You fill a swimming pool with water at a rate of 17 gallons per minute.
a. Is the amount of water in the pool a function
of the number of minutes? Explain.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.

The value of the expression (x != 7) && (x <= y) is: B. true

The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.

Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.

To know more about mathematical expression click below:

https://brainly.com/question/29176690#

#SPJ4

At the point where x = 0, the equation simplifies to 8e^y = 8e, which can be rearranged to e^y = 1. This means that y = 0.

1. Substitute x = 0 into the equation: xy + 8e^y = 8e

2. Simplify the equation: 8e^y = 8e

3. Rearrange the equation to isolate the exponent: e^y = 1

4. Take the natural logarithm of both sides: y = ln(1)

5. Evaluate the natural logarithm: y = 0

At the point where x = 0, the given equation simplifies to 8e^y = 8e. Rearranging this equation to isolate the exponent on the left hand side, we get e^y = 1. Taking the natural logarithm on both sides, we get y = ln(1). Finally, evaluating the natural logarithm of 1, we get y = 0. Therefore, the value of y" at the point where x = 0 is 0.

Learn more about equation here

https://brainly.com/question/11897796

#SPJ4

Answer:

16

Step-by-step explanation:

48 divided by 3 is 16, so each of his friends will get 16 cookies.

Answer:

1200

Step-by-step explanation:

12 multiplied by 2 is 24.

24 divided by 2 is 12.

12 times 100 is 12 plus 2 zeros, or 1200.

Answer:

1/5, 20 diveded by 5 is 4, 20%

Answer:

3/4

Step-by-step explanation:

1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.

The comparison of the expressions is 7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

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

7 + 3^2-2x5÷4-1x2 and (¾+ ⅛) ÷ ⅛ - 2^2

Express the exponents properly

This gives

7 + 3² -2  * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 2²

Evaluate the exponents

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 4

Evaluate the expressions in brackets

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and 7/8 ÷ ⅛ - 4

Solve the products and quotients

7 + 9 - 2.5 - 2 and 7 - 4

So, we have

11.5 and 3

11.5 is greater than 3

So, we have

11.5 > 3

Rewrite as

7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

The maximum load that can be applied to the wire made of that kind of steel is 21195 N. The result is obtained by using the tensile strength equation.

Tensile strength is the maximum load or stress that a material can withstand without fracture when being stretched or pulled per its cross-sectional area.

The statement can be expressed as

σ = F/A

Where

The tensile strength of a certain steel wire is 3000 MN/m². The diameter of the wire is 3.0 mm. Find the maximum load that can be applied to the wire!

Let's count the cross-sectional area!

A = πr²

A = 3,14 (½d)²

A = 3,14 [½(3.0 × 10⁻³)]²

A = 3,14 (1.5 × 10⁻³ m)²

A = 3,14 (2.25 × 10⁻⁶) m²

A = 7.065 × 10⁻⁶ m²

The maximum load is the maximum value of the force acting on it.

σ = F/A

3000 MN/m² = F / 7.065 × 10⁻⁶ m²

3000 × 10⁶ N/m² = F / 7.065 × 10⁻⁶ m²

F = 3 × 10⁹ × 7.065 × 10⁻⁶  N

F = 21.195 × 10³ N

F = 21195 N

Hence, the steel wire can have the maximum load of is 21195 N.

Learn more about tensile strength here:

brainly.com/question/14786237

#SPJ4

Step-by-step explanation:

if the three numbers are x,x+1,x+2

2x+3(x+2)=(x+1)4+14

5x+6=4x+18

×=12

Answer:

14/3

Step-by-step explanation:

Flip the second fraction's numerator and denominator to get its reciprocal of 7/3. Then, you simply multiply it by 2, which equals 14/3.

The probability that the Canadian Rounders have 0 players injured for their next match is 1/4 or 25%.

This implies the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happeing of the event.

The total number of matches = 4+5+2+3+2

The total number of matches = 16

Total, that has zero injured players = 4

The probability will be:

= 4 / 16

= 0.25

The probability is 0.25.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

Complete question

The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.

Number of injured players Number of matches

0 | 4

1 | 5

2 | 2

3 | 3

4 | 2

Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 0 players injured for their next match?

We know that the volume of a rectangular box is given by length times width times height. So, we have:

V = x * (x - 5) * (x + 2) = 180

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

We can use this equation to find the length of the box.

Expanding the equation:

x^3 - 5x^2 + 2x = 180

Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52

So the length of the box is 9.52 inches.

