start by writing all numbers like decimals
[tex]\begin{gathered} 3\frac{2}{3}=3.66666667 \\ \pi\cong3.1416 \\ \sqrt[]{3}=1.732 \end{gathered}[/tex]then using the decimals we can say that the least is square root 3 and the greatest is 3 2/3
The correct order should be
[tex]\sqrt[]{3};\bar{3.1};3.141;\pi;3\frac{2}{3}[/tex]given the fuction g(x)=-4x-7 find g(3)
Diego, this is the solution:
We have the following function:
g (x) = 4x - 7
In consequence,
g (3) = 4 * 3 - 7
g (3) = 12 - 7
g (3) = 5
Substitute values for h, k, and r into the circle (x - 2)² + (y - k)² = r² (x - 5)2 + (y - (-3))2 = 34 (x - 5)2 + (y + 3)2 = 34 Exercises 12.2 Complete the following: . 1. Find the equation of the circle having the given center and ra (a) C(0, 0), r = 3 (b) C (-2 (c) C(4, 3), r = 5 (d) C (2
x² +y² = 9, (x+2)² +(y +5)² = 16
1.) Let's find the equation of the circle given C(0,0), r=3 and b) C(-2,-5) and r =4
The equation of a circle is given by
(x-h)²+(y-k)²= r² C(h, k)
2) Since the Center of the Circle has been given, then let's plug it in, and the radius as well
a) C(0,0) and r=3
(x-h)²+(y-k)²= r²
(x-0)²+(y-0)²= 3²
x² +y² = 9 Circle centered at the origin of the Cartesian Plane
b) C(-2,-5) and r =4
(x-h)²+(y-k)²= r²
(x+2)² +(y +5)² = 16 Since the coordinate of the center are negative
What is equivalent to 0.05*0.8
Notice that:
[tex]0.05\times0.8=\frac{5}{100}\times\frac{8}{10}=\frac{40}{1000}.[/tex]Simplifying the above fraction and putting it in decimal form, we get:
[tex]\frac{4}{100}=0.04.[/tex]Answer: [tex]0.04[/tex]The radius of a sphere is tripled. What happens to the volume?Hint: Test two scenarios and compare the volumes! Show your work. Used 3.14 for piC. It is 15 times largerD. It is 27 times largerA. It triplesB. It quadruples
First, we need to test two scenarios using the sphere volume formula:
The volume for a sphere is given by:
[tex]A_s=\frac{4}{3}\pi r^3[/tex]Let us set r=3
Then:
[tex]\begin{gathered} A_{s}=\frac{4}{3}\pi r^{3} \\ A_s=\frac{4}{3}\pi(3)^3 \\ A_s=36\pi \\ A_s=113.04 \end{gathered}[/tex]If we tripled the radio= 3r = 3(3)= 9. Then:
[tex]\begin{gathered} A_s=\frac{4}{3}\pi(9)^3 \\ A_s=3052.08 \end{gathered}[/tex]Now, we need to compare both results:
A1 = 113.14
A2 = 3052.08
If we multiply A1 by 27=
27(113.14) = 3052.08
Hence, the volume when the radius is tripled is the product of the first volume by 27.
Therefore, the correct answer is option D.It is 27 times larger
The football team gained 14 yards on the first play, then the lost 20 yeards on second play. what was the total change in yards for the team
We can calculate the net yard as adding the two events in respect to the same reference value.
The first event is gaining 14 yards, so we have a=14.
The second event is losing 20 yards, which according to our reference is a negative value: b=-20.
Then, we can calculate the net effect as:
[tex]N=a+b=14+(-20)=14-20=-6[/tex]This correspond, as it has a negative value, to a loss of 6 yards.
Answer: the total change is 6 yards lost.
Renaldo makes 886.75 for each car he sells. witch is the best estimate of how much he makes if he sells 19 cars.
By selling 19 cars Renaldo gets an amount of $16848.25.
What is estimation?Number estimation is the process of estimating/approximating or rounding off numbers so that the value can be used for another purpose and avoid complicated calculations. There is a distinction to be made between the terms exact and estimation.Estimation is concerned with drawing conclusions about the numerical value of unknown population values based on incomplete data, such as a sample. Point estimation is the process of calculating a single figure for each unknown parameter.Estimating is the process of projecting project costs and resource requirements into the future. To minimize errors and achieve reliable results, a consistent procedure or set of steps for preparing an estimate is required.So, calculate according to the question:
Let x be the total amount of 19 cars.Price of each car = $886.75He sells 19 cars.Forming the equation:
x = 19 x 886.75x = $16848.25He gets an amount of $16848.25 by selling 19 cars.
Therefore, by selling 19 cars Renaldo gets an amount of $16848.25.
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Find the equation for thefollowing parabola.Vertex (-2,-4)Focus (-4,-4)A. (7-4)2 = -8(x-2)B. (x+4)2 = 8(yl)C. (y+4)2 = 8(x+2)D. (y+4)2 = -8(x+2)
The vertex of the parabola is of the form,
[tex](h,k)[/tex]The vertex given is,
[tex](-2,-4)[/tex]The general equation of parabola is
[tex](y-k)^2=4p(x-h)[/tex]Here, p is the distance between vertex and focus.
[tex]p=\sqrt[]{(-4-(-4))^2}+(-2-(-4)^{})^2[/tex][tex]p=\sqrt[]{4}[/tex][tex]p=2[/tex]Susbtitute the values,
[tex](y+4)^2=8(x+2)[/tex]The correct option is C.
Please help me on this question! (Type an integer or decimal rounded to the nearest hundredth as needed)
EXPLANATION:
Given;
We are given the dimensions of a cone shaped sculpture as follows;
[tex]\begin{gathered} Height=5ft \\ Base\text{ }circumference=28.260ft \end{gathered}[/tex]Required;
We are required to find the volume of this cone-shaped sculpture.
Step-by-step solution;
To calculate the volume of a cone, the formula to be used is;
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\pi r^2\frac{h}{3} \end{gathered}[/tex]To determine the value of r, w shall take the variable r and make it the subject of the formula;
[tex]\begin{gathered} Circumference\text{ }of\text{ }a\text{ }circle: \\ Cir=2\pi r \\ make\text{ }r\text{ }the\text{ }subject: \\ \frac{C}{2\pi}=\frac{2\pi r}{2\pi} \\ \\ Therefore: \\ \frac{C}{2\pi}=r \end{gathered}[/tex]With the value of the circumference already given we now have;
[tex]\begin{gathered} \frac{28.260}{2(3.14)}=r \\ \\ \frac{28.260}{6.28}=r \\ \\ 4.5=r \end{gathered}[/tex]This means the radius of the circular base of the sculpture is 4.5 feet.
The volume of the sculpture therefore is;
[tex]Vol=\pi r^2\frac{h}{3}[/tex][tex]\begin{gathered} Volume=3.14\times(4.5)^2\times\frac{5}{3} \\ \\ Volume=\frac{3.14\times20.25\times5}{3} \\ \\ Volume=105.975 \end{gathered}[/tex]The volume rounded to the nearest hundredth therefore is,
ANSWER:
[tex]Volume=105.98ft^3[/tex]find the distance of the line segment joining the two points: 21
Given two points (x1, y1) and (x2,y2) the distance d between the points is given by:
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]In this case,
x1 = √2, y1 = 0, x2 = 0, and y2 = -√2
Therefore, d is given by:
[tex]\begin{gathered} d=\sqrt{(\sqrt{2}-0)^2+(0-(-\sqrt{2}))^2} \\ d=\sqrt{2+2}=\sqrt{4}=2 \end{gathered}[/tex]Therefore, the required distance is 2.
what is the perimeter of a square if one of the sizes is 3mi
Given the side length of the square = 3 mi
The perimeter of the square = 4 times the length of one side
So, the perimeter = 4 x 3 = 12 mi
So, the answer will be perimeter = 12 mi
Three of the vertices of a parallelogram are A(2, 4), B(6,2) and C (8, 6).(a) Plot the point A, B and C in the coordinate plane(b) Find the mid-point of diagonal AC(c) Find the fourth vertex D(d) Find the length of diagonal AC(e) Find the perimeter of ABCD.
