Evaluate the expression. 4−[(11+12(−2)÷6)+1] What is the value of the expression? Enter your answer in the box.

Answer:

x+2y=0

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=-1/2(x-4)

y+2=-1/2x+4/2

y+2=-1/2x+2

y-(-1/2x)=2-2

y+1/2x=0

1/2x+y=0

2(1/2x+y)=2(0)

x+2y=0

The system of inequalities fits in this scenario are x + y & lt; = 2815x + 10Y & lt;= 300.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a & gt; b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered. In the given questions the inequalities are x + y & lt;= 2815x + 10y & lt;= 300

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Answer:

hope this helps you

...............

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

If we denote the probability of hitting a bullseye on a dartboard with radius 12 inches as a function of the size of the bullseye, we can refer to this function as PS.

The function PS represents the probability of hitting the bullseye and is dependent on the size of the bullseye. The larger the bullseye, the higher the probability of hitting it, and vice versa. By adjusting the size of the bullseye, we can determine the corresponding probability of hitting it using the function PS.

It's important to note that without specific information about the relationship between the bullseye size and the probability, it's not possible to provide a specific mathematical expression or further details about the PS function. The function would need to be defined or provided to calculate the probability accurately.

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Answer:

To solve for x in the equation 8x - 2y = 48 when y = 4, we can substitute y = 4 and then solve for x:

8x - 2y = 48

8x - 2(4) = 48 (substituting y = 4)

8x - 8 = 48 (simplifying)

8x = 56 (adding 8 to both sides)

x = 7 (dividing both sides by 8)

Therefore, the value of x in the equation 8x - 2y = 48, when y = 4, is x = 7.

Answer:

x=7

Step-by-step explanation:

-2y=-8

48+8=56

56÷8=7

x=7

Answer:

-2x^2 + 2x^2 is equal to zero,  -2+2=0 the negative 2 cancels the positive 2

Step-by-step explanation:

The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

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Answer: 26.8

Step-by-step explanation:

\(\frac{8.2}{m}=\tan 17^{\circ}\\\\\frac{m}{8.2}=\frac{1}{\tan 17^{\circ}}\\\\m=\frac{8.2}{\tan 17^{\circ}}\\\\m \approx 26.8\)

Answer:

(5, 18 ) ; (- 5, 38 )

Step-by-step explanation:

let y = f(x) , then

y = x² - 2x + 3 → (1)

y = - 2x + 28 → (2)

substitute y = x² - 2x + 3 into (2)

x² - 2x + 3 = - 2x + 28 ( subtract - 2x + 28 from both sides )

x² - 25 = 0 ( add 25 to both sides )

x² = 25 ( take square root of both sides )

x = ± \(\sqrt{25}\) = ± 5

substitute these values into (2) for corresponding values of y

x = 5 : y = - 2(5) + 28 = - 10 + 28 = 18 ⇒ (5, 18 )

x = - 5 : y = - 2(- 5) + 28 = 10 + 28 = 38 ⇒ (- 5, 38 )

Answer:

I think the answer is 247.25, tho I'm not entirely sure

Answer:

$0.02

Step-by-step explanation:

0.60/30

The probability that each of the final rolls is at least as large as the roll preceding it is \(1/6^6\) or 1/46656.

Given data,

A fair die is rolled n times. We have to find the probability that each of the final rolls is at least as large as the roll preceding it.The probability that each of the final rolls is at least as large as the roll preceding it means the probability of getting each number greater than the preceding one. So, there will be no duplicates.

First, find the total possible outcomes on a fair die. The total possible outcomes on a fair die are 6 because the numbers are 1,2,3,4,5,6. The number of possible outcomes for each roll of the die is 6. Then the total number of possible outcomes on the nth roll of a die is\(6^n\). There will be only one possible sequence in which each of the final rolls is at least as large as the roll preceding it. Let's check it from the following table.

