What is the domain and range help plz

Answer:

The circumference of the garden is 62.84 ft

Step-by-step explanation:

Given;

diameter of the fountain, d = 5 feet

radius of the fountain, r = d / 2 = 2.5 feet

distance between the outer edge of the fountain and the garden = 7.5 feet

The radius of the garden = radius of the fountain + outer edge distance

The radius of the garden = 2.5 feet + 7.5 feet = 10 feet

The circumference of the garden = 2πr

The circumference of the garden = 2 x π x 10

The circumference of the garden = 62.84 ft

Therefore, the circumference of the garden is 62.84 ft

True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

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Answer:

  see the attached graph

Step-by-step explanation:

You want to graph these inequalities and identify their solution space.

The boundary line associated with the solution of an inequality is found by replacing the inequality symbol with an equal sign. Here, that means the boundary lines are given by the equations ...

These lines can be plotted by finding their x- and y-intercepts, then drawing the line through those points. In each case, the intercept is found by setting the other variable to zero and solving the resulting equation.

x-intercept of x+y=8:  x = 8, or point (8, 0)

y-intercept of x+y=8:  y = 8, or point (0, 8)

The inequality symbol for this inequality is "less than or equal to", so the boundary line is included in the solution set. That means the line is drawn as a solid (not dashed) line.

When we look at one of the variables with a positive coefficient, we see ...

  x ≤ ... — shading is to the left of the boundary line

or

  y ≤ ... — shading is below the boundary line

The solution space for this inequality is shown in blue in the attached graph.

The x- and y-intercepts are found the same way as above. They are ...

  x-intercept:  x = 2, or point (2, 0)

  y-intercept:  y = -2, or point (0, -2)

The boundary line is solid, and shading is to its left:

  x ≤ ...

The solution space for this inequality is shown in red in the attached graph.

The solutions of the set of inequalities are all the points on the graph where the shaded areas overlap. This is the left quadrant defined by the X where the lines cross.

__

Additional comment

To summarize the "step-by-step", you want to ...

In this process, you make use of your knowledge of plotting points and lines. You also make use of your understanding of "greater than" or "less than" relationships in the x- and y-directions on a graph.

Answer: As given, relationship between the number of hours a plumber works and the total work fee she charges is proportional.

The meaning of proportional is Ratio of number of hours a plumber works and the total work fee she charges is constant.

Using Unitary method

5 hours of work = $350

1 hours of work = $70

Let number of hours worked = x hours

Amount earned for x hours of work is represented by = $ y

For , x hours of work amount earned = 70 x (x=1,2,3...)

→y= 70 x

→→

Step-by-step explanation:

By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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Answer:

59˚

Step-by-step explanation:

The sum of all the angles in a triangle is always 180 so:

38 + 83 + x = 180

121 + x = 180

x = 59

The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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Answer:

A) 5.84

B) 3 significant figure

C)5.8

D)0.0056

2.A) 31 , 35

The simplified expression is, \(10*2125x^{3}\) so the option d is correct.

When a person is experiencing "joy," for instance, the user wants them to feel shocked or very happy. Your user will be favourably impression if they convey surprise or extreme joy. When someone is experiencing "fright," managers want them to feel extremely saddened or disgusted.

There are three primary categories of algebraic expressions, including: Numeral Expression. Binary Expression. Expression of a polynomial. Mathematical operator like adding, subtraction, multiplication, or division are used to create expressions in writing.

We can simplify \(8*2375x + 2\sqrt{3x} 7\) by factoring out the greatest common factor (GCF) of the two terms, which is \(2\sqrt{3x}\)

\(8x2375x + 2√3x7 = 2\sqrt{3x} (4x2375x + 7)\)

Now, we can simplify the expression inside the parentheses by dividing both terms by 4x:

\(4*2375x + 7 = 2*2125x + 7\)

Therefore, the simplified expression is:

\(8*2375x + 2\sqrt{3} *7 = 2\sqrt{3x} (2*2125x + 7)\)

\(10*2125x^{3}\)

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The ordered pair given in the bottom row can be written using function notation as f(9)=5 thus, option (A) is correct.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given,

At x = 9 , f(x) = 5 or f(9) = 5

Hence "The ordered pair given in the bottom row can be written using function notation as f(9)=5".

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The z-scores that bound the middle 66% of the area under the standard normal curve are -0.43 and 0.43.

To find the z-scores that bound the middle 66% of the area under the standard normal curve using the TI-84 Plus calculator, you can follow these steps:

1. Turn on the calculator and press the "2nd" button, followed by "Vars" to access the DISTR menu.

2. Scroll down to "2: normalcdf(" and press enter.

3. Enter the lower bound of the middle 66% (left tail) as 0.17 (since 50% - 33% = 17%) and press comma ",".

4. Enter the upper bound of the middle 66% (right tail) as 0.83 (since 50% + 33% = 83%) and press comma ",".

5. Enter 0 for the mean and 1 for the standard deviation (since we are working with the standard normal distribution) and press enter.

