Solve for X
Please show step by step

(X - 4)^2 = 25

Answer:

The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both things together. This principle can be applied to find the total number of possible outcomes in a given situation.

For example, if you have 3 shirts, 4 pants, and 2 shoes to choose from, and you want to find the total number of possible outfits you can make, you would use the Fundamental Counting Principle as follows:

Number of possible outfits = (number of shirt choices) x (number of pants choices) x (number of shoe choices)

= 3 x 4 x 2

= 24

Therefore, there are 24 possible outfits that you can make from the given choices of shirts, pants, and shoes.

Answer:

The volume of a cube with a length of 11 meters is 33 m³.

Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)

The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,

                                     [tex]Area=length*width[/tex]

Now, Solving given problem,

The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft

Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft

The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft

Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft

To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:

(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft

So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft

The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft

Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft

The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft

Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft

Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:

Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft

So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft

Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.

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Answer:[tex]\frac{21}{2} x^{2/3} - \frac{12}{5}x^{\frac{5}{3} } + C[/tex]

Step-by-step explanation:

[tex]\int {\frac{7}{x^{1/3} }-4x^{2/3} } \, dx \\\int {7x^{-1/3}} - 4x^{2/3}\, dx \\= 7*\frac{3}{2}x^{2/3} - 4*\frac{3}{5}x^{\frac{5}{3} } + C\\ =\frac{21}{2} x^{2/3} + \frac{12}{5}x^{\frac{5}{3} } + C\\\\\\ Assuming: (x^{2})^\frac{1}{3}[/tex]

Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:

300 + 40x = 9300 - 50x

Simplifying and solving for x:

90x = 9000

x = 100

Now that we know x, we can use either equation to find y:

y = 300 + 40(100) = 4300

So the equilibrium point is when x = 100 and y = 4300.

Step-by-step explanation:

Answer:

14.4 yards^2

Step-by-step explanation:

area of a trapezoid is (a+b/2)*h with a and b being the bases and h being the height so,

((3 1/5 + 5 3/5)/2)*8=14.4yards^2

Answer:

its 160

Step-by-step explanation:

Answer:

  160°

Step-by-step explanation:

You want the central angle marked x defined by the radii to two tangents that meet at a 20° angle.

The central angle AOB (marked x) and the exterior angle ACB are supplementary. This means x is ...

  x = 180° -20° = 160°

The value of x is 160°.

__

Additional comment

The sum of all angles in the kite shape is 360°. The angles at A and B are both 90°, leaving 180° for the total of the angles at O and C.

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The values are;

1. x = 6 ,y = 6√2

2. x = 9√2, y = 18

3. x = y = 9

4. x = 12, y = 12√2

5. x = y = 4√2

6. x = y =( 3√2)/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

There are some special angles , in which 45 is part of them.

sin 45 = 1/√2

cos 45 = 1/√2

tan 45 = 1

1. x = 6 ( isosceles triangle)

y = 6 × √2 = 6√2

2. x = 9√2 ( isosceles triangle)

y = 9√2 × √2 = 9×2 = 18

3. x = 9√2/√2 = 9

x = y = 9 ( isosceles triangle)

4. x = 12 ( isosceles triangle)

y = 12×√2 = 12√2

5. x = 8/√2 = 8√2/2 = 4√2

x = y = 4√2( isosceles triangle)

6. x = 3/√2 = (3√2)/2

x = y =( 3√2)/2 ( isosceles triangle)

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From given sample space, No. of toothpicks each student will get is 51.

What exactly is a sample space?

In mathematics, a sample space is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is a fundamental concept used in calculating probabilities. For example, when flipping a coin, the sample space is {heads, tails}. When rolling a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The sample space for a more complex event may involve multiple variables and outcomes.

Now,

Total Toothpicks = 918

Total students = 18

then

Toothpicks per student = 918/18=51

Hence,

           No. of toothpicks each student will get is 51.

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Answer:

  51.5

Step-by-step explanation:

You want the median of the data set {55, 44, 40, 55, 48, 44, 58, 67}.

There are an even number of elements in the set of data, so the median will be the average of the middle two.

Sorted into increasing order, the data set is ...

  {40, 44, 44, 48, 55, 55, 58, 67}

The middle two elements are (48, 55). Their average is ...

  median = (48 +55)/2 = 103/2 = 51.5

The median of the data is 51.5.

