If x = 4, y = 2, and z = 10, evaluate the following expression: yz(x + y) – x? Enter​

Answer:

x=6

Step-by-step explanation:

2x-4y=8

    +4   +4

2x=12

---   ---

2x   2x

x=6

The range, given the cost of surfboard rentals, would be $ 140.

The interquartile range of the cost of surfboard rentals is $ 56.

There is an outlier which is the cost of 6 days of rentals which is $ 168.

To find the range, the formula is :

= Largest cost - Lowest cost

To find these costs, find the cost of the days of rentals :

1 day :                                  2 days                            3 days :

= 28 x 1                                = 28 x 2                         = 28 x 3

= $ 28                                   = $ 56                          = $ 84

6 days :

= 28 x 6

= $ 168

The range is therefore :

= 168 - 28

= $ 140

To find the Interquartile range, first find the First Quartile and the Third Quartile after ordering the costs:

Order of costs :

28, 28, 28, 56, 56, 56, 84, 84, 84, 168

First quartile position :

= 1 / 4 x ( n + 1 )

= 1 / 4 x ( 10 + 1 )

= 3 rd position which is $ 28

Third quartile position :

= 3 / 4 x ( n + 1 )

= 3 / 4 x ( 10 + 1 )

= 8 th position which is $ 84

The Interquartile range is :

= 84 - 28

= $ 56

The outlier is the cost of 6 days which is $ 168. This is a rental as it is much larger than other costs.

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Answer:

80 yards2

Step-by-step explanation:

Area = l × w

= 16 × 5

= 80 yards2

The statement is true for all real numbers x and y, and the true set VXEY is the set of all real numbers.

The truth value of the statement "∀x∃y (Y ∧ 2x² + y ≤6)" is determined by the domain of x and y.

Assuming that x and y are real numbers:

The truth value of the statement is where the inequality 2x² + y ≤ 6 is true for all x and some y.

Rewriting the inequality in y as y ≤ 6 - 2x²

For any given value of x, y = 6 - 2x².

This satisfies the inequality, since:

2x² + y = 2x² + (6 - 2x²) = 6 ≤ 6

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answer/explanation:

hope this helps

Answer:66.871

Step-by-step explanation:

The mean=67

The population standard deviation=9.9

Let the minimum score representing grade D above the bottom 10% is x1.

so

P(x<x1)=0.10

P(Z<z)=0.10

z~=-1.48

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

\(\sf\longrightarrow sin^2\theta + cos^2\theta = 1 \)

Imagine a right angled triangle with one of its acute angle as \(\theta\) .

\(\sf\longrightarrow sin\theta =\dfrac{p}{h} \\\)

\(\sf\longrightarrow cos\theta =\dfrac{b}{h} \)

And by Pythagoras theorem ,

\(\sf\longrightarrow h^2 = p^2+b^2 \dots (i) \)

Where the symbols have their usual meaning.

Now , taking LHS ,

\(\sf\longrightarrow sin^2\theta +cos^2\theta \)

\(\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\\)

\(\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\ \)

\(\sf\longrightarrow \dfrac{p^2+b^2}{h^2} \)

\(\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\ \)

\(\sf\longrightarrow \bf 1 = RHS \)

Since LHS = RHS ,

Hence Proved !

I hope this helps.

Answer:

First way:

1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Second way:

4/10 + 3/10

Answer:

  g(x) = 3 + tan(πx/4)

Step-by-step explanation:

A tangent function has a period of π. In order to make it have a period of 4, it needs to be stretched horizontally by a factor of 4/π. A function is stretched horizontally by a factor of k by replacing x with x/k.

In order for the function to be shifted vertically up by 3 units, 3 must be added to the function value. That is, the transformed function becomes ...

  g(x) = tan(x/(4/π)) +3

  g(x) = tan(πx/4) +3

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer:

y= -1/2x+1

Step-by-step explanation:

Answer:

10000000 - 6872536 = 3127474

Hence 68,72,536 is 31,27,474 less than 1,00,00,000.

Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

The area remaining in shaded region is  14.25 cm².

Half of such a circle is a semicircle. It is a 2D reconstructed by dividing a circle into two equal portions.

For, the given question;

The formula for the area of the triangle area is given:

A = 1/2bh

b is the base and h is the height.

Here base is diameter; b = 10 cm and height is radius; h = 5 cm.

Put the values;

Triangle's area = (1/2)(10 cm)(5 cm)

                         = (5 cm)²

                         = 25 cm².

The semicircle is found as half the area of a circle given with radius 5 cm.

