Write log3(X)+2log(y) into a single logarithm

The total area of the shaded portion is approximately 111.2 cm², given that a circle is inscribed in a square with a radius of 7 cm and an angle of 80 degrees, and the shaded area is a sector of the circle and a portion of the square.

To find the shaded area, we need to first find the area of the square and the area of the circle, and then subtract the area of the unshaded portion of the circle from the area of the square.

The diameter of the circle is equal to the side of the square, so the side of the square is 2 * 7 = 14 cm. Therefore, the area of the square is

Area of square = side² = 14² = 196 cm²

The area of the circle is

Area of circle = πr² = π(7)² = 49π cm²

The angle between the two radii of the circle that form the shaded sector is 80°, which is 80/360 = 2/9 of the total angle around the center of the circle. Therefore, the area of the shaded sector is

Area of shaded sector = (2/9)πr² = (2/9)π(7)² = 22.4π cm²

The unshaded area of the circle is the difference between the area of the circle and the area of the shaded sector

Unshaded area of circle = Area of circle - Area of shaded sector

= 49π - 22.4π

= 26.6π cm²

Finally, the area of the shaded portion is

Area of shaded portion = Area of square - Unshaded area of circle

= 196 - 26.6π

≈ 111.2 cm²

Therefore, the total area of the shaded portion is approximately 111.2 cm².

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Answer:

Since the machine fills 250 bottles every 20 minutes, we can write the proportion:

250 bottles / 20 minutes = y bottles / x minutes

Simplifying this proportion, we get:

y = (x/20) * 250

This equation represents a linear relationship between the number of bottles (y) and the number of minutes (x), where the slope is 250/20 = 12.5 bottles per minute.

To create a graph, you can plot the points (0, 0) and (9, 112.5) since the y-axis only goes up to 125. This will give you a straight line that starts at the origin and goes up to about 112.5 on the y-axis at x = 9.

Step-by-step explanation:

The slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.

Hence the correct option is (G).

Here in the given graph we can see that H, P, K are on the same line that is the points H, P, K are collinear.

We know that in Cartesian Coordinate Plane, the slope of one line is unique.

Slope = (Change in y coordinate)/(Change in x coordinate)

We can see that the coordinates are:

H = (-12, 10)

K = (-4, 5)

P = (4, 0)

So the slope of HK = (10 - 5)/(-12 - (-4)) = 5/(-8) = -5/8

Slope of PK = (5 - 0)/(-4 - 4) = 5/(-8) = -5/8

Hence the slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.

So the correct option will be (G).

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The question is incomplete. The complete question will be -

Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 1/4, since there are 4 equally likely outcomes.

The probability of rolling an even number on a fair 6-sided die is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.

To find the probability of both events happening together (landing on blue and rolling an even number), we multiply their probabilities:

P(blue and even) = P(blue) x P(even)

= 1/4 x 1/2

= 1/8

Therefore, the probability of the spinner landing on blue and rolling an even number is 1/8.

Answer:

B

Step-by-step explanation:

The time for which the animal lived based on the given parameters is: 1018 years

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y = a(1 - b)ˣ

where:

y is the final amount

a is the original amount

b is the decay factor

x is the amount of time that has passed.

We are told that a paleontologist finds a fossil of animal remains with 88.5% as much Carbon-14 as the animal would have contained if the animal were alive today. Thus:

y/a = 88.5% = 0.885

Thus:

0.885 = e^(−0.00012t)

In 0.885 = -0.00012t

t = 1018 years

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To solve for x in the equation -2cosx+2cos2x=0, we can use the trigonometric identity cos2x = 2cos^2x - 1 to rewrite the equation as:

-2cosx + 4cos^2x - 2 = 0

Next, we can rearrange the terms and factor out a 2 to obtain:

2cos^2x - cosx - 1 = 0

This is now a quadratic equation in terms of cosx. We can solve for cosx using the quadratic formula:

cosx = [1 ± sqrt(1 - 4(2)(-1))] / (2(2))

cosx = [1 ± sqrt(9)] / 4

cosx = (1/2) or (-1/2)

Now, we need to find the values of x that correspond to these values of cosx. We can use inverse trigonometric functions to do this:

cosx = 1/2 => x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.

cosx = -1/2 => x = 2π/3 + 2πn or x = 4π/3 + 2πn, where n is an integer.

Therefore, the solutions for x are:

x = π/3 + 2πn, x = 2π/3 + 2πn, x = 4π/3 + 2πn, x = 5π/3 + 2πn, where n is an integer.