Given:
Three of the vertices of a parallelogram are given as
[tex]\begin{gathered} A\left(2,4\right)_ \\ B\left(6,2\right) \\ C(8,6) \end{gathered}[/tex]Required:
(a) Plot the point A, B and C in the coordinate plane
(b) Find the mid-point of diagonal AC
(c) Find the fourth vertex D
(d) Find the length of diagonal AC
(e) Find the perimeter of ABCD.
Explanation:
Take D coordinate as (x,y)
now midpoint of AC and BD is same so
[tex]\begin{gathered} (\frac{2+8}{2},\frac{4+6}{2})=(\frac{x+6}{2},\frac{2+y}{2}) \\ \\ (5,5)=(\frac{x+6}{2},\frac{2+y}{2}) \\ \\ x=4,y=8 \end{gathered}[/tex]midpoint of AC
[tex](\frac{2+8}{2},\frac{4+6}{2})=(5,5)[/tex]length of diagonal AC
[tex]AC=\sqrt{36+4}=2\sqrt{10}[/tex]perimeter of ABCD
[tex]AB=\sqrt{16+4}=\sqrt{20}[/tex][tex]BC=\sqrt{4+16}=\sqrt{20}[/tex]perimeter is
[tex]2(AB+BC)=4\sqrt{20}[/tex]Final answer:
(b) Find the mid-point of diagonal AC
[tex]\begin{equation*} (5,5) \end{equation*}[/tex](c) Find the fourth vertex D
[tex](4,8)[/tex](d) Find the length of diagonal AC
[tex]2\sqrt{10}[/tex](e) Find the perimeter of ABCD.
[tex]\begin{equation*} 4\sqrt{20} \end{equation*}[/tex]what is understand function
There are differnet definition from what a function is.
The most precisely definition of a function is that a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
For example:
Let define the following function: y= 3x + 2
The graph for the function y=3x + 2 would be as follow:
As you can clearly see above, for example the number 1 in X would correspond to the number 5 in y.
The regression equation y = 1.37x +75 approximates the number of minutes it takesan employee to drive to work, y. given the number of miles the employee has todrive, X. Based on this equation, for every mile the car is driven, how much does thedriving time increase?
We have the equation
[tex]y=1.37x+75[/tex]Where y = time in minutes and x = number of miles
Then, for every mile, this is x = 1, we have:
[tex]y=1.37(1)+75=1.37+75=76.37[/tex]Answer: the driving time increase in 76.37 minutes
the guy took 15 pieses and there is 4 left
The number of pieces in the bowl before she added the 20 is 8 pieces of candy
Here, we want to get the number of pieces in the bowl before the addition of the 20 pieces
Let the number of pieces before the addition be n
she added 20 pieces to what is there initially, this brings the total to;
[tex]n\text{ + 20}[/tex]Now, two days after the addition, half of the above is gone
Half of the above is;
[tex]\frac{n+20}{2}[/tex]Now, the difference between the number of pieces in the bowl after the addition of the 20 and the half gone is 14; we have the equation as thus;
[tex]\begin{gathered} n\text{ + 20 - (}\frac{n+20}{2})\text{ = 14} \\ \\ 2(n+20)-(n+20)\text{ = 28} \\ n\text{ +20 = 28} \\ n\text{ = 28-20} \\ n\text{ = 8} \end{gathered}[/tex]suppose that the initial amount of an element is 120 grams. The amount remaining after t days can be modeled by the equation y=120x0.93^t. Use a graph to determine the half life.
Given the equation:
[tex]y=120\cdot0.93^t[/tex]we know that the half life is the amount of time it takes for there to be half the initial amount. Therefore, since the initial amount is 120, then for the half life will be y=60, then:
[tex]\begin{gathered} 60=120\cdot0.93^t \\ \Rightarrow\frac{60}{120}=0.93^t \\ \Rightarrow\frac{1}{2}=0.93^t \end{gathered}[/tex]Now we apply natural logarithm on both sides of the equation to solve for t:
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.93^t) \\ \Rightarrow\ln (\frac{1}{2})=t\cdot\ln (0.93) \\ \Rightarrow t=\frac{\ln (0.5)}{\ln (0.93)}=9.55 \\ t=9.55 \end{gathered}[/tex]therefore, we have that the half life will be after 9.55 days, and we can watch this on the graph of y:
Explain differentials. Explain the difference between ∆y and dy, is there difference between ∆x and dx?
