The circle below is centred at O.
a) Work out the size of angle X.
b) Which of the circle theorems below allows you to calculate this angle?

Using compound interest, we can find that at age 59 retirement option 1 will be better than retirement option 2.

Compound interest is computed on the principal and the accrued interest for a given time period. The interest that has accumulated on the principal over time is added to it, and the combined amount acts as the new principal for the subsequent time period. Once more, the interest for the following period is calculated using the total cumulative principal amount.

Compound interest is the term used to describe the method of computing interest employed in all financial and business transactions globally. The benefit of compounding is that it is consistently better than or comparable to other strategies, such simple interest.

At age 59,

Option 1 = 30000 × 34

= $1020000

Option 2 = 15000 (1+12/408) ^34

= 15000 × (1.02) ^34

= 15000 × 1.9606

= $29409.

So, when you retire at 59, option 1 is better than option 2.

At age 69,

Option 1 = 30000 × 44

= $1,320,000

Option 2 = 15000 (1+12/528) ^44

= 15000 × (1.02) ^44

= 15000 × 2.390

= $35,850.

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At age 59, retirement option 1 will outperform retirement option 2, according to compound interest.

On the principal and the interest that has accrued over a specific length of time, compound interest is calculated. The principal is increased by the interest that has accrued on it over time, and the combined sum serves as the new principal for the term that follows. Once more, the entire cumulative principal amount is used to determine the interest for the upcoming period.

The term "compound interest" refers to the technique of calculating interest used in all financial and commercial transactions worldwide. Compounding has the advantage of constantly outperforming or being on par with other approaches, like simple interest.

At age 59,

Option 1:

= 30000 × 34

= $1020000

Option 2:

[tex]=15000(\frac{1+12}{408} )^{34} \\\\=15000\times 1.02^{34}[/tex]

= 15000 × 1.9606

= $29409.

So, when you retire at 59, option 1 is better than option 2.

At age 69,

Option 1:

= 30000 × 44

= $1,320,000

Option 2:

[tex]=15000(\frac{1+12}{528} )^{44} \\\\=15000\times 1.02^{44}[/tex]

= 15000 × 2.390

= $35,850.

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Step-by-step explanation:

r = 250   ( thousand)   and   r = 180 + 35 log4 (x)    <====base 4 LOG

    sooooo     250 = 180 + 35 log4(x)       find 'x' thousands

                      (250 -180)/35 = log4 (x)

                        2 = log4(x)         these are exponents of 4 ...anti log base 4:

                      4^2 = 4^(log4 x)

                       16   = x          

                     But x is thousands of $ (per the question info)

                                     so  $ 16 000

Step-by-step explanation:

The inscribed angle BAD =  1/2 arc BD

                     56° = 1/2 BD

                       arc BD = 112°

   and  arc BAD  would then be 360 - 112 = 248°

For the EXTERNAL angle y

    y = 1/2 ( difference of intercepted arcs ) = 1/2 ( 248 -112)° = 68°

Answer: The regular tube is the better buy

Step-by-step explanation: $2.50/3.2 ounces equals $.78 per ounce. $1.00/1.2 ounces equals $.83 per ounce. Therefore, the regular tube is the better buy.

Rewriting the absolute value problems gives us: y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x

The absolute value is simply defined as the distance from zero.

The equation we are to rewrite is:

y = |x − 3| + |x + 2| − |x − 5|, if -2 < x < 3  

Modulus value means that it always gives positive value. Thus:

if x < a, then |x - a| is positive when |x - a | = a -x, which is positive as a is larger than x.

and if x >a, then |x-a| is positive when |x-a| = x - a, which is positive as a is smaller than x.

Applying the same,

For  -2 < x < 3,

|x - 3 | = 3 - x, as x <3

| x + 2 | = | x - (-2)| = x - (-2) = x+2 as x> -2

| x - 5 | = 5 -x , as x < 5

Therefore, y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x

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The dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

What is Rectangular prism ?

A rectangular prism is a three-dimensional geometric shape that has six faces, all of which are rectangles.

To label the dimensions of the net for the current cereal box, you need to identify the six faces of the rectangular prism that makes up the cereal box.

Start by drawing a rectangular prism with the given dimensions (12 inches high, 8 inches wide, and 2 inches deep).

Then, label each face with its dimensions, as follows:

The top face (which will be the same size as the bottom face) has dimensions 8 inches by 2 inches.

The front and back faces have dimensions 12 inches by 8 inches.

