Answer:$168 per hour
Step-by-step explanation: so in a half hour they charge $84 .
a half hour is 30 minutes and you need another half hour so double $84
$84x2=168
Choose the formula that expresses the described relationship. A varies inversely as h.
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
The formula that expresses the described relationship where A varies inversely as h is A = k/h, where k is the constant of proportionality.
In an inverse relationship, one variable increases as the other variable decreases. In this case, as h increases, A decreases, and as h decreases, A increases. The constant of proportionality, k, remains the same throughout the relationship.
To find the value of k, you can use the formula and plug in known values for A and h. For example, if A = 4 and h = 2, you can plug these values into the formula and solve for k:
4 = k/2
k = 8
Once you know the value of k, you can use the formula to find the value of A or h, given the value of the other variable. For example, if you know that h = 3 and k = 8, you can plug these values into the formula and solve for A:
A = 8/3
A = 2.67
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
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Figure 1 and figure 2 are right triangles. two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long What scale factor was used to produce Figure 2 from Figure 1? 7 over 3, 3 over 7, 7 or 3
The scale factor used to produce Figure 2 from Figure 1 is given as follows:
7/3.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The side lengths are given as follows:
Figure 1: 3 units.Figure 2: 7 units.Hence the scale factor of the dilation is given as follows:
7/3.
(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).
Missing InformationThe problem asks for the scale factor used from figure 1 to figure 2.
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Answer:
C 7/3 because i got it right
Tyler took out a five-year loan with a principal of $12,000. He made monthly payments of $215 for the entire period, at which point the loan was paid off. How much did Tyler pay in interest?
Responses
$15
$60
$75
$900
Answer:
D, $900
Step-by-step explanation:
and monthly payments of $215, we can use the following formula:
Total interest = Total amount paid - Principal
where:
Total amount paid = Monthly payment x Number of payments
Number of payments = Number of years x 12
In this case, Tyler made monthly payments of $215 for 5 years, which is a total of 5 x 12 = 60 payments.
Substituting these values into the formula, we get:
Total amount paid = $215 x 60 = $12,900
Total interest = $12,900 - $12,000 = $900
Therefore, Tyler paid $900 in interest over the five-year period. The answer is option D: $900.
whats smaller than 1/2
Answer:
1/4
Step-by-step explanation:
Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)
Hope it helps! :D
Is(8, 2)a solution to the inequality y ≥ 3x + 4?
No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.
To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.
y ≥ 3x + 4
Substituting x = 8 and y = 2:
2 ≥ 3(8) + 4
2 ≥ 24 + 4
2 ≥ 28
The inequality is not true since 2 is not greater than or equal to 28.
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Warm-Up: Suppose you have 60 dollars to deposit into a savings account. If you put your money into Bank A, they will deposit an additional 6 dollars per year into your account. If you put your money into Bank B, they will increase your balance by 10 percent per year.
How much money would you have after one year if you put your money into Bank A? How about Bank B?
Bank B may be a better option because the 10 percent increase is applied to the new balance each year, whereas Bank A only adds a flat 6 dollars each year.
If you put your money into Bank A, you will have to equate it as 60 + 6 = <<60+6=66>>66 dollars after one year.
If you put your money into Bank B, you will have 60 + (60 * 0.10) = 60 + 6 = <<60+(60*0.10)=66>>66 dollars after one year of the investment.
So, after one year, you will have the same amount of money in both Bank A and Bank B.
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34. The table below shows the number of new restaurants in a fast food chain that opened during the years
of 1988 through 1992. Using an exponential model, write an equation for the curve of best fit, then
estimate the number of new restaurants that opened in 2005.
1486
Year
1988
1989
1990
1991
1992
New
Restaurants
49
81
112
150
262
Equation:
Answer:
As a result, we can assume that the fast-food business added about 3,454 new outlets in 2005.
What are equations used for?
A mathematical equation, such as 6 x 4 = 12 x 2, states that two variables or values are equivalent. a meaningful noun. An equation is used when two or maybe more factors must be considered jointly in order to understand or explain the whole situation.
We can apply the following formula to find an exponentially model that matches the data:
y = abˣ
Where x is the length of time after 1988, y is the number of fresh restaurants that open each year, and a and b are undetermined constants.
We may use the information from the years 1988 and 1989 to get the constants a and b:
49 = ab⁰
81 = ab¹
As a result of the first equation, a = 49. When we put it in the second equation, we obtain this result:
81 = 49b¹
b = 81/49
The following is the exponentially model that best matches the data:
y = 49(81/49)ˣ
Since 2005 is 17 years after 1988, we need to determine the value of y when x = 17 in order to figure out the number of new eateries that debuted in 2005:
y = 49(81/49)¹⁷
y ≈ 3,454
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Subtract mixed numbers problem help
9 1/4-12 7/8
Therefore , the solution of the given problem of fraction comes out to be -3 5/8 as a result.