Given:
∆y and dy.
∆x and dx.
Required:
To explain the difference between ∆y and dy, is there difference between ∆x and dx.
Explanation:
∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.
Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.
In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.
Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.
Final Answer:
∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.
Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.
In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.
Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.
3ft by 4ft and 6in tallgind the volume
To find the volume of the box, start by converting the 6 inches into feet, using that 1 feet has 12 inches.
[tex]6in\cdot\frac{1ft}{12in}=0.5ft[/tex]use the formula of the volume of a box
[tex]V=w\cdot h\cdot l[/tex]w = 3ft
l = 4ft
h = 0.5ft
[tex]\begin{gathered} V=(3ft)\cdot(4ft)\cdot(0.5ft) \\ V=6ft^3 \end{gathered}[/tex]The box holds 6 cubic feet of sand.
Hi can you please help me understand how to you standard form or the truth table to see if the argument is valid or invalid
Let us first translate the argument to symbolic form. So, let be:
P: The car is a Corvette
Q: The car is fast
~Q: The car is not fast
Then, the argument in the symbolic form will be
[tex]\begin{gathered} P\rightarrow Q \\ \text{ \textasciitilde}Q\text{ } \\ -------- \\ \therefore\text{ \textasciitilde}Q\text{ } \end{gathered}[/tex]Now, let us see if the argument is valid or invalid.
The argument is in the form of the Modus Tollendo Tollens inference rule.
The modus tollendo tollens is an application of the general truth that, if a statement is valid, so is its counterposition.
Therefore, the argument is valid.
what number does B stand for in this equation 3b = 12 A 1 B 2C 3D 4
Answer
Option D is correct.
b = 4
Explanation
We are asked to solve for b in the equation
3b = 12
We divide both sides by 3
(3b/3) = (12/3)
b = 4
Hope this Helps!!!
Olivia picked 482 apples from the orchard’s largest apple tree. She divided
the apples evenly into 4 baskets. How many apples are in each basket? How
many are left over? pls make the solution detailed! :)
There are 120 apples in each basket and 2 leftovers
How to determine the number of apples in each basket?From the question, the given parameters are:
Number of apples = 482
Number of baskets = 4
the number of apples in each basket is calculated as
Apples in each basket = Number of apples/Number of baskets
Substitute the known values in the above equation
So, we have the following equation
Apples in each basket = 482/4
Evaluate
Apples in each basket = 120.5
Remove the decimal
Apples in each basket = 120
The number of leftoverIn (a), we have
Apples in each basket = 120.5
The decimal part is
Decimal = 0.5
The number of leftover is then calculated as
Leftover = Decimal * Baskets
So, we have
Leftover = 0.5 * 4
Evaluate
Leftover = 2
Hence, there are 2 leftovers
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Which expressions are equivalent to the one below? Check all that apply.
7*3.7^x
A. 73-*
B. 493x
C. 343.7
D. (7.7)3
E. 73x
F. 73 + x
Is this the only one that applys
Answer: We have to simplify the provided expression and pick the answer out of the options which matches the final result.
Simplification:
[tex]\begin{gathered} a^b\times a^c=a^{(a+c)} \\ \\ ------------------- \\ \\ 7^3\times7^x=7^{(3+x)} \end{gathered}[/tex]Therefore the answer is Option(F).
Andres has $1.50 in dimes and nickels. If he has 9 more nickels than dimes, how many of each coin does he have?He has ? nickels and ? dimes.
Let's use the variable x to represent the number of dimes and y to represent the number of nickels.
If the total value is $1.50, we can write the equation:
[tex]0.1x+0.05y=1.5[/tex]Also, if there are 9 more nickels than dimes, we have our second equation:
[tex]y=x+9[/tex]Using this value of y from the second equation into the first one, we have:
[tex]\begin{gathered} 0.1x+0.05(x+9)=1.5 \\ 0.1x+0.05x+0.45=1.5 \\ 0.15x=1.5-0.45 \\ 0.15x=1.05 \\ x=\frac{1.05}{0.15} \\ x=7 \\ \\ y=x+9 \\ y=7+9 \\ y=16 \end{gathered}[/tex]Therefore Andres ha 16 nickels and 7 dimes.
what is the answer of typing at an average rate of 42 words per minute?
