Answer: red sus tbh
Step-by-step explanation:
Roberto wrote the number 60, if the rule is subtract 3, what is the fifth number in the pattern?
A wire 24inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x:
Determine the domain of the function and use a graphing utility to graph the function over that domain
Use the graph of the function to approximate the maximum area of the rectangle. Make a conjecture about the dimensions that yield a maximum area. ...?
Answer:
Area function : [tex]A(x)=12x-x^2[/tex]
Domain: (0,6)
The area of rectangle is maximum at x=6. The area of a rectangle is maximum if it is a square.
Step-by-step explanation:
It is given that the length of wire is 24 inches. It is to be cut into four pieces to form a rectangle.
Let x be the length of shortest side.
Perimeter of a rectangle is
Perimeter = 2( Shortest side + longest side).
[tex]24 = 2( x + \text{longest side})[/tex]
[tex]12 = x + \text{longest side}[/tex]
[tex]12 - x = \text{longest side}[/tex]
So, length of longest side is (12-x) inches.
Area of a rectangle is
[tex]A=length \times width[/tex]
Area function is
[tex]A(x)=x(12-x)[/tex]
The area of rectangle and dimensions of a rectangle can not be a negative.
[tex]A(x)>0[/tex]
[tex]x(12-x)>0[/tex]
It means,
[tex]x>0[/tex]
[tex]12-x>0\Rightarrow 12>x[/tex]
One side is less that the other side.
[tex]x<12-x[/tex]
[tex]2x<12[/tex]
[tex]x<6[/tex]
It means the domain of the function is (0,6).
The simplified form of the area function is
[tex]A(x)=12x-x^2[/tex]
Differentiate with respect to x.
[tex]A'(x)=12-2x[/tex]
[tex]A'(x)=0[/tex]
[tex]12-2x=0[/tex]
[tex]x=6[/tex]
Differentiate A'(x) with respect to x.
[tex]A''(x)=-2<0[/tex]
Therefore the area of rectangle is maximum at x=6.
[tex](12-x)=12-6=6[/tex]
It means the area of a rectangle is maximum if it is a square.
which ordered pair is a solution of the equation: y=4x/
1.(1,3)
2.(-1,-4)
3.(-4,-1)
4.(1,-4)
Kayla has a bowl of beads that contains 42 yellow beads, 28 green beads, 12 white beads, and 18 red beads. She randomly draws a bead from the bowl.
The probability of Kayla not drawing a yellow or a green bead is______ %. The probability of Kayla drawing a red or a green bead is______ %.
Answer:
1. 30%
2.46%
Step-by-step explanation:
The probability of Kayla not drawing a yellow or a green bead is 30 %. The probability of Kayla drawing a red or a green bead is 46 %.
Correct for plato! :)
At sumer camp the ratio of boys to girls is 7:3 if there were 63 boys how many girls were there
If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(x + 1)?
A. 2x^2 + 2
B. x^2 + 3
C. 2x^2 + 4x + 1
D. 2x^2 + 4x + 5
Answer:
option (d) is correct.
[tex]f(x+1) = 2x^2+4x+5[/tex]
Step-by-step explanation:
Given : [tex]f(x) = 2x^2 + 3[/tex]
We have to choose out of given option which represent f(x + 1)
Consider the given function [tex]f(x) = 2x^2 + 3[/tex]
Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,
[tex]f(x+1) = 2(x+1)^2+3[/tex]
Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,
[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]
Simplify the expression by multiplying 2 with each term in bracket, we have,
[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]
Simplify , we have,
[tex]f(x+1) = 2x^2+4x+5[/tex]
Thus, option (d) is correct.
what is the value of h in the figure below?
the answer on APEX is 6
Which of the following sets of four numbers has the largest possible standard deviation? (1, 2, 5, 6) (4, 5, 5, 6) (1, 3, 5, 7) (6, 7, 8, 9)
What is the value of the function y = 2x + 3 when x=−1
5
2
1
−5
Answer:
I took the test its 1
Step-by-step explanation:
What is the answer to
3n-5=7n+11
Find the equation of the line tangent to the graph of y = cos(2x) at x = pi/4 ...?
WHICH CONSTRUCTION DOES THE IMAGE BELOW DEMONSTRATE??
A square circumscribed about a circle
A square inscribed in a circle
The circumcenter of a square
The incenter of a square
Answer:
This is a square inscribed in a circle.
Step-by-step explanation:
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar. How much of the jar is now full of marbles?
Four less than the quotient of a number and 3 is - 10
To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.
Explanation:To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:
x/3 - 4 = -10
To solve for x, we can start by adding 4 to both sides:
x/3 = -6
Next, we can multiply both sides of the equation by 3 to isolate x:
x = -18
Therefore, the solution to the equation is x = -18.
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Which is a correct first step in solving 5 – 2x < 8x – 3?
choices
5 < 6x – 3
3x < 8x – 3
5 < 10x – 3
2 – 2x < 8x
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt? Check all that apply.