Roller 1Roller 2Roller 3Roller 4Roller 5Roller 61-2-3-4-5-6

Here, we got only one sequence 1,2,3,4,5,6 to have each number greater than the preceding one. So, the probability of getting this sequence is \(1/6^6\).

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Answer:

\((2,2)~ \text{and}~ (-2,-2)\)

Step by step explanation:

\(x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\\)

\(\text{Hence,}~ (x,y) = (\pm2, \pm 2)\)

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The equation that has the same solution as x² - 10x -  11 = 0 is (x - 5)² = 36

From the question, we have the following parameters that can be used in our computation:

x² - 10x -  11 = 0

Rewrite as

x² - 10x = 11

Add to both sides the square of half the coefficient of x

So, we have

x² - 10x + (-10/2)² = 11  + (-10/2)²

Evaluate

x² - 10x + 25 = 36

So, we have

(x - 5)² = 36

Hence, the equation is (x - 5)² = 36

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Each large box weighs 50 pounds, and each small box weighs 5 pounds.

Let's assume the weight of a large box is L pounds, and the weight of a small box is S pounds. We can set up a system of equations based on the given information.

From the given information, we know that the combined weight of a large and small box is 55 pounds, so we have the equation: L + S = 55. This equation represents the total weight of the boxes.

We also know that the truck is transporting a total of 130 boxes, which is the sum of 70 large boxes and 60 small boxes: 70L + 60S = 3700. This equation represents the total weight of all the boxes on the truck.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can express L in terms of S: L = 55 - S.

Substituting this value of L into the second equation, we have: 70(55 - S) + 60S = 3700.

Simplifying the equation, we get: 3850 - 70S + 60S = 3700.

Combining like terms, we have: -10S = -150.

Dividing both sides by -10, we find: S = 15.

Substituting this value of S back into Equation 1, we can solve for L: L + 15 = 55, which gives L = 40.

Therefore, each large box weighs 40 pounds, and each small box weighs 15 pounds.

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Answer:

see the screenshot below

Step-by-step explanation:

The value of Hope's car decreased by 82%. Therefore, the correct answer choices are:

A. Decreased.

A. 82%.

In Mathematics and Statistics, a physical asset such as a car that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

\(P(t) = I(1 - r)^t\)

Where:

By substituting given parameters, we have the following:

\(A = 19,995(0.82)^t\)

By comparison, we have:

Rate of change per unit interval, r = 0.82 = 82%.

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Answer:

WE DONT KNOW

Step-by-step explanation:

How much does a ticket cost? How much does the pass cost???

tell us and we help

Answer: cost without monthly pass- $56.25

And you should buy the monthly pass

Step-by-step explanation:

IN question a it say $1.25 for every student so u just 45 times 1.25 and end up with 56.25...

Answer:

Step-by-step explanation:

You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.

The side markings show congruent triangles with corresponding vertices (and angles) ...

  L (3x+24)° ⇔ P (8x -11)°

  M 84° ⇔ Q 84°

  N (2x +y)° ⇔ R (no marking)

Corresponding angles L and P have the same measure, so ...

  3x +24 = 8x -11

  35 = 5x . . . . . . . . add 11-3x

  7 = x . . . . . . . . . divide by 5

The measures of these angles are ...

  (3(7) +24)° = 45°

The sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...

  L +M +N = 180°

  45° +84° +N = 180°

  N = 51°

This lets us find the value of y from ...

  (2x +y)° = 51°

  2(7) +y = 51

  y = 37 . . . . . . . . subtract 14

The value of x is 7. The value of y is 37.

1) Number of 200 notes = 17,923,275

Number of 100 notes = 35,846,550

Number of 50 notes = 71,693,100

Number of 20 notes = 179,232,750

2) Number of 200 notes = 428,800

Number of 100 notes = 857,600

Number of 50 notes = 1,715,200

Number of 20 notes = 4,288,000

3) Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Ghana credits 200,100,50 and 20 notes.

Now,

Since, Ghana credits 200,100,50 and 20 notes.

