The length of Ms. Sheahan's office is
3x yards and the width is x + 4 yards.
Write a polynomial that represents the
area. Find the area if x = 1 yd.

Answer:

Step-by-step explanation:

The answer would look like (30n-44)/7

Answer:

area 202.93, perimeter  62.78

Step-by-step explanation:

the triangle:

18² +14² = 520

√520 = 22.8

the curve, without further info, we'll have to assume it's 1/2 circle.

so circumference = 2πr =2 π (14/2) = 14 π = 43.96, 1/2 of it is 21.98

so perimeter of the whole thing is 18+22.8 +21.98 = 62.78

area: 1/2 circle = 1/2 π r² = 1/2 * 3.14*7² = 76.93

triangle area + 1/2 *18*14 = 126

total 202.93

Area of semi circle

Area of Triangle

Total area

Perimeter

Answer: I am not able to create images such as tree diagrams. But I can explain to you how it could be done.

A tree diagram is a visual representation of the possible outcomes and their probabilities.

The tree diagram to show the above information would have two branches: one representing the event that the bus is late and the other representing the event that the bus is not late.

The first branch, "Bus is Late", would have a probability of 0.1 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.8) and the other representing the event that Andrew is not late to school (with a probability of 0.2).

The second branch, "Bus is not Late", would have a probability of 0.9 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.05) and the other representing the event that Andrew is not late to school (with a probability of 0.95).

This tree diagram will help you to understand the relationship between the different events and their probabilities, as well as the overall probability of Andrew being late to school.

Step-by-step explanation:

Answer:

BD = 36

Step-by-step explanation:

• the diagonals of a parallelogram bisect each other , so

BE = DE , that is

15x - 12 = 9x ( subtract 9x from both sides )

6x - 12 = 0 ( add 12 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Then

BD = BE + ED

     = 15x - 12 + 9x

     = 24x - 12 ( substitute x = 2 )

    = 24(2) - 12

    = 48 - 12

    = 36

It costs $0.208 more per hour to park in Lot A than in Lot B.

We know that the total parking hours = 48

Also, the cost of parking for Lot A= ($)19. 00/33. 00 and for Lot B = ($)20. 00/32. 00

To find out how many more dollars it costs per hour to park in Lot A than in Lot B, we will subtract the hourly rate of Lot B from the hourly rate of Lot A.

The hourly rate of Lot A is (33.00 - 19.00) / 48 = $0.541 (dollars and cents)

Similarly, the hourly rate of Lot B is (32.00 - 20.00) / 48 = $0.333 (dollars and cents)

So the difference in cost per hour is $0.541 - $0.333 = $0.208 (dollars and cents)

Therefore, it costs $0.208 more per hour to park in Lot A than in Lot B.

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246960 6-digit numbers contain exactly one 3, one 4, and one 5 as digits.

There are a total of 6 digits that make up any of the numbers in 0 to 999999 with the given condition

The total numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

This can be represented as UVWXYZ

Digit 3 can occupy any of the 6 positions

Digit 4 can occupy any of the (6 - 1) positions

Digit 5 can occupy any of the (6 - 2) positions

The remaining 7 digits will occupy the last 3 positions in the following ways:

The first of the 7 digits can be selected from any of  7 ways

The second can be selected from any of 7 ways

The third can be selected from any of 7 ways

So, the total number of selection is:

= 6 × 6 × (6 - 1) × (6 - 2) × 7 × 7 × 7

= 36 × 5 × 4 × 343

= 246960

Therefore there are 246960 numbers.

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Becca is not correct because her probability of 2/14 is not equal to the true experimental probability of 2/16.

We are given the tools in the box as;

Hammer = 2 nos

Pliers = 5 nos

Screw drivers = 6 nos

Wrench = 3 nos

Thus;

Total number of tools in the box = 2 + 5 + 6 + 3

= 16

Probability of selecting a hammer = 2/16

Now, Becca says that   for every 14 tools in a toolbox, there are 2 hammers. This means she is suggesting a probability of 2/14.

This is wrong because it is different from the experimental probability that we got.

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The volume of water that are left in the tank is equal to 3.2 gallons.

Mathematically, the volume of a cuboid tank is a measure of its capacity and it can be calculated by using this following formula:

Volume of a tank = L × W × H

Where:

In order to determine the quantity (volume) of water that are left in the tank, we would use this mathematical expression:

Volume of water left = capacity of tank A - volume of water poured

Volume of water left = 9.5 gallons - 6 1/3 gallons

Volume of water left = 9.5 gallons - 6.3 gallons

Volume of water left = 3.2 gallons.

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Note that the square feet of carpet that will be required for this area is:  42 Square Feet of Carpet.

This is solved using the knowledge of the area of rectangles and right-angled triangles.

A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees.

Note that the area  of a right-angled triangle is given as:
A = (½)×b×h square units

Where b is breath and h is height.

