Construct the truth table and determine the truth value of the following compound statement.
a)p⟾¬(p ʌ r)
b) (q ʌ r) ⟾(p ⇔ q)​

Answer:

By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°

Step-by-step explanation:

Opposite angles of two intersecting straight lines are congruent

Therefore ∠DLE = ∠GLH

Here ∠DLE = 2x = ∠GLH

Sum of all angles on a straight line is 180°

Therefore ∠ELG + ∠GLH = 180°

Given that ∠ELG = 124°

124° + ∠GLH = 180°

124° + 2x  = 180°

2x = 180° -  124°

2x = 56°

x = 28°

hence proved that x = 28°

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The probability that s+d > 3 and sd > 3 is 0.03.

Plot the inequalities

The region -5 ≤ s,d ≤ 5 is the square shaded in grey.

The region s + d > 3 is the region Q shaded to the right of the straight line.

The region sd > 3 is the region R shaded to the right of the curve d = 3/s.

Find the intersection of the three regions

From the figure, the region satisfying all the above three inequalities is the region to the left of the curve d = 3/s, bounded by the square region, i.e. the region R.

Probability of region R

The required probability is the Geometric probability of the intersection region R. It is calculated as

P(R) = ar(region R) / ar(square region P).

Calculate the areas of the regions

ar(region R) = area of the rectangle to the right in the first quadrant formed by dropping a vertical from point F - area under the curve d = 3/s in the first quadrant

[tex]\[\Rightarrow \;\; \mathrm{ar(\mathbf{R}) =} \int_{3/5}^5\frac{3}{s}ds = 25-3-3\ln\frac{25}{3} = 15.64.\][/tex]

ar(region P) = 25 × 25 = 625.

Calculate P(R)

The probability of the region R, P(R) = 15.64 / 625 = 0.025.

Rounding it to the hundredth place of decimal, P(R) = 0.03.

The probability that s+d >3 and sd>3, where -5 < s,d < 5, is 0.03.

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Disclaimer: The question was incomplete. Please find the full content below.

What is the probability that s + d > 3 and sd > 3, where -5 ≤ s,d ≤5? Write your answer as a decimal rounded to the hundredth place.

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The length of the base is 40 meters

We have:

Area= 160 square meters

Height = 4 meters

The area is calculated using:

Area = Base * Height

So, we have:

160 = Base * 4

Divide both sides by 4

Base = 40

Hence, the length of the base is 40 meters

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Answer: 180 degrees

Step-by-step explanation:

Angles on a line add to 180 degrees since they form a straight angle.

The statements can be completed by using the following :

1) -2 is multiplied with (5x+8)

2)  transposing of numeral values and variable values

3) The numerical values are taken one side and added to each other

4) 30 is divided by -16

5) The numerator and denominator are cancelled to the lowest possible value

x= -15/8

Given:  -2(5x+8)=14+6x  

and steps for solving them have also been given

In the first step, -2 is multiplied with (5x+8) and we get

-10x -16 = 14 +6x

In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14

In step 3,

The numerical values are taken one side and added to each other and we get -16x=30

In step 4, 30 is divided by -16

In step 5, they are cancelled to the lowest possible value and we get

x= -15/8

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Option A. is correct for the given condition.

Lets solve it through steps of range and functions,

First of all, Solve the equation:
[tex]f(x) = |x|+5[/tex]
[tex]= > x = -5[/tex] (1)

[tex]= > x = 5[/tex] (2)

So these would be the ranges of X in between 5 and -5.

Hence option A. [tex]R{f(x)eR [f(x) < 5}[/tex] is correct.

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Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3)  Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6)  Solve the 2nd equation:  - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18  does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

Answer:

14m

Step-by-step explanation:

Area = πr²

A = 153.86m²

153.86 = 3.14 *r²

r² = 153.86/3.14

r = √49

r = 7

d = 2r

d = 2*7

d = 14

1)  The volume of the quarter sphere shaped tank is; V =  20510 ft³

2) The volume of the smaller mock-up tank is; 230790 ft³

1)  The volume of the quarter sphere shaped tank is;

V = ⁴/₃πr²

V = ⁴/₃π * 70 * 70

V =  20510 ft³

2) We multiply dimensions by 2 not radius to make 1 whole cylinder. Thus

r = 35 feet remains the same as radius can only be half of a joined circle,

Since vertically cut, we have;

h = 125 * 2 = 250ft

Let's find the Area;

A = πr²

A = π * 35 *  35

A = Surface Area = 3846.5 ft²

Volume = Surface area * h

V = 3846.5 * 120 = 461580 combined.

For each; V = 461580/2 = 230790 ft³

3) Volume of smaller mock-up tank is;

V = (1/6) * 20510

V = 3418.33 ft³

4) 5/6 * 20510 = 17091.66 ft³

For the larger tank the increase is 17092 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage is 1/6 = 16.67% and 5/6 = 83.33%

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Answer:

For section A, the average rate of change is 12. For section B, the average rate of change is 300. The average rate of change in Section B is greater than Section A by 25. The rate of change keeps on increasing because the slope of the function is increasing.

Step-by-step explanation:

Concept: For a function f(x), the rate of change is given by [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]. Given function is h(x) = 3(5∧x).

For x = 0 to x = 1, the value of function would be f(0) = 3 to f(1) = 15.

The rate of change would be (15-3) / (1-0) = 12.

For x = 2 to x = 3, the value of function would be f(2) = 75 to f(3) = 375.