The calculator will calculate the area under the standard normal curve between the given z-scores.

The z-scores that bound the middle 66% of the area under the standard normal curve are approximately -0.43 and 0.43 (rounded to two decimal places).

Therefore,To find the z-scores that bound the middle 66% of the area under the standard normal curve using the TI-84 Plus calculator, you can follow these steps:

1. Turn on the calculator and press the "2nd" button, followed by "Vars" to access the DISTR menu.

2. Scroll down to "2: normalcdf(" and press enter.

3. Enter the lower bound of the middle 66% (left tail) as 0.17 (since 50% - 33% = 17%) and press comma ",".

4. Enter the upper bound of the middle 66% (right tail) as 0.83 (since 50% + 33% = 83%) and press comma ",".

5. Enter 0 for the mean and 1 for the standard deviation (since we are working with the standard normal distribution) and press enter.

The calculator will calculate the area under the standard normal curve between the given z-scores.

The z-scores that bound the middle 66% of the area under the standard normal curve are approximately -0.43 and 0.43 (rounded to two decimal places).

Therefore, the z-scores that bound the middle 66% of the area under the standard normal curve are -0.43 and 0.43.

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t=46°

u=134°

v=23°

w=23°

Answer:

Solution given;

v=w [base angle of triangle]

<SPQ+<SRQ=180°[sum of opposite angle of a cyclic quadrilateral is 180°]

81+v+53+w=180°

134°+v+v=180°

2v=180°-134°

v=46/2

v=23°

w=v=23°

In triangle ∆ PQR

v+w+u=180°[sum of interior angle of a triangle]

23+23+u=180°

u=180°-46°

u=134°

again

In triangle ∆ PSR

t+81+53=180°

t=180°-134°

t=46°

Answer:

t and u are supplementary as opposite angles of a cyclic quadrilateral.

v and w are equal as opposite angles to equal sides.

Answer:

105

Step-by-step explanation:

0 (104) is equal to 0, so let's cross that out. 103 times 102 is definitely not equal to 105. The third one is 105. The fourth one is not 105. The last one is not 105 either.

The sewing kits bought by Ms, Clark is 17 in number.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.

Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17

Thus, the sewing kits bought by Ms, Clark is 17 in number.

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We are given the following equation:

To solve for "k" we will divide both sides by -4:

Solving the operations:

\(6 + 36x + 72x^2 + 96x^3\) / 3! + ... this is the Maclaurin series for f(x). Note that since e^x has a well-known Maclaurin series, we were able to simplify the original expression before finding the series.

The problem asks us to find the Maclaurin series for the function:

\(f(x) = 6e^x e^4x\) sigma^infinity_n=0 (1^n / n!)

To do this, we first need to recognize that the expression inside the sigma notation is actually the Maclaurin series for e^x:

sigma^infinity_n=0 (1^n / n!) = e^x

We can substitute this expression into the original function to get:

\(f(x) = 6e^x e^4x e^x\)

Now we can simplify this expression using the laws of exponents:

\(f(x) = 6e^x * e^(4x) * e^x\)

f(x) = 6e^(6x)

Now we need to express this function as a Maclaurin series. We can start by writing out the first few terms of the series:

\(f(x) = 6e^(6x)\)

\(= 6(1 + 6x + (6x)^2 / 2! + (6x)^3 / 3! + ...)\)

\(= 6 + 36x + 72x^2 + 96x^3 / 3! + ...\)

This is the Maclaurin series for f(x). Note that since e^x has a well-known Maclaurin series, we were able to simplify the original expression before finding the series.

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The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.

Let r be the radius of the circle. The circumference of the circle will be given as,

C = 2πr units

The diameter of the circle is 28 cm. Then the radius is calculated as,

r = d / 2

r = 28 / 2

r = 14 cm

Then the circumference of the circle is given as,

C = 2 · π · 14

C = 28 × 3.14

C = 87.92 cm

The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

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The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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Answer:

The coordinates of the vertex are (7,-3)

Step-by-step explanation:

To find the coordinate of vertex, since it is at the intersection of the graphs, we shall need to solve both equations simultaneously;

That would be;

2x + 3y = 5

3x + y = 18

From the second equation;

y = 18-3x

We can easily substitute this into the first equation;

We have;

2x + 3(18-3x) = 5

2x + 54 -9x = 5

2x-9x = 5-54

-7x = -49

x = -49/-7

x = 7

Kindly recall;

y = 18-3x = 18-3(7) = 18-21 = -3

So the coordinates of the vertex are (7,-3)

To find p(b/), we need to use the formula for conditional probability:

p(b/a) = p(a and b) / p(a)

We already know that p(a and b) = 0.2, but we need to find p(a) first.