The answer is B. 9.52 in

Learn more about rectangle

brainly.com/question/2607596

#SPJ1

Answer:

2x + 40

Step-by-step explanation:

Given ,

L = x

B = 20cm

To Find: Expression that represents the Perimeter

Perimeter of rectangle = 2(l+b)

                                       = 2(x+20)

                                        = 2x + 40

On solving the provided question, we can say that - the of the function f(x) = 0.5x + 7.8 = 9.8

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here, we are provided with the function -

f(x)= 0.5x + 7.8

and given from question, x = 4

f(x) =  2 + 7.8 = 9.8

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The line ED has a length of 4 units.

Given,

Points E and D in the ΔCAB

equation represent the midpoints of the segments AC and BC, respectively.

AB is 8 units as well.

The length of segment ED needs to be determined.

We are aware that a triangle's third side and the line segment connecting its midpoint are both said to be parallel to the triangle's third side and to be half its length. The mid point theorem is what is known as this.

E and D are the midpoints of AC and BC in the equation CAB, and E's length is equal to half of AB's length is

=> 8/2  

=> 4 units

so the length of the segment ED is 4 units

To learn more about mid point :

https://brainly.com/question/9391115

#SPJ4

The measure of segment ED is 4 units.

4 units

We know that the measure of segment AB is 8 units and that point E is the midpoint of segment AC and point D is the midpoint of segment BC. This means that the measure of segment AC is 8/2, or 4 units. Since point E is the midpoint of segment AC, it is also the midpoint of segment ED, meaning that the measure of segment ED is 4 units.

The measure of segment ED is 4 units.

Learn more about segment here

https://brainly.com/question/13136123

#SPJ4

Answer:

3.75

Step-by-step explanation:

Just divide 1.5 by 0.4

just ask your teacher for extra help if needed

The area of the deck in terms of s is 2s^2 + 7s + 15. The expression can be written in standard form as A = 2s^2 + 7s + 15.

The area of the deck can be expressed in terms of s using the standard form of a rectangular area equation, A = lw, where l is the length and w is the width. The side length of the pool is s and the length of the deck is twice the side length of the pool plus 5, or 2s+5. The width of the deck is 3 units longer than the side length of the pool, or s+3. Substituting these values into the area equation gives us:

A = (2s+5)(s+3)

A = 2s^2 + 7s + 15

Therefore, the area of the deck in terms of s is 2s^2 + 7s + 15.

The expression can be written in standard form as A = 2s^2 + 7s + 15.

Learn more about rectangular area here:

https://brainly.com/question/20693059

#SPJ4

The area of the rectangular deck built around the square pool of side, s in terms of s is 2s² + 11s + 15.

Therefore the answer is 2s² + 11s + 15.

The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool, that is

l = 2s + 5

The width of the deck is 3 units longer than the side length of the pool, that is

b = s + 3

Deck is in rectangular shape, thus the area of the deck in terms of s can be calculates by

A = lb = (2s + 5)×(s + 3)

= 2s² + 6s + 5s + + 15

= 2s² + 11s + 15

To know more on similar area problems

https://brainly.com/question/15531454

#SPJ4

A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).

∠1 ≅ ∠5 (corresponding angle theorem)

∠7 ≅ ∠5 (vertical angle theorem)

∠1 ≅ ∠7 (Transitive property of congruence)

Complete question is at the end of solution.

As per the given data, a transversal line intersects two parallel lines a and b.

The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)

Line a is parallel to line b.

Therefore,

a ║ b

Let's prove ∠1 ≅ ∠7

Hence,

∠1 ≅ ∠5 (corresponding angle theorem)

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.

∠7 ≅ ∠5 (vertical angle theorem)

Vertical angles theorem or vertically opposite angles theorem:

According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.

Vertical angles are the angles formed when two lines intersect each other.

∠1 ≅ ∠7 (Transitive property of congruence)

Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.

For more questions on angles and parallel lines

https://brainly.com/question/27987060

#SPJ4

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4

Step-by-step explanation:

we create 2 equations with 2 variables by using the given point coordinates in both :

A×1 + B×-2 = 7

A - 2B = 7

A×1 - B×-2 = 3

A + 2B = 3

to solve we can simply add both equations to temporarily eliminate B and solve for A :

A - 2B = 7

A + 2B = 3

-------------------

2A 0 = 10

A = 10/2 = 5

now, we use one of the original equations to solve for B :

5 + 2B = 3

2B = -2

B = -2/2 = -1

Answer:

5-30

Step-by-step explanation:

expectation of single

The solution to the system of equations is (3,1).