A fraction is what?Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction.
Here,
=> 9 1/4 = (4 x 9 + 1)/4 = 37/4
=> 12 7/8 = (8 x 12 + 7)/8 = 103/8
4 and 8 have the same shared factor, which is 8.
=> 37/4 - 103/8 = (2 x 37)/(2 x 4) (2 x 4) - 103/8
=> 74/8 - 103/8
=> -29/8
There is no simpler way to describe the outcome.
Since the outcome is already an incorrect fraction, we can change it back to a mixed integer as follows:
-29/8 = -3 5/8
9 1/4 - 12 7/8 Equals -3 5/8 as a result.
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Julia deposits $2000 into a savings account that
earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04)^t, where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?
Please show work
The equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex]. Option D is the correct answer.
What is compound interest?The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
Given that, the function of the model of the account is:
[tex]y = 2000(1.04)^t[/tex]
The monthly interest rate is:
r = 4% / 12 = 0.00333
The model in terms of monthly interest rate can be written as:
[tex]y = 2000(1 + r)^{12t/12}[/tex]
Substituting the value of r:
[tex]y = 2000(1 + 0.0033)^t[/tex]
Hence, the equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex].
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Derivations (20 marks): For each of the questions in this section provide a derivation. Other methods will receive no credit i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks) iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
Proof:
1. ∃x(Fx & Gx) [Premise]
2. Fx & Gx [∃-Elimination, 1]
3. ∃xFx [∃-Introduction, 2]
4. ∃xGx [∃-Introduction, 2]
5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]
6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)
Proof:
1. ¬ 3x(Px v Qx) [Premise]
2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]
3. Vx ¬ Px [∀-Introduction, 2]
4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]
iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Proof:
1. ¬ Vx(Fx → Gx) v 3xFx [Premise]
2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]
3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]
4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]
5. Fx → Gx [Resolution, 3, 4]
6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
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A number y, when rounded to 2 decimal places, is equal to 9. 68. Find the upper and lower bound
If the number when rounded to 2 decimal places is equal to 9.68, then the upper bound is 9.685 and lower bound is 9.675 .
In order to find the upper bound of the number y, we need to add 0.005,
and to find the lower bound of the number y, we need to subtract 0.005 ,
We know that, the number y, when rounded to 2 decimal places is equal to 9.68 ;
So, the Upper Bound is = 9.68 + 0.005 = 9.685, and
The Lower Bound is = 9.68 - 0.005 = 9.675.
Therefore, the lower bound of y is 9.675 and upper bound of y is 9.685.
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I need some assistance with this
Answer:
In believe it’s 68 but I might be wrong so if it is sorry
Step-by-step explanation:
(8x^(3)+24x^(2)+14x+2)-:(2x+5) Your answer should give the quotient and the remainder.
4x^(2)+2x+2 with a remainder of -8.
The quotient and remainder of the given expression can be found by performing polynomial long division.
First, divide the leading term of the dividend, 8x^(3), by the leading term of the divisor, 2x. This gives a quotient of 4x^(2).
Next, multiply the divisor, (2x+5), by the quotient, 4x^(2), to get 8x^(3)+20x^(2).
Then, subtract this product from the dividend to get a new dividend of 4x^(2)+14x+2.
Repeat this process by dividing the leading term of the new dividend, 4x^(2), by the leading term of the divisor, 2x, to get a new quotient of 2x.
Multiply the divisor, (2x+5), by the new quotient, 2x, to get 4x^(2)+10x.
Subtract this product from the new dividend to get a new dividend of 4x+2.
Finally, divide the leading term of the new dividend, 4x, by the leading term of the divisor, 2x, to get a new quotient of 2.
Multiply the divisor, (2x+5), by the new quotient, 2, to get 4x+10.
Subtract this product from the new dividend to get a remainder of -8.
So, the final quotient is 4x^(2)+2x+2 and the final remainder is -8.
Therefore, the answer is: (8x^(3)+24x^(2)+14x+2)-:(2x+5) = 4x^(2)+2x+2 with a remainder of -8.
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Will the graph y=2(4)^x be increasing or decreasing? Explain how u know
Answer:
Step-by-step explanation:
Decreasing.
This is because the as you increase the X value and solve for Y, the Y value decreases.