Semicircle's area = (1/2)π(5 cm)²

                             = 12.5π cm²

                             ≈ 39.25 cm²

The shaded region is given as the difference between area of triangle and semicircle:

Shaded area = 39.25 cm² - 25 cm²

Shaded area = 14.25 cm²

Thus, the area of the shaded region is found as 14.25 cm².

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The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

(c) 65

Step-by-step explanation:

(f ⁰ g)(x) = 3(x² + 4) + 5

(f ⁰ g)(4) = 3(4² + 4) + 5 = 3*20 + 5 = 65

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

x=2 y=12

Step-by-step explanation:

Answer:

the monthly payment is $18,750

Step-by-step explanation:

The computation of the monthly payment is shown below:

= (Loan amount × given percentage) ÷ number of months in a year

= ($300,000 × 75%) ÷ 12 months

= $18,750

Hence, the monthly payment is $18,750

Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.

Answer:

Domain is all real numbers.

Step-by-step explanation:

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

Q1

\(by \ pythagoras \ theorem : \\(3x +1 )^2 = (3x - 1)^2 +x^2\\\\9x^2 + 6x +1 = 9x^2 + 1 -6x +x^2\\\\9x^2 + 6x +1 = 10x^2 + 1 -6x \\\\ 10x^2 + 1 -6x - 9x^2 -6x -1 = 0 \\\\x^2 -12x = 0\\x(x - 12) = 0\\x = 0, 12\\since \ length \ cannot \be \ 0, x = 12\\OJ = 3x + 1 = 3(12) +1 = 37\)

Q2

\(by \ pythagoras \ thm, \\(7x -12) ^2 = (5x +10)^2 +(2x)^2\\\\49x^ 2 +144 - 168x = 25x^2 +100+ 100x +2x^2\\\\49x^ 2 +144 - 168x - 25x^2 -100- 100x -2x^2 = 0\\\\22x^2 -268x -44 = 0\\11x^2 - 134x - 22 = 0\\x=12.0154\)

This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.

Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.

Here,

When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.

According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.

Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.

In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.

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Answer

The answer = 5,184,000,000

There are 5,184,000,000 possible phone numbers.

Explanation

The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.

- N can only be numbers: 2-9;

- Y can only be numbers 0-7

- and A&C cannot be 2

We are then told to calculate the number of phone numbers possible.

This question is a special type of permutation and combination.

To solve it, it will be a multiplication of the possible numbers that can take up each position.

N, can only be numbers 2 to 9. Number of possible digits = 8

Y, can only be numbers 0 to 7. Number of possible digits = 8

Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10

A, number cannot be 2. Number of possible digits = 9

B, no restriction, can have numbers 0 to 9. Number of possible digits = 10

C, number cannot be 2. Number of possible digits = 9

X, no restriction, can have numbers 0 to 9. Number of possible digits = 10

X, no restriction, can have numbers 0 to 9. Number of possible digits = 10

X, no restriction, can have numbers 0 to 9. Number of possible digits = 10

X, no restriction, can have numbers 0 to 9. Number of possible digits = 10

Total number of possible phone numbers

= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10

= 5,184,000,000

Hope this Helps!!!

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:

nth term =

-3 + (n - 1) * 5, if n mod 5 ≤ 5

5 + (n - 1) * 15, if n mod 5 > 5

To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:

The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.

Based on this pattern, we can divide the sequence into two parts:

Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)

Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)

Now, to determine the nth term, we can consider the formula for arithmetic sequences:

nth term = first term + (n - 1) * common difference

For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:

nth term = -3 + (n - 1) * 5

For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:

nth term = 5 + (n - 1) * 15

However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:

If n mod 5 is less than or equal to 5, then the nth term is from Part 1.

If n mod 5 is greater than 5, then the nth term is from Part 2.

Let's calculate a few terms to illustrate this:

For n = 1, the sequence starts with -3, so the 1st term is -3.

For n = 2, we are still in Part 1, so the 2nd term is 0.

For n = 3, Part 1 continues, so the 3rd term is 5.

For n = 4, we are still in Part 1, so the 4th term is 10.

For n = 5, Part 1 ends, and the 5th term is 25.

For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.

For n = 7, Part 2 continues, so the 7th term is 20.

For n = 8, we are still in Part 2, so the 8th term is 35.

Based on this analysis, we can conclude that the nth term for the given sequence is:

If n mod 5 ≤ 5:

nth term = -3 + (n - 1) * 5

If n mod 5 > 5:

nth term = 5 + (n - 1) * 15

Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.

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