plz help. The amount of pages in a 3rd graders book can be modeled by f(x) = x^2 + 6x where x represents the number of chapters. If 135 pages are in the book, how many chapters are there?​

Answer:

landing on a 4 would be 1/3 chance

and

landing on a number less than 4 would be 2/3 chance

Step-by-step explanation:

The probability of landing on a 4 is 1/3 and then landing on a number less than 4 is 2/3.

Probability is the chance of happening an event or incident.

The probability of landing on a 4 is 1/3.

Then, the probability on landing on a number less than 4 = 2/3.

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3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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The given differential equation is y′′′−7y′′+16y′−12y=e^−2x+cosx. Let's find the general solution to the given differential equation. As it is a third-order linear non-homogeneous differential equation, we can find the general solution by solving its characteristic equation.

So, let's first find its characteristic equation. The characteristic equation of the given differential equation:

y′′′−7y′′+16y′−12y=0 is r³ - 7r² + 16r - 12 = 0.

This can be written as (r-1)(r-2)² = 0.The roots of the above equation are:r₁=1, r₂=2 and r₃=2. The repeated root "2" has a general solution (C₁ + C₂x) e^(2x). On substituting this in the differential equation, we get C₁ = -1 and C₂ = -1.Now, the general solution to the given differential equation is:

y(x) = c₁ + c₂e^2x + (c₃ + c₄x) e^(2x) + (Ax + B) e^(-2x) + (Ccos(x) + Dsin(x)).

Let's find the general solution to the given differential equation:

y′′′−7y′′+16y′−12y=e^−2x+cosx.

As it is a third-order linear non-homogeneous differential equation, we can find the general solution by solving its characteristic equation. The characteristic equation of the given differential equation:

y′′′−7y′′+16y′−12y=0 is r³ - 7r² + 16r - 12 = 0.

This can be written as (r-1)(r-2)² = 0.The roots of the above equation are:r₁=1, r₂=2 and r₃=2. The repeated root "2" has a general solution (C₁ + C₂x) e^(2x). On substituting this in the differential equation, we get C₁ = -1 and C₂ = -1.Now, the general solution to the given differential equation is:

y(x) = c₁ + c₂e^2x + (c₃ + c₄x) e^(2x) + (Ax + B) e^(-2x) + (Ccos(x) + Dsin(x)).

Here, the terms e^2x, xe^2x, e^(-2x), cos(x) and sin(x) are particular solutions that satisfy the non-homogeneous part of the given differential equation.Let's find the particular solutions to the given differential equation. The non-homogeneous part of the differential equation is e^(-2x) + cos(x).For e^(-2x), the particular solution is (Ax+B)e^(-2x).For cos(x), the particular solution is Ccos(x) + Dsin(x).On substituting the particular solutions in the given differential equation, we get:

(Ax+B)(-2)^3 e^(-2x) + (Ccos(x) + Dsin(x)) = e^(-2x) + cos(x)

Simplifying the above equation, we get:

-8Ae^(-2x) + Ccos(x) + Dsin(x) = cos(x)

Also, we have to find the values of A, B, C and D. By comparing the coefficients of e^(-2x) and cos(x) on both sides, we get A=0, B=1, C=1/2 and D=0.On substituting the values of A, B, C and D, we get the final solution to the given differential equation:

y(x) = c₁ + c₂e^2x + (c₃ + c₄x) e^(2x) + e^(-2x) + cos(x)/2.

Thus, the general solution to the given differential equation is y(x) = c₁ + c₂e^2x + (c₃ + c₄x) e^(2x) + (Ax + B) e^(-2x) + (Ccos(x) + Dsin(x))

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Answer:

97

Step-by-step explanation:

x has to be more than 60 and less than 100

the primes between those are 61,67,71,73,79,83, 89, 97

97 is two less in the ones than in the tens so it completes all of the requirements of the riddles therefore, 97 is the answer.

Answer:

It is 79

Step-by-step explanation:

9-7 is 2

Answer:

its 12

Step-by-step explanation:

in the bottom right of this question click the button that says brainliest please

Answer: 15%

Step-by-step explanation:

The Percentage decrease will be:

= Decrease in weight / Old weight × 100

= (200 - 170) / 200 × 100

= 30/200 × 100

= 15%

The Percentage decrease is 15%

Answer:

4/5=16/20

Step-by-step explanation:

because

4x4

Answer:

16

Step-by-step explanation:

20 divided by 5 is 4.

This means both numbers on the left side must be multiplied by 4 to get the right side.

4 times 4 is 16.

Answer:

A

B

D

E

F

Step-by-step explanation:

26 can be also written as 26/1 or 52/2 or ...

so, it is part of the rational numbers.

it is clearly a natural number (1, 2, 3, 4, ...).

it is also an integer (... , -2, -1, 0, 1, 2, 3, ...).

it is a whole number (0, 1, 2, 3, 4, ...)

and it is a real number, as it can be written as 26.0. real numbers are the superset of all these mentioned sets of numbers.

but it is NOT an irrational number, as they have infinite digits after the decimal point without any repeating pattern.

in other words, any number that is a member of the rational numbers cannot be an irrational number. and vice versa.