For example:
[tex]x=1 \\y=2(\frac{1}{3} )^1\\y=\frac{2}{3} =0.667\\\\x=2\\y=2(\frac{1}{3} )^1\\y=\frac{2}{9}=0.222\\\\x=3\\y=2(\frac{1}{3} )^3\\y=\frac{2}{27}=0.074[/tex]
Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]
The solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
To solve this system of equations using Cramer's Rule, we will begin by finding the determinant of the coefficient matrix, which is an array of the coefficients of the variables in the equations. We will then find the determinants of the matrices that result from replacing each column of the coefficient matrix with the constant terms of the equations. Finally, we will use these determinants to find the values of x, y, and z.
The coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} \]
The determinant of the coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} = (-3)(-3)(-2) - (-4)(-3)(-1) - (-4)(1)(1) - (-4)(-3)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = -6 + 4 + 4 + 4 - 12 + 8 = -2 \]
The matrix that results from replacing the first column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} = (-8)(-3)(-2) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(-2) = 48 - 36 - 76 + 36 - 76 + 24 = -80 \]
The matrix that results from replacing the second column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} = (-3)(-19)(-2) - (-8)(-3)(-1) - (-4)(1)(3) - (-4)(-19)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = 114 + 24 + 12 + 76 - 12 + 8 = 222 \]
The matrix that results from replacing the third column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} = (-3)(-3)(3) - (-4)(-19)(-1) - (-8)(1)(1) - (-8)(-3)(-1) - (-8)(-19)(1) - (-8)(1)(3) = 27 + 76 + 8 + 24 - 152 + 24 = 7 \]
Using these determinants, we can find the values of x, y, and z: \[ x = \frac{-80}{-2} = 40 \] \[ y = \frac{222}{-2} = -111 \] \[ z = \frac{7}{-2} = -3.5 \]
Therefore, the solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
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Given a circle with center (– 3, 6) and radius 5, what is an equation of the circle?
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-3}{h}~~,~~\underset{6}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-3) ~~ )^2 ~~ + ~~ ( ~~ y-6 ~~ )^2~~ = ~~5^2\implies (x+3)^2+(y-6)=25[/tex]
Identify then number of solutions of the polynomial equation. Then find the solutions. z^(3)+10z^(2) + 28z + 24=0
The solutions are: z = -3, -2, and -1. This equation is a third-degree polynomial equation and it can have up to three solutions. To find these solutions, you can use the Rational Root Theorem.
This theorem states that all rational solutions of a polynomial equation can be written in the form a/b, where a is a divisor of the coefficient of the constant term, and b is a divisor of the coefficient of the leading term.
For this equation, the constant term is 24 and the leading term is 1, so the possible solutions can be expressed as a/b, where a is a divisor of 24 and b is a divisor of 1. Therefore, the possible solutions are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. To find the exact solutions, substitute these values for z into the equation and solve for each value.
The solutions are: z = -3, -2, and -1.
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Feb 28,
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Gabriel went to the store to buy some coffee. The price per pound of the coffee is
$4.50 per pound and he has a coupon for $2 off the final amount. With the coupon,
how much would Gabriel have to pay to buy 4 pounds of coffee? Also, write an
expression for the cost to buy p pounds of coffee, assuming at least one pound is
purchased.
Answer:
The original cost for 1 pound of coffee is $4.50, and Gabriel wants to buy 4 pounds, so the total cost without the coupon would be:
4 pounds x $4.50/pound = $18
With the coupon, Gabriel can subtract $2 from the final amount, so the total cost with the coupon would be:
$18 - $2 = $16
Therefore, Gabriel would have to pay $16 to buy 4 pounds of coffee with the coupon.
To write an expression for the cost to buy p pounds of coffee, we can use the formula:
cost = price per pound x number of pounds - coupon
If Gabriel buys at least one pound of coffee, then the expression would be:
cost = $4.50p - $2
So the cost to buy p pounds of coffee can be calculated by plugging in the desired value for p into this expression.
Henry has 342 marbles in bags. If 9 marbles are in each bag. how many bags does Henry have? How many bags will he have if he gives 15 bags to his brother?
4. c^(3)v^(9)c^(-1)c^0
6. 9y^(4)j^(2)y^(-9)
8. 2y^(-9)h^(2)(2y^(0)h^(-4))^(-6)
10. (-3q^(-1))^(3)q^(2)
expression has the least vitive"? B. n^(n)
D. −n^(n)n^(-4)
vitive is D: −nnn−4.
To answer the question, the expression with the least vitive is D: −nnn−4.
