find the domain and range of the function represented by the graph.

Answer: {x|4<x<10}

Step-by-step explanation:

Answer:

\( \rm \implies \frac{1}{3} (5x - 8) + \frac{2}{3} x \\ \\ \rm \implies \frac{5}{3} x - \frac{8}{3} + \frac{2}{3} x \\ \\ \rm \implies \frac{5x + 2x}{3} - \frac{8}{3} \\ \\ \rm \implies \frac{7x}{3} - \frac{8}{3} \\ \\ \rm \implies 2 \frac{1}{3} x - 2 \frac{2}{3} \)

Answer:

area = 14.28 cm²

Step-by-step explanation:

area of semi circle = 1/2(3.14)(2²) = 6.28 cm²

area of triangle = 1/2(4)(4) = 8 cm²

6.28 + 8 = 14.28 cm²

9 in 8956 = 900

9 in 95675 = 90000

9 = 9 in 124569

9 in 68795 = 90

90000 = 9 in 2549652.........

hope it helps...

Theorem 2.1.1 states that "If p, q, and r are logical expressions, then p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r). To verify the equivalence ∼(p ∨ ∼q) ∨ (∼p ∧ ∼q) ≡ ∼p, we will break it down into smaller parts and use Theorem 2.1.1 to rearrange them. First, note that ∼(p ∨ ∼q) ≡ (∼p ∧ q).

Then we can rewrite the left-hand side as (∼p ∧ q) ∨ (∼p ∧ ∼q). Applying Theorem 2.1.1 to the right-hand side yields ∼p ∨ (q ∧ ∼q). Since q ∧ ∼q is always false, the right-hand side simplifies to just ∼p.

Therefore, we have shown that ∼(p ∨ ∼q) ∨ (∼p ∧ ∼q) ≡ ∼p.

Step 1: Use the distributive property to rewrite p ∧ (q ∨ r) as (p ∧ q) ∨ (p ∧ r):(p ∧ q) ∨ (p ∧ r) ≡ (p ∧ q) ∨ (p ∧ r)

                 Reason: Distributive property

Step 2: The left-hand side and right-hand side are the same, so the statement is logically equivalent. p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

               Reason: Theorem 2.1.151. p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Step 1: Use the distributive property to rewrite p ∨ (q ∧ r) as (p ∨ q) ∧ (p ∨ r):(p ∨ q) ∧ (p ∨ r) ≡ (p ∨ q) ∧ (p ∨ r)

               Reason: Distributive property

Step 2: The left-hand side and right-hand side are the same, so the statement is logically equivalent. p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

               Reason: Theorem 2.1.152. ¬(p ∨ q) ≡ ¬p ∧ ¬q

Step 1: Use De Morgan's laws to rewrite ¬(p ∨ q) as ¬p ∧ ¬q:¬p ∧ ¬q ≡ ¬p ∧ ¬q

              Reason: De Morgan's laws

Step 2: The left-hand side and right-hand side are the same, so the statement is logically equivalent.¬(p ∨ q) ≡ ¬p ∧ ¬q

              Reason: Theorem 2.1.153. ¬(p ∧ q) ≡ ¬p ∨ ¬q

Step 1: Use De Morgan's laws to rewrite ¬(p ∧ q) as ¬p ∨ ¬q:¬p ∨ ¬q ≡ ¬p ∨ ¬q

              Reason: De Morgan's laws

Step 2: The left-hand side and right-hand side are the same, so the statement is logically equivalent.¬(p ∧ q) ≡ ¬p ∨ ¬q

             Reason: Theorem 2.1.154. (p → q) ≡ (¬p ∨ q)

Step 1: Use the definition of implication to rewrite (p → q) as ¬p ∨ q:¬p ∨ q ≡ ¬p ∨ q

       Reason: Definition of implication

Step 2: The left-hand side and right-hand side are the same, so the statement is logically equivalent.(p → q) ≡ (¬p ∨ q)

        Reason: Theorem 2.1.1

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The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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Let the adding value be x

ATQ

\(\\ \sf\longmapsto \dfrac{2+x}{5+x}=\dfrac{5}{6}\)

\(\\ \sf\longmapsto 6(2+x)=5(5+x)\)

\(\\ \sf\longmapsto 12+6x=25+5x\)

\(\\ \sf\longmapsto 6x-5x=25-12\)

\(\\ \sf\longmapsto x=13\)

===================================================

Work Shown:

A = area of smaller rectangle

A = length*width

A = 35*22

A = 770

B = area of larger rectangle

B = length*width

B = 45*30

B = 1350

C = area of the border only

C = B - A

C = 1350-770

C = 580 square cm

Step-by-step explanation:

Dimension of photograph is 35cm and 22cm.

And external dimension of photo frame is 45cm and 30cm

So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.

So, The area of the border surrounding the photograph=45×30−35×22

=1350−770=580cm

2

Answer:

No (1,8) is not a solution to 19x+3y=2.