Note as well that the area of the rectangle is given as Lx B

To solve the above problem, we must create one more right-angled triangle beside the one already created, then solve for the areas of the respective shapes.

Now that the shape has been divided in to two Right-angled Triangles and one rectangle (See the attached) their respective dimensions are given as follows:

1) Right Angled triangled A

B = 2ft

H = 3ft

Area = 1/2 2 * 3 = 3ft

2) Right-Angled Triangle B

B = 4ft

H = 3ft

A = 1/2 * 4 * 3

A = 6ft

3) Rectangle - C

L = 11ft

B= 3ft

A = 11 * 3 = 33 Ft.

Thus total square feet of outdoor carpet required is:

3 + 6 + 33

= 42 Square Feet of Carpet.

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a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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The table is filled considering the numeric values of the function, as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:

y = 2(-6) - 3

y = -12 - 3

y = -15.

The same procedure is applied for x = -3, x = 0 and x = 3.

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The translation rule (x + 7, y - 19) has the meaning given as follows:

The four translation rules are defined as follows:

The meaning of each translation in this problem is given as follows:

The problem asks for the meaning of the translation (x + 7, y - 19).

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Proportionately, an average American household uses 100 BTU of energy per home per year while Californians use 75 BTU, which is 25% less than the national average.

Proportion refers to the ratio or relative size of a value or number compared to another.

Proportions are fractional values equated to each other.

Generally, proportions may be depicted as fractions, decimals, or percentages.

The level of energy per home per year in California = 75 BTU

The national average of BTU use = 100%

California's use = 75% (100 - 25)

Proportionately, if 75% = 75 BTU, 100% = 100 BTU (75/0.75)

Thus, the national average use of energy is expected to be 100 BTU.

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The table that has the correct values for A, B, and C will be:

D. Donuts 2 4 6 8

Cost 15.80 31.60 39.50 56.72

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since we know that 4 donut cost 31.60, the.vost for 2 donut will be:

= 31.60 / 4 × 2

= 15.80

Therefore, we can see that the correct table for this is D.

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If two of the angles of an oblique triangle are equal, the Law of Sines can be used to fill in the remaining lengths or angle measurements.

In the accompanying diagram, two crossing lines are shown, with the angles 1 and 3 being vertical and congruent. In addition, the angles 2 and 4 are vertical and coincide. Vertical angles are two angles that are in opposition to one another, such as D and B in the illustration above.

The sum of the subsequent angles of a ||gm is A+B=180. To view an infinite number of solutions, download the app. Estimating ratios of a particular quantity is what it is. It is created by contrasting a given quantity with the reference unit. These are used to determine something's dimensions, including length, area, perimeter, volume, and amount. Measurement There are formulas for calculating length, area, surface area, volume, circumference, density, mass, etc.

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Complete question:

Which trigonometric law can be used if two of the angles of an oblique triangle are equal?

Option A, (x,y) → (2x,2y) This rule describes an origin-centered stretch with a factor of 2. That is, the image doubles its original size in both the x and y directions.

The new rectangle is similar to the original, but with larger dimensions, so the correct rule is A) (x, y) → (2x, 2y).

In this case, the rule described in option A) (x, y) → (2x, 2y) specifies that the image is twice the size of the original rectangle in both the x and y directions increase. This means that the scale factor is 2. This will result in a similar shape but with larger dimensions. This is the correct rule describing stretching the rectangle URST to the rectangle U'R'S'T'.

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The number of bean plants should she plant will be 60

t = tomato plants

b = beans

To Solve by using system of equations

Clear any fractional coefficients if there are any. Alternate the coefficients of a single variable. Select the variable you want to remove. Multiply one or both equations to make the variable's coefficients opposite.

Total plants = 100

t + b = 100     {equation 1}

20 more tomatoes than beans

t = b + 20       {equation 2}

b + 20 + b = 100

2b + 20 = 100

Finish solving for b to find a number of beans.

Then tomatoes will be b+20

Putting this in equation 1

b+20+b=100

2b+20=100

b=40

then t= b+20  {equation 2}

t=60

Hence the number of bean plants should she plant will be 60

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The actual area of the garden without the scale factor is 6 square feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. Depending on the size and number of sides, different forms have varying areas.

Let the original area of the garden be x.

Given that the scale factor used is 1/3, thus we have:

x (1/3) = 2

x = (2)(3)

x = 6

Hence, the actual area of the garden without the scale factor is 6 square feet.

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The value of 'x' in the equation 8 - x/x = 3/2 is x equal to [tex]3\frac{1}{5}[/tex].

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, An equation in 8 - x/x = 3/2 fractions.

Now, The LCM of both the denominators is 2x, So we'll multiply each term by 2x.

2(8 - x) = 3x.

16 - 2x = 3x.

- 2x - 3x = - 16.

- 5x = - 16.

5x = 16.

x = 16/5.

x = [tex]3\frac{1}{5}[/tex].