For reference, the expressions in the question are:
4. c3v9c−1c0
6. 9y4j2y−9
8. 2y−9h2(2y0h−4)−6
10. (−3q−1)3q2
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exact value of sec(sin^(-1)((3)/(10))) o enter EXACT values ed to simplify any radicals
The exact value of sec(sin-1(3/10)) is 1.049988251.
The exact value of sec(sin-1(3/10)) can be found using the following steps:
Step 1: Enter the value of sin-1(3/10) into a calculator to get the angle measure in radians. This will give you an angle measure of 0.304692654.
Step 2: Take the cosine of this angle measure using a calculator. This will give you a value of 0.952424403.
Step 3: The value of secant is the reciprocal of the value of cosine. So, to find the exact value of sec(sin-1(3/10)), take the reciprocal of 0.952424403. This will give you an exact value of 1.049988251.
Step 4: Simplify any radicals if necessary. In this case, there are no radicals to simplify.
Therefore, the exact value of sec(sin-1(3/10)) is 1.049988251.
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What is the inequality shown?
Answer:
The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
Step-by-step explanation:
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
The inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
How to find the inequality?The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
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A rectangular prism is shown below. What is the LATERAL surfa
area?
11 cm
5 cm
2 cm
The surface area of the rectangular prism is 174 cm^2
What is a Rectangular Prism?Rectangular Prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangle such that all the pairs of the opposite faces are congruent.
To determine the surface area of Rectangular prism
SA = 2(LH + LW + WH)
Where W = Width = 2 cm
L = Length = 5 cm
H = Height = 11 cm
SA = 2[(5*11) + (5*2) + (11*2)]
SA = 2(55 + 10 + 22)
SA = 2(87)
SA = 2 * 87
SA = 174
Therefore, the surface area of rectangular prism is 174 cm^2
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Consider functions f and g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?
What is the value of (g • f)(4)?
O A. 9
O B. B. -
O C. -9
O D. 1
The numeric value of the composite function at x = 4 is given as follows:
|f(4) - 1|.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
If g is the outer function, as is the case for this problem, we have that:
(g • f)(x) = g(f(x)).
At x = 4, the numeric value of the composite function is given as follows:
g(f(4)) = |f(4) - 1|.
Missing InformationThe problem is incomplete, hence the composite function is given in general terms.
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How to write 3/4 with a denominator of 12? Please help
Answer:
9/12
Step-by-step explanation:
3/4 converted is 9/12 3x3 is 9 and 4x3 is 12.
are 8,192 players in a Rock Paper Scissors tournament. In each round half the players ar d to find the number of players remaining in the tournament at the end of x rounds? f(x)=8192(0.05)^(x) B
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.
The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.
To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.
For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:
f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.
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Can somebody help please I’ll give you brainliest and 30 points!!!!!
Answer:
$512.17
$286.48
$1,958.40
$1,628.85
$56.37
$324.24
$135.55
Note: These calculations were made assuming simple interest. If the interest is compounded, the final amounts will be slightly different.
Step-by-step explanation:
Find the remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3. Compare this with P(-3) where P(x)=12-5x+3x^(2)+2x^(3).
The remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3 is -39.
This can be found by using long division or synthetic division. The result of the division is 2[tex]x^{(2)}[/tex]-11x+21 with a remainder of -39.
To compare this with P(-3), we need to plug in -3 for x in the original polynomial P(x)=12-5x+3[tex]x^{(2)}[/tex]+2[tex]x^{(3)}[/tex].
This gives us:
P(-3)= 12-5(-3)+3(-3)[tex]^{(2)}[/tex]+2(-3)[tex]^{(2)}[/tex]
=12+15+27-54=-39
Therefore, the remainder is the same as P(-3) for the given polynomial.
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About 72 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected.
2. What is the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%?
The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0107.
To find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%, use the formula for the standard error of a proportion:
SE = √(p(1-p)/n)
Where p is the proportion of the population that is making an effort to conserve water or electricity, and n is the sample size.
In this case, p = 0.72 and n = 110. Plugging these values into the formula gives:
SE = √(0.72(1-0.72)/110) = 0.0347
Next, we need to find the z-score for the proportion of 0.80. The z-score is given by:
z = (P - p)/SE
Where P is the sample proportion and p is the population proportion. In this case, P = 0.80 and p = 0.72. Plugging these values into the formula gives:
z = (0.80 - 0.72)/0.0347 = 2.30
Finally, we can use the z-score to find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%. This is given by:
P(z > 2.30) = 1 - P(z < 2.30) = 1 - 0.9893 = 0.0107
Therefore, the probability is 0.0107 or 1.07%.
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In a class 45% of the students are girls. If there are 18 girls in the class, then find
the total number of students in the class.
Answer:
i dont think its possible