:z =max:z = 0,2플max:z = 0, 7, 2nC. min:z = max:z =D. min:z =Reset Selection
Recall that the maximum/minimum value of a function is the place where a function reaches its highest/lowest point.
We know that:
[tex]\begin{gathered} For\text{ }all\text{ }x\in[0,2\pi] \\ -1\leq\sin(x)\leq1. \end{gathered}[/tex]Multiplying the above result by 2 we get:
[tex]\begin{gathered} -1\times2\leq\sin(x)\times2\leq1\times2, \\ -2\leq2\sin(x)\leq2. \end{gathered}[/tex]Subtracting 1 from the above inequality we get:
[tex]\begin{gathered} -2-1\leq2\sin(x)-1\leq2-1, \\ -3\leq2\sin(x)-1\leq1. \end{gathered}[/tex]Therefore f(x) reaches a minimum at:
[tex]x=\frac{3\pi}{2}.[/tex]And f(x) reaches a maximum at:
[tex]x=\frac{\pi}{2}.[/tex]Answer: Option C.
Select one or more expressions that together represent all solutions to the equation. Your answer shouldbe in degrees. Assume n is any integer.8 sin(8x) + 9 = 3Choose all answers that apply:--48.59° + n. 180°-16.43° + n. 45--6.07° + n. 45-6.07° + n. 180
ANSWER
[tex]x=-6.07\degree+n\cdot45\degree[/tex]EXPLANATION
We want to solve the trigonometric equation given:
[tex]8\sin (8x)+9=3[/tex]First, subtract 9 from both sides of the equation:
[tex]\begin{gathered} 8\sin (8x)=3-9 \\ 8\sin (8x)=-6 \end{gathered}[/tex]Then, divide both sides by 8:
[tex]\begin{gathered} \sin (8x)=-\frac{6}{8} \\ \sin (8x)=-\frac{3}{4} \end{gathered}[/tex]Now, apply the trigonometric inverse property i.e. find the sine inverse of both sides of the equation:
[tex]\begin{gathered} 8x=\sin ^{-1}(-\frac{3}{4})+360n \\ 8x=-48.5904+360n \end{gathered}[/tex]where n = 0, 1, 2, 3. . .
Finally, divide both sides by 8:
[tex]\begin{gathered} x=\frac{-48.5904}{8}+\frac{360n}{8} \\ x=-6.07\degree+n\cdot45\degree \end{gathered}[/tex]That is the answer.
Ecology question 15 points
Let's say there is a population with starting abundance of 100. You are trying to calculate future population abundance based on a geometric rate of increase of 0.75. What is the population abundance predicted to be at the 6th generation? (Round to the nearest whole number, and only type in the number (no words)).
The population abundance predicted to be at the 6th generation is 1641.
there is a population with starting abundance of 100.
so a = 100
geometric rate of increase of 0.75.
1 + 0.75 = 1.75
We need to calculate the population abundance predicted to be at the 6th generation
To calculate the nth term in a geometric progression the formula is
aₙ = arⁿ⁻¹ the
Where a represents the initial population, r represents the growth rate, n represents the number of term
aₙ = 100 (1.75)⁶⁻¹
aₙ = 100(1.75)⁵
aₙ = 1641
Therefore, the population abundance predicted to be at the 6th generation is 1641.
To learn more about geometric progression refer here
https://brainly.com/question/24643676
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5. The aspect ratio (the ratio of screen width to height) of arectangular flat-screen television is 16:9. The length of the diagonalof the screen is the television's screen size. Determine and state, thethe nearest tenth of an inch, the screen size (diagonal) of this flat-screen television with a screen height of 22.3 inches.
1) In this problem, we're dealing with ratios and then we can write out the following:
[tex]16:9\Rightarrow\frac{16}{9}[/tex]2) Since the screen height is 22.3 and the aspect ratio we can write out the following proportion:
[tex]\begin{gathered} \frac{16}{9}=\frac{x}{22.3} \\ 9x=16*22.3 \\ 9x=356.8 \\ \frac{9x}{9}=\frac{356.8}{9} \\ x=39.64 \end{gathered}[/tex]3) Note that we need to consider a right triangle, in which the hypotenuse is the diagonal so we can write ou the following:
[tex]\begin{gathered} a^2=b^2+c^2 \\ a^2=\left(39.64\right)^2+\left(22.3\right)^2^ \\ a^=\sqrt{\left(39.64\right)^2+\left(22.3\right)^2} \\ a=45.48 \end{gathered}[/tex]Note that we used the Pythagorean relation.