p(a) = p(a and b) + p(a and b/) = 0.2 + p(a0)*p(b0/) = 0.2 + 0.4*0.5 = 0.4

Now we can substitute these values into the formula:

p(b/a) = 0.2 / 0.4 = 0.5

This means that the probability of b occurring given that a has occurred is 0.5. To find the probability of b occurring without any knowledge of a, we use the law of total probability:

p(b) = p(a)*p(b/a) + p(a/)*p(b/a/) = 0.4*0.5 + 0.6*p(b0/) = 0.2 + 0.6*p(b0/)

We don't know p(b0/), but we can use the fact that probabilities must add up to 1:

p(b) = 0.2 + 0.6*(1-p(b))

Solving for p(b), we get:

p(b) = 0.5

So the probability of b occurring is 0.5, whether or not we know whether a has occurred.

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Step-by-step explanation:

Tan = opposite / adjacent

use pythagorean theorem to find CD first.

A² = B² + C²

9² = (SqRt (66) )² + C²

81 - 66 = C²

C = SqRt (15)

now find tan

SqRt (66) / SqRt (15 = tan

tan = 2.0976

tan^¹(2.0976) = 64.51 degrees

and if the length of the shadow is 15, we get

The simplified exponential notation of the given expression is x⁸.

Given that, simplified exponential notation, x³·x⁵,

x³·x⁵ we need to simplify it,

We know that,

mᵃ × mᵇ = mᵃ⁺ᵇ

x³·x⁵ = x³⁺⁵

x³·x⁵ = x⁸

Hence, the simplified exponential notation of the given expression is x⁸.

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Answer:

5x

Step-by-step explanation:

=> 6x-x

Taking x common

=> x(6-1)

=> x(5)

=> 5x

The area of triangle TUV with vertices T(-8,2), U(-2,8), and V(-9,9) are 13.4 units.

A triangle is a closed two-dimensional plane figure that has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles. Some common types of triangles include equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are a fundamental concept in geometry and are used in many areas of mathematics and science.

Here,

To find the area of triangle TUV, we can use the formula:

Area = 1/2 * base * height

We can choose any two sides of the triangle as the base and the corresponding height. Let's choose TU as the base and the perpendicular distance from V to TU as the height.

First, let's find the length of TU:

TU = √[(8 - 2)² + (-2 - (-8))²]

= √[6² + 6²]

= 6√(2)

Next, let's find the slope of TU:

mTU = (8 - 2) / (-2 - (-8))

= -3/2

The line perpendicular to TU passing through V has a slope equal to the negative reciprocal of mTU:

mVQ = 2/3

The equation of the line passing through V and perpendicular to TU is:

y - 9 = (2/3)(x + 9)

Solving for x and y at the point where this line intersects TU, we get:

y = (2/3)x + 19

(2/3)x + 19 = -3x/2 + 7

x = -8/7

y = 94/21

The perpendicular distance from V to TU is the absolute value of y - 8:

|94/21 - 8| = 2/21

So, the area of triangle TUV is:

Area = 1/2 * TU * (2/21)

= (1/21)√(2)

To find the area of rectangle QRS, we need to find the length and width. We can use the distance formula to find the length QR and the width QS:

QR = √[(9 - (-8))² + (9 - 2)²]

= √[289]

= 17

QS = √[(9 - (-9))² + (2 - 2)²]

= √[324]

= 18

So, the area of rectangle QRS is:

Area = QR * QS

= 17 * 18

= 306

Area of triangle QRS = Area of rectangle QRS - Area of triangle TUV

= 306 - (1/21)√(2)

≈ 13.4 units

So, the answer is (C) 13.

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Complete question:

Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle. What is the area, in square units, of the triangle TUV?

A. 7

B. 10

C. 13

D. 18

Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.

First, we need to find the total number of cups of M&Ms Jen has

5 1/2 cups = 11/2 cups

Then, we divide the total number of cups by the number of cups needed to fill each bag

(11/2 cups) ÷ (1 1/4 cups/bag)

To divide by a fraction, we can multiply by its reciprocal

(11/2 cups) x (4/5 cups/bag)

= 44/10 cups

Simplifying, we get

= 4 2/10 cups

= 4 1/5 cups

So, Jen can fill 4 bags completely.

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Answer:

B. 432 feet

Step-by-step explanation:

36 yards * 3 = 108 feet

108 feet * 12 = 1296 inches

Answer:

5:05

6

10

Step-by-step explanation:

3:30 + 1 hour = 4:30

4:30 + 35 mins = 5:05 pm

5 days per 1 gallon, 30 days for :

30/5 = 6

500/50 = 10

$0.38×192=$72.96

So the answer is $72.96

Answer:

Step-by-step explanation:

circumference is 2πr

r=d/2

r=4.46m

C=2π(4.46)=28.02