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The measure of each interior angle is calculated to be 172° and each exterior angle is calculated to be 8°.

Each interior angle in a polygon can be calculated using the formula, (n - 2) ×180°/n

where, n is the polygon's number of vertices.

So, each exterior angle can be calculated as, 180 - (n - 2) 180°/n

Now, let us put the number of vertices into these formulae,

Each interior angle = (45 - 2)×180°/45 = 43×180°/45 = 172°

Each exterior angle = 180 - (45 - 2) 180°/45 = 8°

So, the interior angle is 172° and the exterior angle is 8°.

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Answer: t = d/s

Step-by-step explanation:

Time = Distance/Speed
Substitute values in
E.g.
Jenny went for a drive in her new car. She drove for 8 miles at a speed of 4 miles per hour. For how many hours did she drive?

8/4 = 2 hours

Answer: slope = [tex]\frac{1}{4} x[/tex]

               point on the line= (0,-4.25)

Step-by-step explanation:

[tex]y+3\\[/tex] = [tex]\frac{1}{4} (x-5)[/tex]

     [tex]y=\frac{1}{4} x-\frac{5}{4} -3\\\\y= \frac{1}{4}x -3\frac{5}{4} \\\\y=\frac{1}{4}x -\frac{17}{4}[/tex]

therefore the value with the x is the gradient so the gradient (slope) is [tex]\frac{1}{4} x[/tex]

since the y-intercept is [tex]-\frac{17}{4}\\[/tex] get the simplified version in decimals which is -4.25... so the point will be (0,-4.25)

The average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph is 50.39 mph.

We have to find the average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph.

Let the speed be x.

The total average we want = 33.6 mph

The distance from your home to town = 90 miles

Time = Distance/Speed

Time = 90/33.6

At 45 miles (half way), you find you have averaged only 25.2 mph. So

Time first leg = 45/25.2

Time second leg= 45/x

Now the average speed;

45/25.2 + 45/x = 90/33.6

Subtract 45/25.2 on both side, we get

45/x = 90/33.6 - 45/25.2

After solving the ratio, we get

45/x = 0.893

Multiply by x on both side, we get

0.893x = 45

Divide by 0.893 on both side, we get

x = 45/0.893

x = 50.39 mph

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The complete question is:

On a drive from your home to town, you wish to average 33.6 mph. The distance from your home to town is 90 miles. However, at 45 miles (half way), you find you have averaged only 25.2 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph?

Answer:

43 centigrams > 31.7 milligrams

Step-by-step explanation:

Since 43 centigrams is equal to 430 milligrams, it is therefore greater that 31.7 milligrams.

Answer: The perimeter of a parallelogram is the sum of all its sides.

In this case, since all sides of the parallelogram WXYZ are given as 34 units, the perimeter of parallelogram WXYZ is the sum of all its four sides.

So the perimeter of parallelogram WXYZ = 34 + 34 + 34 + 34 = 136 units

It's important to notice that the given value of perimeter = 60 is not correct.

The perimeter of parallelogram WXYZ is 136 units, not 60 units.

Step-by-step explanation:

The vertex of the function is at - 2

The vertex of the function is at the point (a, 2), where the value of x, denoted as 'a', is the x-coordinate of the vertex.

To find the value of 'a', we can use the formula for the x-coordinate of the vertex, which is -b/2a, where b and a are the coefficients of the x-squared and x terms, respectively, in the standard form of the equation (y = ax^2 + bx + c).

Since the function is already in vertex form, we can directly read the value of 'a' from the equation which is -2.

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Answer: a = 2

Step-by-step explanation: 2.5 x 2 = 5 5 + 4.2 = 9.2

[tex]4.2+2.5a=9.2[/tex]

Rearrange:

[tex]2.5a+4.2=9.2[/tex]

Subtract 4.2 from both sides:

[tex]2.5a+4.2-4.2=9.2-4.2[/tex]

[tex]2.5a=5[/tex]

Divide both sides by 2.5:

[tex]\dfrac{2.5a}{2.5} =\dfrac{5}{2.5}[/tex]

[tex]\fbox{a = 2}[/tex]

The angle of depression of the airplane is 3.6⁰.

The angle of depression of the airplane is calculated by forming a triangle with base displacement of the airplane and the altitude.

base of the right triangle = 15 miles = 79,200 ft

height of the right triangle = 5,000 ft

The angle of depression is calculated as follows;

θ = arc tan ( h / b )

θ = arc tan ( 5000 / 79,200 )

θ = 3.6⁰

Thus, the angle of depression of the airplane is a function of the altitude and base displacement of the airplane.

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Answer:

1: 5/10, square root of 2, 2.5, square root of 25 3: 4.5

Step-by-step explanation:

2.5

5 divided by 10 comes to 0.5

25 square rooted is 5

2 square rooted is 1.4

the biggest number is 5 and the smallest is 0.5

subtract 0.5 from 5 and you get 4.5