Find the sum and enter it in the box below. Enter your answer as a polynomialin descending order, and use the caret() for exponents. For example, youwould write 4x2 as 4x^2.2x3 - 3x2 - 4x + 3-3x6 - 2x2 + 2x2 - 4x + 7+
We have the next polynomial sum
[tex]\begin{gathered} \text{ 2x}^3-3x^2-4x+3 \\ +-3x^6-2x^3+2x^2-4x+7 \end{gathered}[/tex]We sum like terms
[tex]3x^6+(2x^3-2x^3)+(-3x^2+2x^2)+(-4x-4x)+(3+7)[/tex][tex]\begin{gathered} 3x^6-x^2-8x+10 \\ \end{gathered}[/tex]ANSWER
[tex]3x^6-x^2-8x+10[/tex]Identify the following number as prime composite it or neither if the number is composite it right it has a product of prime factors 67
Given number is 67.
The divisors of 67 are 1 and 67.
Since 67 can't be written as the product of primes it has no other divisors except 1 and 67, therefore, it is a prime number.
Hence, the correct option is (C)
Consider the following equation.x - 2y = 3Step 2 of 2: Determine the missing coordinate in the ordered pairso that it will satisfy the given equation.
Given:
The equation is given as,
[tex]x-2y=3[/tex]The objective is to find the missing coordinate in the ordered pair (?, 5/2).
Explanation:
Consider the given coordinate as,
[tex](x,y)=(x,\frac{5}{2})[/tex]To find x :
Substitute the value of y in the given equation to find the missing term.
[tex]\begin{gathered} x-2y=3 \\ x-2(\frac{5}{2})=3 \\ x-5=3 \\ x=3+5 \\ x=8 \end{gathered}[/tex]Hence, the missing term in the ordered pair is 8.
What is the solution to the equation –3(x + 5) = -3(x + 1)?
First, apply the distributive property to solve the parenthesis
[tex](-3)x+(-3)5=(-3)x+(-3)1?[/tex][tex]-3x-15=-3x-3[/tex]Add and subtract like terms:
[tex]-3x+3x=-3+15[/tex][tex]0=12[/tex]The equation has no solution.
10 × 20 -15 + 4 -1 × 10
Therefore the answer is 179
What is the smallest degree polynomial which could have the following graph?
Given,
The graph of the polynomial is shown in the quesion.
As known that,
The degree of the polynomial shoes the number of times curve intersect the x-axis.
Here,
The curve intersect the x-axis 6 times.
Hence, the degree of the polynomial is 6.
A person plans to invest twice as much in a.) Putnam Global Equity fund at 11.9% annual interest as in b.) Bridgeway Small Cap at 20% annual interest. How much will the person have to invest in each fund to earn a total of $2800 in one year?
He has to invest $9,169 in Putnam Global Equity and $4,584.5 in Bridgeway small cap to earn a total of $2,800 in interest for one year
Here, we want to find how much has to be invested in each fund
From the question, the investment in a is twice that of b
So, if he invests $x in b, he would be investing $2x in a
Let us work with the interests now
In the case of the interests, the total amount of interest in both will equal $2800 per year
Thus, we have that;
[tex]\begin{gathered} 11.9\text{ percent of 2x + 20 percent of x = 2,800} \\ \\ \frac{11.9}{100}\text{ }\times\text{ 2x + }\frac{20}{100}\times x\text{ = 2,800} \end{gathered}[/tex]Multiply through by 100;
[tex]\begin{gathered} 2x(11.9)\text{ + 20(x) = 100(2,800)} \\ 23.8x\text{ + 20x = 200,800} \\ 43.8x\text{ = 200,800} \\ x\text{ = }\frac{200,800}{43.8} \\ x\text{ = 4584.5} \end{gathered}[/tex]To get the investment in a, we simply multiply this result by 2 and we have 2(4584.5) = $9,169
Can you please help me out with a question
Given:
Radius of circle, r = 2 + 1 + 3 = 6 inches
Radius of unshaded region = 1 inch
Radius of shaded region = 3 + 2 = 5 inches
To find the area of the shaded, apply the formula below:
[tex]A=\pi r^2[/tex]Let r be the radius of the shaded region
[tex]\begin{gathered} A=\pi\ast5^2 \\ \\ A=\pi\ast25 \\ \\ A=25\pi in^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 25π square inches
ANSWER:
[tex]\text{ c. 25}\pi in^2[/tex]