1) Hence, To credit the amount 3584655000,

Number of 200 notes = 3584655000/200 = 17,923,275

Number of 100 notes =3584655000/100 = 35,846,550

Number of 50 notes =3584655000/50 = 71,693,100

Number of 20 notes = 3584655000/20 = 179,232,750

2) To credit the amount 85760000;

Number of 200 notes = 85760000/200 = 428,800

Number of 100 notes = 85760000/100 = 857,600

Number of 50 notes = 85760000/50 = 1,715,200

Number of 20 notes = 85760000/20 = 4,288,000

3) To credit the amount 146737000;

Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) To credit the amount 5555627000;

Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) To credit the amount 7777000;

Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

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The value of x that satisfies the equation (1 + x) / x = √5 is (1 + √5) / 4.

What is the rational numbers?

A rational number is a number that can be written as a fraction, is a whole number, is a decimal that stop or is a repeating decimal.

Starting with the equation:

(1 + x) / x = √5

We can first multiply both sides by x to eliminate the fraction:

1 + x = x√5

Next, we can isolate the x term on one side of the equation and all the other terms on the other side:

x√5 - x = 1

Factor out the x on the left side:

x(√5 - 1) = 1

Finally, divide both sides by (√5 - 1):

x = 1 / (√5 - 1)

To simplify this expression, we need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is (√5 + 1):

x = (1 / (√5 - 1)) * (√5 + 1) / (√5 + 1)

Simplifying the numerator by distributing:

x = (√5 + 1) / ((√5 - 1) * (√5 + 1))

The denominator simplifies to:

(√5 - 1) * (√5 + 1) = 5 - 1 = 4

Therefore:

x = (√5 + 1) / 4

Hence, the value of x that satisfies the equation (1 + x) / x = √5 is (1 + √5) / 4.

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Answer:

320

Step-by-step explanation:

800 = 10

x = 4

800 x 4 = 10 x

3200= 10x

x = 320

Given: x_i are independent random variables with all of them having the same mean, 3, and same variance 5.

To find: v(x1-x_2-3).

The formula used: If X and Y are independent random variables, then

V(aX + bY) = a²V(X) + b²V(Y)  where a and b are constants.

Now, v(x_1 - x_2 - 3) = v(x_1) + v(-x_2) + 2Cov(x_1, -x_2)......(1)

We know that Cov(x_1, -x_2) = E[x_1 * -x_2] - E[x_1]E[-x_2]

Since x_1 and x_2 are independent,

E[x_1 * x_2] = E[x_1]E[x_2]E[x_1 * -x_2] = E[x_1]E[-x_2] = 3 * 3 = 9... (2)

So, Cov(x_1, -x_2) = 9 - 3*3 = 0... (3)

Now, v(x_1) = v(x_2) = 5...(4)

From (1), (2), (3) and (4), we get:

v(x_1 - x_2 - 3) = v(x_1) + v(-x_2) + 2Cov(x_1, -x_2)

= v(x_1) + v(x_2) = 5 + 5 = 10.

Therefore, the variance of v(x_1 - x_2 - 3) is 10.

Hence, the correct option is (D).

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The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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f(x) = -1/x is not a linear function.

Option (B) is correct,

What is a function?

A function is a mathematical relationship between two sets of quantities, called the domain and the range. In other words, a function is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range). The most common way to represent a function is using an equation of form f(x) = y, where x is the input variable (or independent variable) and y is the output variable (or dependent variable).

A linear function is a function whose graph is a straight line. A linear function can be represented by an equation of the form f(x) = mx + b, where m and b are constants.

Out of the given options, the function which is not linear is B) f(x) = -1/x

This function is not linear because it's graph is not a straight line.

All the other options are linear functions, option A) f(x) = x/4 is a function with a slope of 1/4, option C) f(x) = 2x + 1 is a function with a slope of 2, and option D) f(x) = -3 is a constant function with a slope of 0.

Hence, f(x) = -1/x is not a linear function.

Option (B) is correct.

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