2x - 3y = 6

3x + 2y = 7

(3,1)

Multiply the first equation by 3:

6x - 9y = 18

Add the two equations:

9x - 7y = 25

Divide both sides by 9:

x - y = 25/9

Substitute 25/9 for x in the second equation:

3(25/9) + 2y = 7

Simplify:

25 + 18y = 63

Subtract 25 from both sides:

18y = 38

Divide both sides by 18:

y = 38/18

Substitute 38/18 for y in the equation x - y = 25/9:

x - (38/18) = 25/9

Simplify:

x = (25/9) + (38/18)

Simplify:

x = 63/9

Therefore, the solution is (63/9, 38/18) or (3,1).

The solution to the system of equations is (3,1).

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

-090

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

6/3 = 2

According to the question quadrilateral pqrs, the russell jamie both neither is neither.

The Quadrilateral pqrs is located at p (−4, 1), q (−2, 3), r (1, 1), and s (−2, −2).

Russell:

PQRS is a parallelogram because both pairs of opposite sides are parallel

Segment pq is p (−4, 1), q (−2, 3).

Slope=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]& m=\frac{3-1}{-2+4}=\frac{2}{2}=1[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& m=\frac{1+2}{1+2}=\frac{3}{3}=1[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& m=\frac{-2-1}{-2+4}=\frac{-3}{2}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]m=\frac{1-3}{1+2}=\frac{-2}{3}[/tex]

Segments pq and sr are parallel, and segments ps and qr are parallel.

Jamie:

pqrs is a parallelogram because both pairs of opposite sides are congruent

Distance between two points is the length of the line segment that connects the two points in a plane

Segment pq  is p (−4, 1), q (−2, 3).

[tex]& d=\sqrt{(-2+4)^2+(3-1)^2}=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& d=\sqrt{(1+2)^2+(1+2)^2}=\sqrt{9+9}=\sqrt{18}=3 \sqrt{2}[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& d=\sqrt{(-2+4)^2+(-2-1)^2}=\sqrt{4+9}=\sqrt{13}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]d=\sqrt{(1+2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}[/tex]

Segments pq and sr are congruent, and segments ps and qr are congruent.

Therefore, the correct option is neither.

For more such questions on Quadrilateral.

https://brainly.com/question/13805601

#SPJ4

Both Russell and Jamie are correct. PQRS is a parallelogram with slope because both pairs of opposite sides are parallel, and it is also a parallelogram because both pairs of opposite sides are congruent.

Russell is correct because he used the slope of the lines to prove that both pairs of opposite sides are parallel. He calculated the slope of the lines using the equation m = (y2 - y1)/(x2 - x1) and found that the slopes of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are parallel.

Jamie is also correct because he used the distance formula to prove that both pairs of opposite sides are congruent. He calculated the distance between the points using the equation d = √((x2 - x1)^2 + (y2 - y1)^2) and found that the distances of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are congruent.

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4

To find 1/3 of a line segment, divide the line segment into three equal parts. Measure the length of one of these parts and this will be 1/3 of the line segment.

This can be done by using a ruler or a measuring tape. Alternatively, if the length of the line segment is known, divide it by 3 to find 1/3 of the line segment. For example, if the line segment has a length of 12 inches, then the length of 1/3 of the line segment is 4 inches. If the line segment is curved, you can divide it into three equal arc lengths using a compass.

You can then measure the length of one of these arcs to find 1/3 of the line segment. To make sure that the three parts are equal, you can use the Pythagorean theorem or the triangle inequality theorem. This will help you to accurately divide the line segment into three equal parts.

To know more about line segment refer to the  link  brainly.com/question/30072605

#SPJ4

Number of green chairs in the inventory is 208.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total number of chairs in the inventory = 520

Fraction of chairs that are green = 2/5 of 520

2 parts out of 5 parts are green.

Number of green chairs = 2/5 × 520

                                        = 1040 / 5

                                        = 208

Hence there are 208 green chairs in the inventory.

To learn more about Fractions, click on the link given below :

https://brainly.com/question/1301963

#SPJ1

An image is always formed at the back of a mirror. Thus, the flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = opposite / adjacent

         = 1.65 / 1.7

Tan θ = 0.9706

θ =  Tan⁻¹(0.9706)

 = 44.2°

θ = 44.2°

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = opposite / adjacent

        = h / 8.75

0.9706 = h / 8.75

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m tall.

Learn more about image of object at:

https://brainly.com/question/11776784

#SPJ1

Answer:1/4

Step-by-step explanation:3/8-1/8=1/4

The equivalent expression when we apply distributive property is -10w -20

You should understand that distributive property states that every term inside a grouping symbol multiplied by every term outside the grouping symbol yields the same result.

To this effect, the formula to do this is x(y+z) = xy+xz

The given expression is

5×(−2w−4)

= 5*-2w- 5*4

= -10w -20

In the expression every term outside the symbol is multiplied by every term inside the symbol to give the result of the expression

Learn more about distributive property on https://brainly.com/question/5637942

#SPJ1