<95141404393>

So, the answer as a fraction is 16/36.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as one number (the numerator) placed above another number (the denominator) and separated by a horizontal line. For example, 3/4 is a fraction where 3 is the numerator and 4 is the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up the whole. Fractions can also be written in decimal or percentage form. Fractions are commonly used in everyday life, such as in cooking recipes, measurements, and financial calculations.

There are 6 purple marbles and 10 blue marbles, so there are 6 + 10 = 16 marbles that are either blue or purple.

The total number of marbles in the bag is 9 + 6 + 4 + 10 + 7 = 36.

Therefore, the probability of selecting a blue or purple marble is 16/36.

So, the answer as a fraction is 16/36

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Answer:

To find the point that best represents 331% of the distance between 0 and 1, we need to first calculate 331% of the distance between 0 and 1, which is:

331% of (1 - 0) = 3.31 * (1 - 0) = 3.31

So we want to find the point on the number line that is 3.31 units away from 0.

Looking at the number line, we can see that the distance between W and X is 1 unit, the distance between X and Y is 1/3 unit, and the distance between Y and Z is 2/3 unit.

Therefore, the point that best represents 331% of the distance between 0 and 1 is the point that is 1 unit away from 0 and then an additional 0.31 units away from that point. This point is on the segment between W and X, and is closer to X.

So, the point that best represents 331% of the distance between 0 and 1 is Point X.

Therefore, the answer is (B) Point X.

Step-by-step explanation:

5 cos (307)  = 3

5 sin (307) = -4  

just plot the point   ( 3, -4 )     Done.

Answer:

The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4

Answer:

c = 35.493

Step-by-step explanation:

Because this is a right triangle, we can use one of the trigonometric ratios to solve for c.

If we allow angle A to be our reference angle, we see that b is the side adjacent to angle A and side c is the hypotenuse.  Thus, we can use the cosine ratio as

[tex]cosine(x)=\frac{adjacent}{hypotenuse}[/tex]

In context of the problem, we can rewrite the equation as

[tex]cos(65)=\frac{15}{c}[/tex], where we're solving for c:

[tex]c*cos(65)=15\\c=15/cos(65)\\c=35.49302375\\c=35.493[/tex]

The value of n is equal to: E. 15.

Since 28 is equal to 4 more than 3 times a number, the number is equal to: B. 8.

An equation that could be used to solve for the number of boys is: C. x + (x + 20) = 120.

The distance from Parker to Davis is equal to: E. 140.

In this exercise, you are required to determine the unknown number as follows;

n = 60 - 3n

3n + n = 60

4n = 60

By dividing both sides of the equation by 4, we have the following:

n = 60/4

n = 15.

Assuming the unknown number is x, we have the following;

28 = 4 + 3x

3x = 28 - 4

3x = 24

By dividing both sides of the equation by 3, we have the following:

x = 24/3 = 8.

An equation that could be used to solve for the number of boys is given by;

x + (x + 20) = 120.

Total distance = x + 10 + 2x

220 = 3x + 10

3x = 210

x = 210/3

x = 70

From Parker to Davis, we have;

2x = 2(70) = 140 miles.

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Answer:

the value of $s$ is 13.

Step-by-step explanation:

We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.

Substituting $r=9$ into the second equation, we get:

$4(9) + 3s = 75$

Simplifying the left-hand side, we get:

$36 + 3s = 75$

Subtracting 36 from both sides, we get:

$3s = 39$

Dividing both sides by 3, we get:

$s = 13$

Therefore, the value of $s$ is 13.

The appropriate measurement unit for force is  kg.m/s²

A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.

From Newton's Second Law, force is expressed as;

F = m × a

Where is mass of object and a is the acceleration

One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Since F = m × a

Plug in m = kg and a = m/s²

F = kg × m/s²

F = kg.m/s²

Therefore, the unit of measurement is kg.m/s².

Option B is the correct answer.

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Answer:

a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.

b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.

Step-by-step explanation:

Answer:

122.30 cm²

Step-by-step explanation:

Divide the polyhedron into shapes:

+) 2 triangles with the same area.

The area of the triangle is
(4.3×11)÷2 = 23.65 cm².
And with two triangles of the same area we take the sum of both areas
23.65 + 23.65 = 47.3 cm²

+) 3 rectangles with different areas.