The left and right faces have dimensions 12 inches by 2 inches.

Top face: 8 in. x 2 in.

Front and back faces: 12 in. x 8 in.

Left and right faces: 12 in. x 2 in.

Therefore, Note that the dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

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The ratio means that for every 2 motor boats, there are 3 sail boats. 6 sail boats must also enter so that the ratio remains the same. A possible missing information will be the total number of ships in the armada.

A ratio is a mathematical expression that represents the relationship between two quantities or numbers. It is a comparison of two numbers, often written in the form of a fraction or with a colon. Ratios are used to express how much of one thing there is in relation to another.

1. a. The ratio of motor boats to sail boats can be written in three ways:

As a fraction: 2/3

With a colon: 2:3

With the word "to": 2 to 3

This ratio means that for every 2 motor boats, there are 3 sail boats. Alternatively, it can be interpreted as for every 3 sail boats, there are 2 motor boats. The ratio does not specify the total number of boats, only the relative proportion of motor boats to sail boats.

b. To keep the ratio between motor boats and sail boats the same, we need to maintain the same ratio of motor boats to sail boats.

Currently, the ratio of motor boats to sail boats is 2:3.

Let x be the number of sail boats needed to maintain the ratio.

After x sail boats enter, the total number of boats will be 2 + x motor boats and 3 + x sail boats.

The ratio of motor boats to sail boats will still be 2:3, so we can write,

[tex]\frac{(2 + x)}{(3 + x)}[/tex] = [tex]\frac{2}{3}[/tex]

Cross-multiplying, we get,

2(3 + x) = 3(2 + x)

6 + 2x = 6 + 3x

x = 6

Therefore, 6 sail boats must also enter so that the ratio remains the same.

2. To find the total number of galleons and galleys in the Spanish armada, we need at least one additional piece of information. The ratio of 5:1 tells us that for every 5 galleons, there is 1 galley. However, we don't know the total number of galleons and galleys in the armada.

One possible missing information that could help us find the total number of galleons and galleys is the total number of ships in the armada. If we knew the total number of ships, we could find the number of galleons and galleys in the armada.

For example, let's say the total number of ships in the armada is 100. And let number of galleons = a and number of galleys = b. Then,

a + b = 100

[tex]\frac{a}{b}[/tex] = 5/1

b = a/5

Substituting this expression into the first equation, we get:

a+ (a/5) = 100

(6a/5) = 100

a = 500/6 ≈ 83.33

Then b = (1/5)(83.33) = 16.67

However, since we cannot have a fractional part of a ship, we can round up or down to get whole numbers. Therefore, we can conclude that the Spanish armada had approximately 83 galleons and 17 galleys, based on the given ratio of 5:1.

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Answer:

Step-by-step explanation:

um

Therefore, we can't calculate the difference in blood pressure between the control and treatment groups. Difference in means: 244.9 - 226.5 = 18.4 mg/dL.

by the question.

The question appears to be incomplete. It asks for the "difference," but it doesn't specify what difference it's referring to. Based on the information provided, I can provide some possible interpretations and calculations:

Difference in cholesterol levels before and after treatment:

Since all patients started with a cholesterol level of 245 mg/dL, we can't calculate the difference in cholesterol levels before and after treatment. We don't have any data on the patients' cholesterol levels after treatment.

Difference in average cholesterol levels between the control and treatment groups:

Control group mean: (241+243+242+245+250+248+246+245+242+247)/10 = 244.9 mg/dL

Treatment group mean: (230+225+220+218+224+240+232+221+235+224)/10 = 226.5 mg/dL

Difference in means: 244.9 - 226.5 = 18.4 mg/dL

Difference in average blood pressure between the control and treatment groups:

The prompt states that the experiment tested whether the cholesterol medication lowers the overall blood pressure for male patients, but it doesn't provide any data on blood pressure.

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The coordinates of vertex A' are (1, 1)

The coordinates of vertex B' are (2, 3).

The coordinates of vertex C' are (2, 1).

In Geometry, a reflection over or across the x-axis is represented or modeled by the following transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate (x-value) while the sign of the y-coordinate (y-value) changes from positive to negative or negative to positive as the case may be.