The rate of change would be (375-75) / (3-2) = 300.

The average rate of change in Section B is greater than Section A by

300 / 12 = 25.

Looking at the function, that is h(x) = 3(5∧x), we see that this function is an increasing function. The slope of an increasing function keeps on increasing with the value of x. The rate of increase is also a slope. That is why the rate keeps on increasing.

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Answer:

< $0 --------------$35------ $50>

Step-by-step explanation:

I see it's still the same, the maximum discount can be put off is still $50

and you can find that out by discount 30% off 50 to get $35 :)

< $0 --------------$35------ $50>

Answer:

20

Step-by-step explanation:

To calculate f(2), just replace x in the equation of f(x) with 2:

[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]

Answer:

x = 3

Step-by-step explanation:

8/2 = 4

6/2 = 3

x = 3

Answer:

1 HR ---> 42 km

? .----> 119 km

119 * 1/42

2.833

Answer:

[tex]\boxed {2 \frac{5}{6}}[/tex]

Step-by-step explanation:

Formula used :

[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]

Solving :

Time = 119/42

Time = 17/6

Time = 2 5/6 hours

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

To find the gradient of the graph, we use the formula,

[tex]gradient \: (m) = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

From the graph, we obtain values for x and y

x1 = 4, x2 = 8

y1 = 2, y2 = 3

Substitute the values into our formula.

[tex]m \: = \frac{(3 - 2)}{(8 - 4)} \\ = \frac{1}{4} [/tex]

Therefore, the gradient, m, =

[tex] \frac{1}{4} [/tex]

Note:-

Answer:

The given tessellated plane has translational and rotational symmetry. From the given options, we find that option A is correct.

Step-by-step explanation:

Concept: The symmetry has to be decided in such a way that when it applies to a figure, we get exactly the next figure. In the given figure, we have translational and rotational symmetries. We can translate the triangles to the next position and get the same triangle. Or we can rotate the triangle about the point of contact and get the same triangle.

For example, take the top left triangle. If it is translated towards approximately 30° direction, then we will get the triangle present at the top.

Or when we turn that triangle about the point of contact of that and the topmost triangle, then we can get the topmost triangle.

But there is no reflectional symmetry due to the absence of symmetry line.

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The equation is [tex]\boxed{y-2=6(x+9)}[/tex].

Answer:

1764

Step-by-step explanation:

[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]

Hii!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]

1764

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

Stick in the values: 9 for r and 14 for t, and simplify.

[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]

[tex]\bullet[/tex] Square 14 first

[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]

[tex]\bullet[/tex] Multiply the numbers

[tex]\twoheadrightarrow\sf 1764}[/tex]

[tex]\bullet[/tex] Great job! We found the answer

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

[tex]y=200(0.5)^2^t[/tex] is Decay

[tex]y=\frac{1}{2}(2.5)^\frac{t}{6}[/tex] is Growth

[tex]y=(0.65)^\frac{t}{4}[/tex] is Decay

Answer:

2025 $

Step-by-step explanation:

275 multiply 3 +1200

Answer:

A.$2,025

Step-by-step explanation:

$275 x 3 years + $1,200

= $2,025

An equivalent ratio to the tape diagram shown is 1 to 2

From the tape diagram, we have:

Red = 2

Blue = 4

Express as a ratio

Red : Blue = 2 : 4

Divide by 2

Red : Blue = 1 : 2

Hence, an equivalent ratio to the tape diagram shown is 1 to 2

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The equation of the red graph is g(x)=^x+2-3.

Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.

The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.

Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.

Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.

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Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]

Step-by-step explanation:

This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].

The sequence has 7 terms, so the sigma notation is:

[tex]\sum^{7}_{n=1} (-2+9n)[/tex]

Hey there!

10/4

≈ 10 ÷ 2 / 4 ÷ 2

≈ 5/2

≈ 2 1/2

Therefore, your answer should be:

2 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 6 years ago

Step-by-step explanation: Since Chad is 34 years younger than Johann, Chad is currently 26. 60 divided by 3 (since the question says three times) is 20, and 26 (Chad’s current age) minus 20 is 6. So, 6 years is the correct answer.

Answer:

  21 years

Step-by-step explanation:

Let x represent the number of years since Johann was 3 times Chad's age. The given relation can be written as the equation ...

  (60 -x) = 3(34 -x)

__

Solving this, we have ...

  60 -x = 102 -3x . . . . . eliminate parentheses

  2x = 42 . . . . . . . . . add 3x-60

  x = 21 . . . . . . . . .divide by 2

21 years ago, Johann was 3 times as old as Chad.

_____

Additional comments

Their ages then were 39 and 13.

If you recognize the age difference is 60-34 = 26 years, and that J will be 3×C when C's age is half that difference, then you know C was 13 at that time. That was 34-13 = 21 years ago.

Answer:

x>-60

Step-by-step explanation:

Combine multiplied terms into a single fraction

2/5x - 9 < 3/5x + 3

2x/5 - 9 < 3/5x + 3

Find common denominator

2x/5 - 9 < 3/5x + 3

2x/5 + 5(-9)/5 < 3/5x + 3

Combine fractions with the common denominator

2x + 5(-9)/5 < 3/5 + 3

I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)

Answer:

[tex]\boxed {x > -60}[/tex]

Step-by-step explanation:

2/5x - 9 < 3/5x + 3

-1/5x < 12

x > -12 x 5

x > -60

Answer: D

Step-by-step explanation:

[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].

This eliminates A and B.

Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D