Answer:

what is the answer?

Step-by-step explanation:

Answer:22.5

Step-by-step explanation:think of 500.000 as an 500 then multiply 0.045 so I got 22.5

Answer:

22.5

Step-by-step explanation:

 500.000

x 0.045

22.5

You just have to use long multiplication

Answer:21 minutes

Step-by-step explanation:

You have to calculate how long it takes you to go around once so divide 7/5 to get 1.4 then multiply that by your friends laps to get 21 minutes.

hope this helped!!

The length of the side of the smaller square is 7 inches.

Let x be the length of the side of the smaller square.

The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is

(x + 3) inches.

The area of the smaller square is

x^2 square inches.

The area of the larger square is

(x + 3)^2 square inches.

We can set up the equation:

x^2 + (x + 3)^2 = 149

Expanding and simplifying the equation gives:

x^2 + x^2 + 6x + 9 = 149

Combining like terms:

2x^2 + 6x - 140 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2

x = (-6 ± √(36 + 1120)) / 4

x = (-6 ± √(1156)) / 4

x = (-6 ± √(596)) / 4

x = (-6 ± 34) / 4

x = -10 or x = 7

The side length of the smaller square can't be negative, so x = 7 inches.

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A value of 0.25 for p(1-p) in the sample size formula when the true value of p is unknown.

This is because the value of p(1-p) is maximum when p=0.5, and since we do not have any information about the true value of p, assuming p=0.5 is the most conservative approach. Therefore, to calculate the sample size required to estimate a proportion using a confidence interval with a margin of error e, we can use the formula:

\(n = [z^2 * p(1-p)] / e^2\)

where z is the z-score corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and e is the desired margin of error. We can use p=0.5 and solve for n to get a conservative estimate of the sample size required for the given confidence level and margin of error.

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If prior knowledge or data suggests that the proportion is significantly different from 0.5, then a more accurate estimate of p should be used in the formula.

To calculate the sample size formula for estimating a proportion using a confidence interval with a margin of error e, we

use the following formula:

\(n = (Z^2 × p × (1-p)) / e^2\)

where n is the required sample size, Z is the Z-score corresponding to the desired level of confidence,

p is the estimated proportion, and

e is the margin of error.

Since the product p(1-p) is not known, a conservative approach is to use p = 0.5, which is the value that maximizes the

product p(1-p) for any given proportion.

This approach ensures that the sample size will be large enough to obtain a reliable estimate of the proportion, even if

the true proportion is close to 0 or 1. However, if prior knowledge or data suggests that the proportion is significantly

different from 0.5, then a more accurate estimate of p should be used in the formula.

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Answer:

Volume 6*6*6=216 cu

pa braintest

The z-score for the value 75, with a mean of 74 and a standard deviation of 5, is 0.20.

The z-score measures the number of standard deviations a particular value is away from the mean.

It is calculated using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

In this case, the value is 75, the mean is 74, and the standard deviation is 5.

Plugging these values into the formula, we get: z = (75 - 74) / 5 = 0.20.

The positive value of the z-score indicates that the value of 75 is 0.20 standard deviations above the mean.

Since the standard deviation is 5, we can interpret this as 75 being 1 unit (0.20 × 5) above the mean.

The z-score is a useful measure as it allows us to compare values from different distributions and determine their relative positions.

It also helps in understanding the significance of a particular value in relation to the distribution it belongs to.

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Based on simultaneous equations, Kaun has deposited in each account the following:

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

The total deposit in the two accounts = R 5,400

The annual interest in Account A = 3% or 0.03

The annual interest in Account B = 2% or 0.02

The total interest earned from both accounts for the year = R 140

Let Account A be designated as a and Account B be designated as b.

a + b = 5,400 ... Equation 1

0.03a + 0.02b = 140 ... Equation 2

Eliminate a by multiplying Equation 1 by 0.03:

0.03a + 0.03b = 162 ... Equation 3

Subtract Equation 2 from Equation 3:

0.03a + 0.03b = 162

-

0.03a + 0.02b = 140

= 0.01b = 22

b = 2,200

From Equation 1, substitute b:

a + 2,200 = 5,400

a = 3,200 (5,400 - 2,200)

Check:

In equation 2:

0.03a + 0.02b = 140

0.03(3,200) + 0.02(2,200) = 140

96 + 44 = 140

140 = 140

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Using the z-distribution, it is found that the 95% confidence interval for the proportion of all U.S. adults who play video games is (0.4681, 0.5119). It means that we are 95% sure that the true proportion of all U.S. adults who play video games is between 0.4681 and 0.5119.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have that:

The lower bound of the interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.96\sqrt{\frac{0.49(0.51)}{2001}} = 0.4681\)

The upper bound of the interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.96\sqrt{\frac{0.49(0.51)}{2001}} = 0.5119\)

The 95% confidence interval for the proportion of all U.S. adults who play video games is (0.4681, 0.5119). It means that we are 95% sure that the true proportion of all U.S. adults who play video games is between 0.4681 and 0.5119.