A. 225(3)
B. (3)(–225)
C. –225 + 3
D. 3 – 225
E. –225(3)
Both B & E; They are both using -225 which represents debt
The expression that shows the given statement will be equal to -225(3). Hence, options B and E are correct.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Gena's food cart business last year = $225 in debt = -225
The dept has tripled this year.
Then, the equation according to the statement will be,
(-225) × 3
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In 2007, the FDIC’s insurance limit was $100,000 per person per bank. If Sam had a $150,000 savings account and $80,000 checking account at Bank J, a $95,000 money market account at Bank K, and a $200,000 savings account at Bank L, how much of Sam’s money was FDIC insured? a. $295,000 b. $300,000 c. $375,000 d. $525,000
20 % of 2 is equal to
A. 20
B. 4
C. 0.4
D. 0.04
Y=log x If y=10, then what is x?
A.
10
B.
1
C.
100
D.
10^2
3.
What is 10*9*8*7*6*5*4*3*2*1?A.
10! or 3628800
B.
100
C.
1000
D.
10^10
Answer:
First question, x= 10^10.
Second question is 10!. or 362880
Step-by-step explanation:
First Question:
Simple logx has a base of 10, i.e log10 x,
the question will be 10 = log10 x,
when taking the base "10" from the right side to the left, the number on the left side becomes the power of the base, in this case 10 from the right will be base and 10 from the left will power and log will vanish.
x=10^10.
Another example with different numbers
Y=logx if Y= 12, What is x?
The base is ten when not given,so:
12=logx
10^12=x
Second Question;
simple multiplication just multiply the numbers.
10! is pronounced as 10 factorial,
5! will be 5x4x3x2x1=120
Compute the amount of interest earned in the following simple interest problem. A deposit of $1,295 at 7% for 180 days = _____. (Note: Use 365 days in a year)
The interest earned on a deposit of $1,295 at a 7% annual rate for 180 days is approximately $44.70.
To compute the amount of interest earned we can use the simple interest formula:
Interest = Principal × Rate × Time
Since simple interest does not complicate by itself, and the time is less than a year, we'll adjust the time and rate accordingly.
First, we express the annual interest rate as a decimal by dividing the percentage by 100:
Rate = 7% / 100 = 0.07
Next, we convert the time period of 180 days into years, considering there are 365 days in a year:
Time = 180 days / 365 days/year = 0.49315 years (approximately)
Now, let's plug the values into the simple interest formula:
Interest = $1,295 × 0.07 × 0.49315
Calculating the interest:
Interest = $44.70
In the game of roulette, a player can place a $4 bet on the number 22 and have a 1/38 probability of winning. If the metal ball lands on 22, the player gets to keep the $4 paid to play the game and the player is awarded $140. Otherwise, the player is awarded nothing and the casino takes the players $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? ...?
Final answer:
The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.
Explanation:
Expected value for the game:
Probability of winning (landing on 22): 1/38Payout for winning: $140 + $4 initial bet = $144Cost of playing (losing bet): -$4Expected value = (Probability of winning * Payout for winning) + (Probability of losing * Cost of losing)Expected value = (1/38 * $144) + (37/38 * -$4)Expected value = -$0.2105 per gameExpected Loss in 1000 Games:
Expected loss per game = -$0.2105Expected loss in 1000 games = Expected loss per game * Number of gamesExpected loss in 1000 games = -$0.2105 * 1000Expected loss in 1000 games = -$210.50Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.
Which three statements below are true about an acute isosceles triangle?two side measures are the sameall angle measures are less than 90°one angle is obtusetwo angle measures are the sameall angle measures are different
Answer:
two side measures are the same
all angle measures less than 90°
two angle measures are the same
Step-by-step explanation:
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
About an acute isosceles triangle are:
- Two side measures are the same:
In an isosceles triangle, two sides have the same length.
In an acute isosceles triangle, all angles are acute, which means they are less than 90°.
Therefore, the two sides that are the same length must be the two sides opposite the acute angles.
- All angle measures are less than 90°:
An acute triangle is a triangle in which all angles are less than 90°.
Since an acute isosceles triangle has two equal acute angles, all three angles in the triangle are less than 90°.
- Two angle measures are the same:
An isosceles triangle is a triangle in which two sides have the same length. In an acute isosceles triangle, the two sides that have the same length are opposite the two equal acute angles.
Therefore, the two angles opposite those sides must also have the same measure.
Thus,
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
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What is the value of x+2x when x=4 ? Enter your answer in the box.
The temperature, t, in Burrtown starts at 21°F at midnight, when h = 0. For the next few hours, the temperature drops 4 degrees every hour. Which equation represents the temperature, t, at hour h?