However, (1,8) is a solution to 3x+y=11.

Step-by-step explanation:

(1,8)

The one represents the x shown in each equation, the eight represents the y.

Substitute the one in for the x and the eight in for the y.

19x+3y=2

19(1)+3(8)

3x+y=11

3(1)+(8)

Next, solve the equation.

19(1)+3(8) = 43

3(1)+(8) = 11

As you can see, 43 does not equal 2.

But, 11 does equal 11.

Answer:

46

Step-by-step explanation:

I found the angle by taking the opposite side of the angle, 38, and dividing it by the hypotenuse, 53.

Then I used the inverse sine function on 38/53 to get the angle 45.81, which I rounded to 46.

Answer:

put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges

Step-by-step explanation:

C) The evidence does not suggest that consumers have a preference among the cookie brands.

Based on the given information, the researcher conducted a chi-square test to determine consumer preferences for four different cookie brands. The researcher set the significance level (alpha) to 0.05, which means that there is a 5% chance of observing the obtained chi-square value (7.50) due to random chance alone.

By comparing this chi-square value with the critical chi-square value for the given degrees of freedom and alpha level, the researcher can determine the correct conclusion. If the obtained chi-square value is less than the critical value, it indicates that the evidence does not suggest a preference among the cookie brands.

In this case, the obtained chi-square value (7.50) does not exceed the critical value, leading to the conclusion that consumers do not have a significant preference for the different cookie brands.

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Answer:

6) 1 over 12

7) 10 over 12

8)9 over 12

6.

\(\tt \dfrac{1}{6}\times \dfrac{2}{2}=\dfrac{2}{12}\)

7.

\(\tt \dfrac{5}{6}\times \dfrac{2}{2}=\dfrac{10}{12}\)

8.

\(\tt \dfrac{3}{4}\times \dfrac{3}{3}=\dfrac{9}{12}\)

If 5/8 of the pupils are boys if there are 15 girls in that class then the number of boys are 25.

A fraction represents a part of a whole.

If 5/8 are boys then

1 - 5/8 = girls

3/8 = girls

3/8 of the total are girls

Let x = total

3/8 ( x) = 15

8/3 * 3/8 * x = 15 * 8/3

x = 40

There are 40 total students

5/8 are boys

5/8 × 40

25 are boys

Hence, if 5/8 of the pupils are boys if there are 15 girls in that class then the number of boys are 25.

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The utilization rate is 83.33

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times,

Then, the utilization rate is 83.33.

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now, we're assuming a 90° clockwise rotation.  Check the picture below.

Answer:

Your answer is 8.

Answer:

Step-by-step explanation:

-24

The probability of picking three black cards in a row, without replacement, from a standard deck of 52 playing cards is 2/17, or approximately 0.1176 (rounded to four decimal places).

The probability of picking a black card on the first draw = 26/52 = 1/2

        (since there are 26 black cards in the deck)

The probability of picking a black card on the second draw, given that a one was picked on the first draw and the card is not replaced = 25/51,    

        (since there are now only 25 black cards left out)

The probability of picking a black card on the third draw, given that the ones picked on the first two draws are not replaced = 24/50 = 12/25,

        (since there are now only 24 black cards left out)

To pick three black cards in a row, we need to multiply the probabilities of each individual draw = (1/2) * (25/51) * (12/25) = 6/51

Simplifying this fraction, we get = 6/51 = 2/17

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Answer:5

Step-by-step explanation:

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

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Answer:

5 feet.

Step-by-step explanation:

The angle of the height and length go down to 5 feet diagonally.

Answer:

25ft

Step-by-step explanation:

To find the length of the top of the flagpole to the end of the shadow, you have to use the Pythagorean theorem a² + b² =c²

15² + 20² = x²

225 + 400 = x²

625 = x²

√625 = √x²

x = 25

Answer:

A positive slope

Step-by-step explanation:

If sales are increasing then the income should increaseing and positive.

Since their were no numbers to the questions i had to write it by the problem

Circle with 9 feet question

C=2(pi)r or C=(pi)d

Circular table question

A=(pi)r^2

Interest question

I=Prt

Volume of a rectangular prism

V=Bh

Triangular pyramid

V=1/3Bh

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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The required graph has been attached below that represents the function y = 2 cos (x + π/4).

The cosine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees. The graph of the cosine function is a wave-like curve that oscillates between -1 and 1, with a period of 2π radians or 360 degrees.

To plot the graph of the function y = 2 cos (x + π/4), we can follow these steps:

The coefficient of the cosine term is 2, so the amplitude is 2.

The coefficient of the angle x is 1, so the period is 2π.

The constant term is π/4, so the phase shift is -π/4.

The y-intercept occurs when x = 0, which gives y = 2 cos (π/4) = √2.

Using the amplitude, period, phase shift, and intercepts, sketch the graph of the function over one period. Then, repeat the graph every 2π to get the complete graph.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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