In which pair do both decimals represent rational numbers?
O A. 2.71828182845904523536... and 0.1222
O B. 3.141592653589793238... and 0.684
O C. 3.141592653589793238... and 0.1222...
O D. 0.684 and 0.1222...

Leviah, this is the solution:

Let's recall that the Remainder theorem says that we can restate the polynomial in terms of the divisor, and then evaluate the polynomial

Therefore: the value of P(x) that satisfies both remainders is:

A. 5

Answer:

2 or 1/50 as a fraction

Step-by-step explanation:

Answer:

The answer is 2

Step-by-step explanation:

9514 1404 393

Answer:

  50°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it intercepts.

  ∠ACB = 1/2 arc AB = (100°)/2

 ∠ACB = 50°

To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:

7x + 21 = 7x + 35

Subtracting 7x from both sides, we get:

21 = 35

This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.

However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.

Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:

7(5 - 3) = 14

Therefore, the missing number is 14, which corresponds to answer option B.

Answer:

write the percent divided by 100

Step-by-step explanation:

1) write the percent divided by 100.

2) if the percent is not a whole number, multiply both top and bottom by 10 for every number after the decimal point.

3) reduce (simplify) the fraction.

Answer:

54

Step-by-step explanation:

multiply 9 and 7 which is 63. then multiply 63 by 150 which is 9,450. then multiply 25 and 7 which is 175. then divide 175 and 9,450. and the answer is 54. Yw!!

We need to write and solve an algebraic equation to find the final company's balance.

The answer is: The final balance is -$275.

Let's see how to get that.

First, we know that the company earns $150 per week for 9 weeks, then the total amount of money that the company earns in these 9 weeks is:

$150*9 = $1,350

Then the company losses $65 per week for 25 weeks, then the amount that the company losses is:

$65*25 = $1,625

The final balance will be the difference between what the company earned and what the company lost, then the final balance is:

balance = $1,350 - $1,625 = -$275

This means that the company's final balance is -$275.

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a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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Answer: y = 17x - 19

Step-by-step explanation:

17x + y = -19

Subtract 17 on both sides

Y= -19 - 17x

Then put it in y= mx + b

Y= -17x - 19

Answer:

y = -17x -19

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

17x+y = -19

Solve for y

y = -17x -19

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:

In the beginning, there is 60 L of water in the bathtub. The water drains out from the bathtub at 2.5 L per minute. How many minutes does it take until all of the water is drained out?

Zero of the function: (24, 0)

The value 24 min represents the number of minutes it takes for the water to completely drain out from the bathtub.

Step-by-step explanation:

Zero of the function is when y=0

0 = 60 -2.5 x

x = 24

Answer:

Option A, 80π

Step-by-step explanation:

4²×5π

= 80π

Answer:

The measures of two angles are 2x⁰ and (3x + 20)⁰. What is the measure of each angle if x = 14?

b 28 and 62

Answer:

the fourth answer is prime.

Step-by-step explanation:

in order to break down a 4 term polynomial, create groups of the polynomials. seperate each in 2 group. then, fine the greatest common fastor of each group that are in parenthesis.It was easy to break the first three. the last one however, was hard to break apart because in the second group, you cant find the greatest common factor between -x and 2. So the bottom one is prime

Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Answer:

refer to the attachments

Step-by-step explanation:

EXPAND IN MATH:

expansion - a function expressed as a sum or product of terms; "the expansion of (a+b)^2 is a^2 + 2ab + b^2". math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement.

( x + 2 ) ( x + 11 ) (EXPAND):

1) USE THE FOIL METHOD: (A+B)(C+D)=AC+AD+BC+BD

X² + 11X + 2X + 22

2) COLLECT LIKE TERMS

X² + (11X + 2X) + 22

3) SIMPLIFY

X² + 13X + 22

Answer:

The answer is "0.15".

Step-by-step explanation:

From the information provided, they can assume that Binomial distribution should proceed, after all, "success". Its bottle cap winner as well as the result is also independent of another trail, but trails are not fixed at all. Yeah, that's how it works. We will claim also that chances of success are P=0.20 so there are no trials n=8.

Let an X=winner probability distribution be on the bottle cap, but this X is a binomial function of P=0.20, but n = 8

That is \(X \sim \ B(0.20,8)\)

There we must find the chance that from 8 trials, this is exactly 3 winners limit that is P(X=3)  if

\(X\sim B(n,P) \ then \ P(X=x) \binom{n}{x} P^{x}(1-P)^{n-x}\)

Therefore, \(P(X=3)= \binom{8}{3} 0.20^{3}(1-0.20)^{8-3}\)

                                  \(= \binom{8}{3} 0.20^{3} (1-0.20)^{5}\\\\= \binom{8}{3} 0.20^{3} (0.80)^{5}\\\\=0.14680064 \\\\ = 0.15\)

Answer:

297 containers and 8 eggs will be left over

Answer:

1/2

Step-by-step explanation:

I did this on paper and I have no idea how to explain.

But I think it is 1/2

Hope this helps!

Answer:

The answer is 1/2

Step-by-step explanation: 2/3 divided by 4/5 is 5/6 and that times 3/5 is 1/2

Answer:

He saved $4

1/5 of the total amount saved

Step-by-step explanation:

20 - 16 = 4

Answer:

0.300 + 0.030 + 0.004

or

0.100 x 3  +  0.01 x 3  +  0.001 x 4

7km/ 4km per hour = 1 3/4 hours

3/4 hour = 45 minutes

Total time = 1 hour and 45 minutes.

The odds ratio of income is 1.00320, rounded to 5 decimal places.

The odds ratio of income can be calculated using the formula given below:

odds ratio = odds of personal loan when income increases by 1 unit

Odds of a personal loan is the ratio of probability of acceptance to probability of rejection.

Odds of personal loan = P(personal loan=yes) / P(personal loan=no)P(personal loan=yes) = 0.0122

P(personal loan=no) = 1 - P(personal loan=yes) = 0.9878

Odds of personal loan = 0.0122 / 0.9878 = 0.0124

The logistic regression model estimated as P(personal loan=yes|income=x) = 1 / (1 + e(-6.3525+0.0392x))

Hence, P(personal loan=yes|income=x) = 1 / (1 + e(-6.3525+0.0392x)) = 0.0122

P(personal loan=yes|income=x+1) = 1 / (1 + e(-6.3525+0.0392(x+1))) = 0.012414

We have, odds ratio = odds of personal loan when income increases by 1 unit

odds ratio = 0.012414 / 0.0124 = 1.0032 ≈ 1.00320

Round the answer to 5 decimal places = 1.00320

The odds ratio of income is 1.00320, rounded to 5 decimal places.

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The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

D

Step-by-step explanation:

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Answer:

=1−12/3≈−3.67

Step-by-step explanation:

The z-score of x = 1, when x ~ N(12, 3), is approximately -3.6667.

To find the z-score of x when x = 1, we'll use the formula for z-score:

z = (x - μ) / σ

Given:

x = 1

μ (mean) = 12

σ (standard deviation) = 3

Substituting these values into the formula, we get:

z = (1 - 12) / 3

Calculating the numerator:

1 - 12 = -11

Dividing the numerator by the denominator:

-11 / 3 ≈ -3.6667

Therefore, the z-score of x = 1, when x follows a normal distribution with a mean of 12 and a standard deviation of 3, is approximately -3.6667.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:

what's that

Step-by-step explanation:

Answer:

Step-by-step explanation: