In a right triangle, sin (9x - 4)° = cos (10x - 1)°. Find the larger of the triangle's
two acute angles.

Answer:

The geometric mean of 9 and 6 is 4/3

Step-by-step explanation:

The geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

The geometric mean of two numbers [tex]x_1[/tex] and [tex]x_2[/tex] is given by the formula:

[tex]GM=\sqrt{x_1\times x_2}[/tex]

The two given numbers are 8 and 6

That is, [tex]x_1=8[/tex] and [tex]x_2=6[/tex]

Substitute [tex]x_1=8[/tex]  and [tex]x_2=6[/tex] into the formula [tex]GM=\sqrt{x_1\times x_2}[/tex]

[tex]GM=\sqrt{8\times 6}[/tex]

Simplifying further:

[tex]GM=\sqrt{48}[/tex]

[tex]GM=4\sqrt{3}[/tex]

Therefore, the geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

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The sum of the two functions  f(x) + g(x)  is  (x+2)/(x^2 - 9) + 11/(x^2 + 3x)

(a) To find f(x) + g(x), we simply add the two functions together:

f(x) + g(x) = (x+2)/(x^2 - 9) + 11/(x^2 + 3x)

(b) To determine the excluded values, we need to look for values of x that make the denominators of the two functions equal to zero. The denominators are:

x^2 - 9 and x^2 + 3x

Setting these equal to zero and solving for x, we get:

x^2 - 9 = 0 => x = ±3

x^2 + 3x = 0 => x(x+3) = 0 => x = 0 or x = -3

Therefore, the excluded values are x = ±3 and x = 0.

(c) To classify the type of discontinuity at each of the excluded values, we need to examine the behavior of the function as x approaches these values.

At x = ±3, the denominators of both functions become zero, which means that the function is undefined at these values. This creates a vertical asymptote, which is a type of infinite discontinuity.

At x = 0, the denominator of g(x) becomes zero, but the denominator of f(x) does not. This creates a removable discontinuity, because we can define f(0) separately to make the function continuous at this point. Specifically, we can set f(0) = 2/(-9) = -2/9 to remove the discontinuity.

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With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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Answer:

180

Step-by-step explanation:

Step-by-step explanation:

To solve the given equation, we can start by taking the square root of both sides of the equation:

(x – 7)^2 = 36

√((x – 7)^2) = ±√36

x – 7 = ±6

Now, we can solve for x by adding 7 to both sides of the equation for each case:

x – 7 = 6 or x – 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The other values, x = -29 and x = 42, do not satisfy the equation.

Answer:

1-d

2-c

3-b

4-a

5-e

To match the quadratic equations to their answers, we need to solve each equation and compare the solutions with the given options. After solving each equation, the answers can be identified as a. x=5,-5; b. x=8,-8; c. x=1.2,-1.2; a. x=5,-5; e. x=4,-4.

To match the quadratic equations to their answers, we need to solve each equation and compare the solutions with the given options. Let's go through each equation:

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The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.

There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.

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Accοrding tο the standard nοrmal distributiοn, the prοbability that z is greater than -0.25 is 0.5987.

Nοrmal distributiοn, alsο knοwn as Gaussian distributiοn οr bell curve, is a prοbability distributiοn that describes the randοm variatiοn οf a cοntinuοus variable in a pοpulatiοn. In a standard nοrmal distributiοn, the mean is 0 and the standard deviatiοn is 1, and the curve is fully described by the parameters οf mean and standard deviatiοn. The nοrmal distributiοn is used in many statistical applicatiοns tο mοdel and analyze cοntinuοus data.

Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the area tο the right οf z=-0.25 is apprοximately 0.5987.

Therefοre,

[tex]$$P(z > -0.25) = 1 - P(z \leq -0.25) = 1 - 0.4013 = 0.5987$$[/tex]

Sο the prοbability that z is greater than -0.25 is 0.5987.

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Complete Question

Find P(Z > 0.25), using the standard normal distribution. The average number of calories in a 1.5-ounce chocolate bar is 250. Suppose that the distribution of calories is approximately normal with standard deviation 10. Find the probability that a randomly selected chocolate bar will have between 230 and 260 calories. A single die is rolled 5 times. Find the probability of getting at least one number which is greater than 4. Given data values: 11, 3, 5, 12, 17, 13, 10, 6, 8, 21, 14, 20, 9, 15, 7. (a) Find the percentile rank for 10. (b) What value corresponds to the 70th percentile? A survey found that the American family rates an average of 25 pounds of glass garbage each year. Assume the standard deviation of the distribution is 7pounds. Find the probability that the mean of a sample of 49 families will be between 19 and 26 pounds.

Answer:

f(x) = (x+3)^2 + 5

Step-by-step explanation:

Hope this is right :)

Let's assume,

We know that perimeter of triangle is sum of all the sides.

a + b + c = Perimeter

3x + 4x + 5x = 84

12x = 84

x = 84/12

x = 7

Hence,

Now,

Semi-perimeter = Perimeter/2

= 84/2

= 42 cm

Using heron's formula,

Where,

= √42(42- 21)(42 ; 28)(42- 35)

= √42( 21 × 14 × 7)

= √42 × 2058

= √ 86,436

= 294 cm²

Therefore, Area of the triangle is 294 cm²

Answer:

Step-by-step explanation:

Given g(x) = 8x2 − x + 5, find the following.

(a). g(0) = 5

(b). g(−1) = 14

(c). g(r) = ?

(d). g(x + h) = ?

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Answer:

Step-by-step explanation:

Area of one base:

  [tex]A=\pi r^2=\pi (3.2)^2 =10.24\pi cm^2[/tex]

Perimeter of circle base:

  [tex]P=2\pi r=2\times \pi \times 3.2 =6.4 \pi cm[/tex]

Height of cylinder:

  [tex]h=8.7cm[/tex]       (given in question)

Total surface area:

[tex]SA=[/tex] area 2 circles + area rectangle

     [tex]=(2\times 10.24 \pi) +(6.4\pi\times 8.7)[/tex]           (Area rectangle = cylinder height x

                                                              circle perimeter)

     [tex]=239.26cm^2[/tex]

The expressions in a single exponent are 9³/9⁹ = 9⁻⁶ and 14⁻³ * 14¹² = 14⁹

Diego's mistake is multiplying the expressions, wrongly

Expression 1

Given that

9³/9⁹

To solve, we make use of the law of indices

So, we have

9³/9⁹ = 9⁻⁶

Expression 2

Here, we have

14⁻³ * 14¹²

Using the law of indices, we have

So, we have

14⁻³ * 14¹² = 14⁹

Diego's expression is given as

6⁴ * 8³ = 48⁷

The mistake in Diego's expression is that he multiplied 6 and 8, and then add the exponents

This is incorrect, and the actual solution is

6⁴ * 8³ = 1296* 512

6⁴ * 8³ = 2¹³ × 3⁴

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To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.

We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:

$130 + $100 = $230

So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.

Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.

Answer:

The total number of fruits Halston can choose is 3 + 4 + 2 = 9.

The number of ways she can choose two fruits without restrictions is 9C2 = (98)/(21) = 36.

The number of ways she can choose two fruits where both are bananas is 2C2 = 1.

Therefore, the number of ways she can choose two fruits that are not bananas is 36 - 1 = 35.

So, the probability that Halston chooses two fruits that are not bananas is:

35/36

Therefore, the probability that Halston chooses two fruits that are not bananas is 35/36.

We will use sine function, and length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

[tex]$\sin 60^\circ = \frac{x}{25}$[/tex]

Simplifying the left side, we have:

[tex]$\frac{\sqrt{3}}{2} = \frac{x}{25}$[/tex]

Multiplying both sides by 25, we get:

[tex]$x = \frac{25\sqrt{3}}{2}$[/tex]

Therefore, the length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

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Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Based on the information we can infer that the number of candy bars they buy depends on the number of guests you have.

To find the number of candy bars they are going to buy we need to look at the graph. In this case, if the maximum number of bars they are going to buy is 10 and the maximum number of people they are going to invite is 10, we can infer that 1 bar would correspond to each person.

Based on the above, we can infer that the relationship is directly proportional between the candy bars and the guests. In accordance with the above, the number of sweets depends on the number of guests.

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Answer: it depends; if exam day, no

Step-by-step explanation:

Answer:2.04

Step-by-step explanation:

To be able to determine the size of the space for the photograph from the frame area, we need to know the area of the frame and the dimensions of the photo frame (length and width). The given information is insufficient.

Most ideally, we determine the size of an object using different measurements and units of measurement. The most common measurement used for size is length or distance, which refers to the distance between two points on an object.

The other measurements used for size include area, volume, mass, weight, and density, which provide additional information about the object's characteristics. In order to determine the size of an object mathematically, we must understand the units of measurement being used and the appropriate formulas or equations for calculating size.

Translated question "Patricia designed the photo frame on the right. She makes frames of different measurements, but keeping its thickness, which is 4 cm, as shown in the drawing. How can you determine the size of the space for the photograph from the frame area?

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The total balance after four years when compounded continuously is $12,615.24.

A technique of calculating interest on a loan or investment where interest is compounded an endless number of times annually is called continuous compounding. Continuous compounding is a method of growing an investment or debt over time by continually adding interest earned over a relatively brief period of time to the principal. In financial computations where interest is earned or charged continuously, such in the bond or mortgage markets, continuous compounding is frequently utilised.

The compound interest is given as:

[tex]A = Pe^{(rt)}[/tex]

Substituting the values:

[tex]A = 12000 * e^{(0.0125 * 4)}\\A = 12000 * e^{(0.05)}[/tex]

A = 12000 * 1.05127

A = 12615.24

Therefore, the total balance after four years is $12,615.24.

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The probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds is  -1.3

What is normal distribution ?

Normal distribution, also known as Gaussian distribution or bell curve, is a continuous probability distribution that is commonly used in statistical analysis to model real-world phenomena. A normal distribution is characterized by its mean (μ) and standard deviation (σ), and is symmetrical around its mean. The bell-shaped curve of a normal distribution is determined by the empirical rule, also known as the 68-95-99.7 rule, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Many natural phenomena, such as human height and weight, tend to follow a normal distribution, and this makes normal distribution a useful tool in statistical analysis and modeling.

According to the question:
(a) To find the probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds, we need to standardize the value using the formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean drive-through time, σ is the standard deviation, and z is the corresponding z-score.

Plugging in the values given, we get:

z = (101 - 137.5) / 27 = -1.3

Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score less than -1.35 is 0.0885. Therefore, the probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds is:

P(X < 101) = P(Z < -1.35) = 0.0885 (rounded to four decimal places).

(b) To find the probability that a randomly selected car will spend more than 176 seconds in the restaurant's drive-through, we again need to standardize the value:

z = (176 - 137.5) / 27 = 1.42

Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 1.42 is 0.0788. Therefore, the probability that a randomly selected car will spend more than 176 seconds in the restaurant's drive-through is:

P(X > 176) = P(Z > 1.42) = 0.0788 (rounded to four decimal places).

(c) To find the proportion of cars that spend between 2 and 3 minutes (120 and 180 seconds) in the restaurant's drive-through, we need to standardize the values of the lower and upper limits:

z1 = (120 - 137.5) / 27 = -0.65

z2 = (180 - 137.5) / 27 = 1.57

Using a standard normal distribution table or a calculator, we find the area between these two z-scores to be 0.6591. Therefore, the proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is:

P(120 < X < 180) = P(-0.65 < Z < 1.57) = 0.6591 (rounded to four decimal places).

(d) To find the probability that a car spends more than 3 minutes (180 seconds) in the restaurant's drive-through, we standardize the value:

z = (180 - 137.5) / 27 = 1.57

Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 1.57 is 0.0582. Since this probability is less than 0.05, it would be considered unusual for a car to spend more than 3 minutes in the restaurant's drive-through.


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Answer:

X = 61,  Angle 57 and 123

Step-by-step explanation:

If you could provide the exact question that would be great, but from the information given what we know is that the entirety of half of a circle is 180 degrees so the angle at x-4 and the angle and 2x+1 must be equal to 180 degrees.

Therefore:

x-4  +  2x+1 = 180 degrees

X = 61,    Therefore:

x-4 -->  61 -4 = 57 degrees

2x+1 ---> 2(61) +1  = 123 degrees

So:

The angles are 57 degrees for x-4 and 123 for 2x+1 .

Answer: 6

Step-by-step explanation: We are told that the large cistern is completely filled shown with the larger volume. To find volume, the formula is lxwxh and if you apply that to the model, the larger cistern has a volume of 24 ft cubed which means 24 is completely filled. If we calculate the volume of the smaller cistern, it is 6. The question asks us how many cubic feet will be left when the larger cistern pours enough water to completely fill up the smaller cistern (24). So we do subtraction, 24-6= 18 meaning 18 is the number that is going to get poured from the big to the small cistern to make it 24 or, completely filled. And when we subtract the 18 from 24 (because we poured 18 from the large one to the small one to make it full), we get 6. 6 is how much is left after the larger cistern poured 18 to fill up the smaller cistern.

The gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

The space-time continuum is subject to gravitational waves, which move at the speed of light. They are caused by the acceleration of large objects that distort space-time around them, such as neutron stars or black holes.

The bending of space-time brought on by the existence of mass and energy is what Einstein's theory of general relativity refers to as gravity rather than a force.

The radius of the sphere can be determined using the formula:

R = Distance / Time

For 1.3 billion light years we have:

R = Distance / Time = 1.239 x 10²⁵ meters

Substituting the value in the volume:

V = (4/3) x π x R³ = 3.244 x 10⁷⁴ cubic light-years (approx)

Hence, the gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

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Answer:

Step-by-step explanation:

The simple interest formula is:

I = Prt

where I is the interest earned, P is the principal or initial investment, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values:

P = $2,926

r = 0.64% = 0.0064 (as a decimal)

t = 19 years

I = 2,926 * 0.0064 * 19

I = $353.21

Therefore, Elisabeth will have earned $353.21 in interest after 19 years.

Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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