(3×6) + (3×8) + (3×11) = 75 cm²

So the surface area is the sum of areas of the triangles and rectangles

47.3 + 75 = 122.3 = 122.30 cm²

Answer:

x = 58.03°

Step-by-step explanation:

Given:

Solve for x:

1. [tex]x=cos^{-1}(\frac{9}{17})=58.03[/tex]

Answer:

So, the measure of angle x is equal to 58.03.

Answer:

10 feet

Step-by-step explanation:

Let's start by finding the current area of the deck:

Area = length x width = 20 ft x 10 ft = 200 sq ft

If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:

Length = 20 ft + x

Width = 10 ft + x

The new area of the deck will be:

New Area = (20 ft + x) x (10 ft + x)

We know that Ian wants the new area to be triple the original area of 200 sq ft, so:

New Area = 3 x 200 sq ft

New Area = 600 sq ft

Substituting this into the equation above and solving for "x", we get:

(20 ft + x) x (10 ft + x) = 600 sq ft

200 + 30x + x^2 = 600

x^2 + 30x - 400 = 0

(x + 40) (x - 10) = 0

We discard the negative solution, and we get:

x = 10 ft

Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.

To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.

If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.

Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.

Ian should increase both the sides by 10 feet each.

This is a simple mathematics problems related to the topic of mensuration.

Firstly we calculate the current area of the deck:

Area of the deck (rectangle) = l x b

Area of the deck (rectangle) = 20 x 10

Area of the deck (rectangle) =  200 square feet

Since Ian wants to triple the area of the deck, the required area is 600 square feet.

We now look at pairs of numbers multiplying which will give us 600:

(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)

Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.

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Let's denote the amount that state D spends on tourism as "x" million dollars. According to the given information, state C spends $1.8 million more than state D, so state C would spend "x + 1.8" million dollars on tourism.

The total amount spent by state C and state D combined is $56.8 million. So we can write the equation:

x + (x + 1.8) = 56.8

Now, we can solve this equation to find the values of x and x + 1.8, which represent the amount spent by state D and state C, respectively.

x + x + 1.8 = 56.8

2x + 1.8 = 56.8

2x = 56.8 - 1.8

2x = 55

x = 55 / 2

x = 27.5

So, state D spends $27.5 million on tourism, and state C spends $27.5 + $1.8 = $29.3 million on tourism.

Answer:

2

Step-by-step explanation:

add them and make them equal to 90 because its a right angle

5m+80=90

subtract 80 to isolate m

5m=10

divide 5 to isolate m even more

m=2!

The length of XY uisng the midpoint theorem is 40 units

The midpoint theorem states that if a line segment is drawn connecting the midpoints of two sides of a triangle, then that line segment is parallel to the third side of the triangle, and its length is half the length of the third side.

In this case, we have a triangle XYZ, and points A, B, C are the midpoints of sides XY, YZ, and ZX respectively.

By the midpoint theorem, we know that AB is parallel to ZX and has a length of half of ZX.

Similarly, BC is parallel to XY and has a length of half of XY, and AC is parallel to YZ and has a length of half of YZ.

We are given that BC has a length of 20, and we want to find the length of XY.

Using the midpoint theorem, we know that

XY is twice the length of BC

So

XY = 2 * BC = 2 * 20 = 40.

Therefore, the length XY is 40 units

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Answer:

Step-by-step explanation:

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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The probability of the given situation through which the given relation is satisfied is 0.78

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2, or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

Probabilities can also be expressed as percentages or fractions. For example, a probability of 0.25 can be expressed as 25%, or as a fraction of 1/4.

Probability theory is a branch of mathematics that deals with the analysis of random events and the quantification of uncertainty. It has applications in a wide range of fields, including statistics, physics, finance, and engineering.

Flexible hour work = 78%

Don't Know = 9%

Rigid hour = 13%

The probability of that 4 people choose flexible hour for work is,

0.78

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Answer: a) Virtual School Gold Card

Step-by-step explanation: To compare the monthly interest rates of the three credit cards, we need to convert the annual and quarterly rates to monthly rates.

For Canadian Express, the monthly interest rate is 19.9% / 12 = 1.6583%.

For Virtual School Gold Card, the monthly interest rate is 1.67%.

For Bank of Brennan Super Credit Card, the monthly interest rate is (4.99% / 4) = 1.2475%.

Therefore, the Virtual School Gold Card offers the lowest monthly interest rate at 1.67%.