A. t = 21h + 4
B. t = 4h + 21
C. t = –4h + 21
D. t = –21h + 4
Answer:
C. t = –4h + 21
Step-by-step explanation:
We know that when h = 0, t = 21°F. Replacing h = 0 in equation A and D we get:
A.
t = 21h + 4
t = 21(0) + 4
t = 4
D.
t = –21h + 4
t = –21(0) + 4
t = 4
So, none of them are correct.
The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in equation B and C we get:
B.
t = 4h + 21
t = 4(1) + 21
t = 25
C.
t = –4h + 21
t = –4(1) + 21
t = 17
In consequence, C is the correct option.
the quotient of a number and four decreased by ten is two
a certain game consists of rolling a single fair die and pays off as follows: $5 for a 6, $2 for a 5, $1 for a 4, and no payoff otherwise. find the expected winnings for this game.
The expected winnings for this game is calculated by multiplying the value of each possible outcome by their probability, providing an overall expected value of $1.33. This indicates that over a long period of repeated games, the average winnings per game would be $1.33.
Explanation:In this question, we're dealing with calculating the expected value in a game of probability. The game involves rolling a dice with outcomes ranging from 1 to 6 and the associated payoffs for roll outcomes of 4, 5, and 6 are $1, $2, and $5 respectively.
We calculate the expected winnings (value) for a single round of the game by multiplying all possible outcomes by their respective probabilities, then summing these products. In this case, symbols represent the payout (in $) and P represents the probability of each outcome.
(6) $5*P(1/6) = $0.83 (5) $2*P(1/6) = $0.33 (4) $1*P(1/6) = $0.17 (1-3) $0*P(1/2) = $0.00Adding up these expected outcomes gives us our overall expected winnings: $0.83 + $0.33 + $0.17 + $0.00 = $1.33 per game
If you play this game repeatedly, over the long term, you'd expect to win around $1.33 on average each game. Note that the exact winnings in a single instance of the game could be $0, $1, $2, or $5, and this value simply provides an average expected outcome over time.
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Ben has $3.40 consisting of quarters and dimes. How many coins of each kind does he have if he has 22 coins?
Show a system of equation to represent the word problem.
There are 8 quarters and 14 dimes.
Step-by-step explanation:Let there are x quarters.
and y dimes.
Also as we know,
1 quarter= 0.25 dollar
Hence, x quarter= $ 0.25x
and 1 dime= $ 0.10
Hence, y dimes= $ 0.10y
Ben has $3.40 consisting of quarters and dimes.This means that:
0.25x+0.10y=3.40
Also, in non-decimal form it could be written as:
25x+10y=340
He has 22 coinsThis means that:
x+y=22
Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.
We get the point of intersection as: (8,14)
i.e. x=8 and y=14
Hence, there are 8 quarters.
and 14 dimes.
What is the ratio 4:6 in simplest form?
A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. The rancher wants the enclosed area to be 350 square meters. What dimensions should the rancher use to obtain this area?
Final answer:
The dimensions of each corral should be 40 meters by 10 meters.
Explanation:
To find the dimensions of the rectangular corrals, we can set up an equation using the perimeter and area of the enclosed space. Let's call the length of one corral x and the width y. The perimeter of the two corrals is 2x + 2y, which equals 100 meters. The area of the enclosed space is xy, which equals 350 square meters.
Using these equations, we can solve for x and y. Rearranging the perimeter equation, we get x = 50 - y. Substituting this into the area equation, we have (50 - y)y = 350.
Simplifying the equation, we get y^2 - 50y + 350 = 0. This is a quadratic equation that can be factored as (y - 35)(y - 10) = 0. Therefore, the possible values for y are 35 and 10.
Since we are looking for positive values for the dimensions, we choose the values y = 10 and x = 50 - y = 50 - 10 = 40. Therefore, the dimensions of each corral should be 40 meters by 10 meters.
To find the dimensions of the rectangular corrals, we can set up a system of equations. By solving the system of equations, we find that the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
Explanation:To find the dimensions of the rectangular corrals, we can set up a system of equations. Let x represent the width of one corral and y represent the length. Since the rancher wants to enclose a total of 350 square meters, we have the equation xy = 350. The perimeter of each corral is 2x + y, so the total amount of fencing used would be 4x + 2y.
Given that the total fencing available is 100 meters, we can set up the equation 4x + 2y = 100. Now we can solve the system of equations:
xy = 3504x + 2y = 100By substituting the value of y from the first equation into the second equation, we can solve for x. After finding the value of x, we can substitute it back into the first equation to find the corresponding value of y. The solutions will give us the dimensions of the rectangular corrals.
Let's solve the system of equations:
350 = x(100 - 2x)350 = 100x - 2x^22x^2 - 100x + 350 = 0x^2 - 50x + 175 = 0(x - 25)(x - 7) = 0The solutions for x are x = 25 and x = 7. Plugging these values back into the equation xy = 350, we find that the corresponding values for y are y = 14 and y = 50, respectively. Therefore, the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
is .485 lower than .5