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The time required for the given investment of $5000 to grow to $7400 at an interest rate of 7.5% per year, compounded quarterly is 5 years 3 months i.e., t = 5.27 years.

The formula for calculating the compound interest is

\(A = P(1 + \frac{r}{n} )^n^t\)

Where A: Future Amount; P: Current investment; r: Interest rate; n: The number of times the amount is compounded; t: The amount of time

It is given that,

Current investment P = $5000

Future amount A = $7400

Interest rate r = 7.5% = 0.075

The amount is compounded quarterly. So, n = 4

On substituting all these in the formula, we get

\(A = P(1 + \frac{r}{n} )^n^t\)

⇒ 7400 = 5000(1 + 0.075/4)^(4t)

⇒ 7400/5000 = (1 + 0.01875)^(4t)

⇒ 1.48 = (1.08175)^(4t)

⇒ (1.08175)^(4t) = 1.48

On applying logarithm on both sides, we get

ln(1.08175)^(4t) = ln(1.48)

⇒ 4t ln(1.08175) = ln(1.48)

⇒ 4t = ln(1.48)/ln(1.08175)

⇒ t = ln(1.48)/4ln(1.08175)

∴ t = 5.27 years

Thus, the time required for the given investment is 5.27 years which is 5 years 3 months.

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Answer:

Answer: 21

Step-by-step explanation:

If cost is the same

\({ \rm{C_{r} =C _{b} }} \\ \\ { \rm{175 + 12(n - 10) = 125 + 14(n - 8)}} \\ \\ { \rm{50 + 12n - 120 = 14n - 112}} \\ \\ { \rm{n = 21}}\)

Answer:

\(\frac{\pi }{4}\)

Step-by-step explanation:

\(sin^{-1}\) ( \(\frac{\sqrt{2} }{2}\) ) = \(\frac{\pi }{4}\)

Answer:

1,2, and 3

Step-by-step explanation:

1+ (2*2) is equal to 5, so it has to be 1 and 2, and you can figure out that 3 goes after that.

Answer:

it would be a 10% chance because think about it you have ten numbers so with each number there is a 10% chance of landing on it.

Answer: 1:2  or 1/2 or 1 to 2

Step-by-step explanation:

Boys=10

Girls= 20

Boys:Girls::10:20::1:2

Answer:

r > -1

Step-by-step explanation:

4r + 10 > 6

4r + 4 > 0

4 > -4r

-4 < 4r

-1 < r

r > -1

Answer:

Step-by-step explanation:

The probability that greater than 99 out of 160 students will graduate on time is 0.1011, or 10.11%

To approximate the probability that greater than 99 out of 160 students will graduate on time given that the probability for a single student is 57%, we will use the normal distribution follow the given steps:

1. Determine the mean (μ) and standard deviation (σ) of the binomial distribution.
  μ = n * p = 160 * 0.57 = 91.2
  σ = sqrt(n * p * (1-p)) = sqrt(160 * 0.57 * 0.43) ≈ 6.498

2. Convert the problem to a standard normal distribution (Z-distribution) by finding the Z-score:
  Z = (X - μ) / σ
  Since we want to find the probability of more than 99 students graduating, we will use 99.5 (continuity correction).
  Z = (99.5 - 91.2) / 6.498 ≈ 1.276

3. Look up the Z-score in a standard normal (Z) table or use a calculator to find the area to the right of Z. The area to the left of Z is 0.8989.

4. Subtract the area to the left of Z from 1 to find the area to the right (our desired probability):
  P(X > 99) = 1 - 0.8989 = 0.1011

So, the probability that greater than 99 out of 160 students will graduate on time is approximately 0.1011, or 10.11% when rounded to four decimal places.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer: Multiply 4.50 x 10= 45.00$

Step-by-step explanation:

Answer:

$7.50

Step-by-step explanation:

Divide the cost by 6 to find the price of one 1lb:

4.50 ÷ 6 = 0.75

Now multiply this by 10 to find the cost of 10lbs:

0.75 x 10 = 7.5

∴ The cost is $7.50.

Hope this helps!

Answer:

\(\sf 7x+5y\)

Step-by-step explanation:

\(\sf 3 ( x-y) + 4 (x+2y)\)

~ Apply the Distributive property

\(\sf 3x-3y+4\left(x+2y\right)\)

\(\sf 3x-3y+4x+8y\)

~ Combine like terms

\(\sf 3x+4x=7x\)

\(\sf 7x-3y+8y\)

~ Combine like terms

\(\sf -3y+8y=5y\)

\(\sf 7x+5y\)

~~~~~~~~~~~~~~~~~~

DONE!!!!!!!

Hope it helps!

Have a good day!

~~~~~~~~~~~~~~~~~~

The simplification of the expression 3 ( x-y) + 4 (x+2y) is 7x + 5y

Given:

3 ( x-y) + 4 (x+2y)

= 3x - 3y + 4x + 8y

= 3x + 4x - 3y + 8y

= 7x + 5y

Therefore, the simplification of the expression 3 ( x-y) + 4 (x+2y) is 7x + 5y

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Answer:

B. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average

Step-by-step explanation:

i took the test