Answer:
Typing of 28 words in 2/3 of a minute.
Explanation:
If one can type and average rate of 42 words per minute, let's confirm how many words one can type in 2/3 and 3/2 of a minute;
[tex]\begin{gathered} 42words\Rightarrow1\text{minute} \\ x\Rightarrow\frac{2}{3}of\text{ a minute} \\ x=42\ast\frac{2}{3}=14\ast2=28\text{ words} \end{gathered}[/tex]Therefore, 28 words can be typed in 2/3 of a minute.
In boot camp, a cadet must use a rope swing to cross an obstacle without falling into the water hazard below. Unfortunately, they miss the platform on the other side and swing back to where they started. If it takes the cadet 4.5 seconds to swing from one side of the obstacle to the other and back, how long is the rope swing? Use the formula:A.5.0 metersB.2.9 metersC.12.6 metersD.4.3 meters
Given:
[tex]T=4.5\text{ seconds}[/tex]Required:
To find the length of the rope swing.
Explanation:
Consider the formula
[tex]T=2\pi\sqrt{\frac{L}{9.8}}[/tex]Now
[tex]\begin{gathered} 4.5=2\times3.142\sqrt{\frac{L}{9.8}} \\ \\ 0.7161=\sqrt{\frac{L}{9.8}} \\ \\ \frac{L}{9.8}=0.5127 \\ \\ L=0.5127\times9.8 \\ \\ L=5.02m \end{gathered}[/tex]Final Answer:
The length is 56.0 meters.
Let y be a college's enrollment (in thousands of students), and let x be the number of years that the college has been open. Assume that the equation y = 0.6x + 6 describes the relationship between x and y. Complete parts a through b. below. a. Complete the following table. Number of years college Enrollment has been open (thousands of students) X. Y 0. _1. _ 2. _ 3. _ 4. _(Type integers or decimals.) b. By how much does the college's enrollment increase each year? The college's enrollment is increasing by:____ thousands of students per year.(Type an integer or a decimal.)
We were told that x represents the number of years and y represents the number of enrollment from the onset. The equation representing teh relationship is
y = 0.6x + 6
a) We would determine the values of y by subsstituting the corresponding values of x into the equation. We would multiply by 1000 since it is expressed in thousands
For x = 0, y = 0.6*0 + 6 = 6*1000 = 6000
For x = 1, y = 0.6*1 + 6 = 6.6 * 1000 = 6600
For x = 2, y = 0.6*2 + 6 =
Write As a decimal round to the nearest thousandth place to 235%
SOLUTION
We want to write 235% as a decimal and round to the nearest thousandth.
This becomes
[tex]\begin{gathered} 235\% \\ =\frac{235}{100} \\ =2.35 \\ =2.350 \end{gathered}[/tex]Hence the answer is 2.350 to the nearest thousandth
how do I find the correct answer for the two blanks?
I need help with this problem I have to all written out I just don’t know how to find the answer and I need to do it on a calculator in degree mode
Formular for calculating area of a kite is given by:
[tex]A=\frac{d_1d_2}{2}[/tex]where d1 and d2 are the diagonals
From the question,
d1 = 32 and d2=10
substitute the values into the formula and evaluate
[tex]A=\frac{32\times10}{2}[/tex][tex]A=160in^2[/tex]A pet store clerk suggested 7 small fish for an 8-gallon fish tank. What size tank would be suggested to hold 35 small fish?
12-gallon tank
23-gallon tank
30-gallon tank
40-gallon tank
Based on the suggestion given for the small fish by the pet store clerk, the tank size that would be able to hold 35 small fish is a 40 gallon tank.
How to find the tank size?To find the tank size that would be able to hold 35 small fish, you first need to find the unit rate. This means you need to find the tank size that is required per small fish.
If there are 7 small fish, then an 8 gallons fish tank is needed. This means that 1 small fish needs:
= 8 / 7
= 8/7 gallon tank size
If there are 35 small fish, the tank needed is:
= Number of small fish x Tank size per small fish
= 35 x 8/7
= 40 gallon tank
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...............need help
Answer:
3472
Step-by-step explanation:
pls mark brainiest I solved it.
Answer:
3.572
Step-by-step explanation:
I don't know what to explain or how