In this exercise, you are required to apply a reflection over the x-axis, a rotation of 90° clockwise about the origin, and finally reflected across the line y = x as shown in the transformation table below;

Original vertex   Reflection (x-axis)   Rotated 90° clockwise   Line y = x

A (1, 1)           →             (1, -1)          →              (-1, -1)           →             (1, 1)

B (2, 3)          →            (2, -3)        →              (-3, -2)         →             (2, 3)

C (2, 1)          →            (2, -1)         →              (-1, -2)         →              (2, 1)

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We can express this interval using set-builder notation as: {x | x > 4}

What is expression?

An expression consists of one or more numbers or variables along with one more operation.

The monthly costs of each plan as functions of the number of movies watched:

A(x) = 22 + x

B(x) = 14 + 3x

To graph these functions, we can plot several points for each one, as shown in follow fig.

A(x) - B(x) < 0

(22 + x) - (14 + 3x) < 0

22 + x - 14 - 3x < 0

-2x + 8 < 0

-2x < -8

x > 4

Therefore, Plan A is cheaper than Plan B for any number of movies watched greater than 4. We can express this interval using set-builder notation as: {x | x > 4}

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On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).

The sample has 100 bottles in total.

As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:

P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles

P(properly positioned and Plastic #4) = 15 / 100

P(properly positioned and Plastic #4) = 0.15 or 15%

Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

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The probability of winning the minimum award in the lottery is 0.00185%.

The possibility of an event occurring is expressed in terms of probability and odds. Probability is often stated as a decimal or percentage and represents the ratio of the number of likely outcomes to all conceivable possibilities. Conversely, odds are often stated as a ratio or fraction and are the ratio of the number of favourable events to the number of negative outcomes.

The probability of correctly matching two out of five white balls is given by the combination formula:

C(5,2) = 5! / (2! * (5-2)!) = 10

The probability of matching the gold ball is = 1/44.

Multiplying we have:

P(win minimum award) = (10 / C(54,5)) * (1 / 44) = 0.0000185, or approximately 0.00185%

Hence, the probability of winning the minimum award in the lottery is 0.00185%.

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an expression for height h in terms of radius r, h=r/4

The quantity of space a three-dimensional solid shape takes up is measured by its volume. Although it is hard to conceive in any shape, it may be likened to shapes. A compass box, for instance, has a bigger volume than an eraser inserted inside of it.

Volume of Sphere=4/3πr³

Volume of Cone=1/3πR²h

Given:

R=4r

4/3πr³=1/3πR²h

4r³=R²h

4r³=(4r)²h

r=4h

an expression for height h in terms of radius r, h=r/4.

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Answer:

Step-by-step explanation:

-8^2 and (-2)^3 are exponents so it should be solved first

-8^2 = -64 and (-2)^3 = -8

(-64)/(-8)

64/8

8

8

To solve this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) from left to right:

First, we need to simplify the exponents: -8^2 means -1 times 8 squared, which is -1 times 64 or -64. (-2)^3 means -2 multiplied by itself three times, which is -2 x -2 x -2 or -8.

Next, we need to perform the division and multiplication, again from left to right: -64 ÷ -8 equals 8.

Therefore, the final answer to the expression -8^2÷(-2)^3 is 8.

Answer:

7s

Step-by-step explanation:

Answer:

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

Angle with the measure of 130° forms a vertical angle pair with the sum of x and 107° angle.

Since vertical angles are congruent we have:

The two angles, x and 2x together form a right angle, since they form a linear pair with another angle, marked as right angle. Therefore, x and 2x are complementary angles:

The steps that should be taken to evaluate the order of operations given are:

To solve with PEMDAS, you first need to solve what is in the brackets in the order of operations given which is 8÷2 (1+3) - 2^3.

= 8÷2 (1+3) - 2^3

= 8÷2 x 4 - 2^3

Then solve for the exponents :

= 8÷2 x 4 - 2^3

= 8÷2 x 4 - 8

Then because the division comes first, you solve for that:

= 8÷2 x 4 - 8

= 4 x 4 - 8

You then solve for the multiplication as this takes precedence over subtraction:

= 4 x 4 - 8

= 16 - 8

Then solve the subtraction:

= 16 - 8

= 8

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X=-10 when the points (-5, 6) and (x, 3) are elements of an inverse variation.

A relationship between two variables known as an inverse variation occurs when one variable increases while the other decreases, resulting in a constant product. Y = k/x, where k is a constant of variation, can be used to explain the relationship between two variables x and y if they are inversely proportional in mathematics.

The fact that their product must be constant allows us to determine the value of x because the points (-5, 6) and (x, 3) are components of an inverse variation.

As a result, x must be 10 to provide the elements of an inverse variation (-5, 6) and (x, 3).

x * 3 = -5 * 6

x = -30/3

x = -10

In conclusion, an inverse variation is a mathematical connection where the product of two variables stays constant.

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Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 ÷ 12 which will give us

1/4

In conclusion MN is approximately 8.73.

How to solve?

In triangle MNK, we know that MN = NK and the angle between them is 110 degrees. Let's call the third angle in this triangle A.

We also know that MK = 5.

Since the sum of the angles in a triangle is always 180 degrees, we can find angle A:

A + 110 + A = 180

2A = 70

A = 35

Now we can use the Law of Sines to find MN:

MN/sin(110) = MK/sin(A)

MN/sin(110) = 5/sin(35)

MN = 5×sin(110)/sin(35)

MN ≈ 8.73

Therefore, MN is approximately 8.73.

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Complete Quedtion:

In triangle AMNK, we have MN = NK, angle M/N = 110 degrees, and MK = 5. What is the length of MN?

Answer:

A) -3

Step-by-step explanation:

To remove the radical on the left side of the equation, cube both sides of the equation.

[tex]\sqrt[3]{4x + 4}^{3}[/tex] = (-2)³

Simplify each side of the equation.

4x + 4 = -8

4x = -12

x = -3

So, the answer is A) -3

The new set B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.

Intersection is the point at which two sets of data meet. It is the common point or element that exists in both sets.

The intersection of the three sets A, B, and C is the set of elements that are common to all three sets.

In this case, the intersection of A, B, and C is the null set, denoted as ∅. This means that there are no elements that are common to all three sets.

To make the intersection set D = {2}, one of the sets must contain the element 2.

In this case, set A already contains the element 2, so it is sufficient to add the element 2 to one of the other sets, either set B or set C.

Let's say we add the element 2 to set B. The new set would be B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.

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The solutions to the quadratic equation  [tex]5x^2 + 20x - 7 = 0[/tex] are[tex]x = -2 + \sqrt{(23/5)[/tex] and [tex]x = -2 - \sqrt{(23/5)[/tex].

A quadratic equation is a second-degree polynomial equation of the form [tex]ax^2 + bx + c = 0[/tex], where x is the variable, and a, b, and c are coefficients, where a is non-zero.

The square root is an important mathematical concept that arises in many areas of mathematics and science, such as geometry, algebra, and physics. It is used to calculate the length of sides of a right triangle, to solve quadratic equations, and to model the behavior of physical systems

The three steps Sergey could use to solve the quadratic equation by completing the square are:

Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex].

Add and subtract [tex](b/2a)^2[/tex] to complete the square:

[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]

Simplify the left side and solve for x by taking the square root:

[tex]5(x + 2)^2 = 11[/tex]

[tex](x + 2)^2 = 11/5[/tex]

[tex]x + 2 = \pm \sqrt{(11/5)[/tex]

[tex]x = -2 \pm \sqrt{(11/5)[/tex]

Therefore, the three correct options are:

[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]

[tex]5(x + 2)^2 = 11[/tex]

[tex](x + 2)^2 = 11/5, x = -2 \pm \sqrt{(11/5)[/tex]

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Answer:

The number of times the tire will have to turn in travelling the length of the street is 30.9 times.

To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.  

Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 1.7m and π = 3.14

∴ C = 3.14 × 1.7

C = 5.338 m

Therefore, the circumference of the tire is 5.338 m

Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 165 m ÷ 5.338 m

Number of times the tire will have to turn = 30.91045 times

Number of times the tire will have to turn ≅ 30.9 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 30.9 times

Answer:

Step-by-step explanation:

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prismz is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

First, 90 + 90 = 180

Second, 320 - 180 = 140

Third, 140 / 2 = 70.

|                                90 * 70 = 6,300
|
|
| 90
|
|____________

         70

Answer:

White

Step-by-step explanation:

Number of favorable outcomes/Number of trails =4/20 or 1/5

Answer:

1. 33 foot

2. 6.2 foot

Step-by-step explanation:

1.

Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:

tangent of the angle of elevation = opposite / adjacent

In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:

tan(35) = h / 47

To solve for "h", we can multiply both sides by 47:

h = 47 tan(35)

Using a calculator, we get:

h ≈ 32.9 feet

So the height of the tree to the nearest foot is 33 feet.

2.

Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(51) = x / 8

To solve for "x", we can multiply both sides by 8:

x = 8 sin(51)

Using a calculator, we get:

x ≈ 6.2 feet

So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.