Answer: 17/33

Step-by-step explanation:

Or means add the 2 probabilities

There are a total of 33 outcomes.

getting a small clip is 15/33

getting a medium clip is 12/33

add the two probabilities 15/33 +12/33 = 17/33

I'm sure of my numbers.  I think the question is off or answers  

Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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Answer:

18.75 or 1.87

Step-by-step explanation:

If its 124n=2325, n is 18.75

If its 124n=232, n is 1.87

There is a 67.03% probability that no customers will arrive at the drive-up teller window in one minute.

The Poisson distribution formula can be used to calculate the probability of a specific number of customer arrivals in a given time interval. For example, if we want to calculate the probability of two customers arriving at the drive-up teller window in one minute, we can use the following formula:

P(X=2) = (e⁻⁰°⁴)*(0.4²)/2!

where P(X=2) is the probability of two customer arrivals, e is the base of the natural logarithm, and 2! is the factorial of 2.

Using this formula, we can calculate the probability of any number of customer arrivals in one minute. For instance, the probability of no customers arriving in one minute is:

P(X=0) = e⁻⁰°⁴ = 0.6703

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The model having number of cell phone users in the city doubled every 10 years is an exponential function not a linear function.

Because it represents the growth rate exponentially.

Last year number of users of the cell phone in a city = 500

Number of cell phones users doubled every 10 years.

The model that represents the number of cell phone users in the city is an exponential function, not a linear function.

This is because the number of cell phone users is doubling every 10 years.

Which means that the rate of growth is increasing exponentially.

In an exponential function, the variable in the exponent increases or decreases at a constant rate.

It is the case here as the number of cell phone users is doubling at a constant rate of every 10 years.

The exponential function that represents the number of cell phone users in the city can be written as,

f(x) = 500 × [tex]2^{x/10}[/tex]

where x is the number of years since the initial count of 500 cell phone users.

This function gives the number of cell phone users after x years,

And the exponent x/10 represents the doubling of the number of cell phone users every 10 years.

Therefore, the model represents the exponential function.

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a) 'they allow researchers to compare two competing models' is true of structural equation models.

a) They allow researchers to compare two competing models.

Structural equation modeling (SEM) is a statistical method used to analyze the relationships between multiple variables. It allows researchers to test and compare different models, including models with latent variables that are not directly observable. SEM can be used for both confirmatory and exploratory purposes, and it is a popular method in many fields, including social sciences, psychology, and business. Therefore, option (a) is true of structural equation models.

Option (b) is incorrect because SEM does not eliminate the third-variable problem in nonexperimental research. Rather, SEM allows researchers to control for and account for the effects of other variables in the model.

Option (c) is incorrect because structural equation models are not represented in a histogram. SEM involves constructing and testing a series of equations that represent the hypothesized relationships between variables.

Option (d) is also incorrect because SEM does not allow researchers to easily calculate the variance of a set of scores. SEM is used to test theoretical models and examine the relationships between variables, but it does not provide a direct measure of variance.

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The measure of the angles which are supplementary to each are 103 and 77 degrees.

Supplementary angles sum up to 180 degrees.

Let the measure of the angle we're trying to find "x".

We know that this angle is 26 degrees more than its supplementary angle, which we can call "y".

So we can write:

x = y + 26

Since x and y are supplementary, their measures add up to 180 degrees:

x + y = 180

Now we can substitute the first equation into the second equation to eliminate "y":

(y + 26) + y = 180

2y + 26 = 180

Subtracting 26 from both sides:

2y = 154

Dividing both sides by 2:

y = 77

To find the other angle, we can use the first equation we wrote:

x = y + 26

Plug in y = 77

x = 77 + 26

x = 103

Therefore, the angles are 103 and 77 degrees.

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The value of x and y are 12.4 and 7.4

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then asinA=bsinB=csinC.

To calculate the value of y;

y/sin60° = 5/sin36

ysin36 = 5 × sin60

0.588y = 4.33

divide both sides by 0.588

y = 4.33/0.588

y = 7.4 ( 1 d.p)

The value of x can be found by using Pythagoras theorem.

x² = 12² + 3²

x² = 144+ 9

x² = 153

x = √153

x = 12.4( 1 d.p)

therefore the value of x and y are 12.4 and 7.4

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The solution to the system of equations is m = 6, n = 5.

To solve for the values of m and n in the given system of equations, we can use the method of substitution. We can solve one equation for one of the variables, for example, we can solve the second equation for n in terms of m: n = (28 - 3m) / 2. Then we can substitute this expression for n into the first equation and solve for m: 4m + 6[(28 - 3m)/2] = 54

Simplifying the equation by distributing the coefficient of 6, we get: 4m + 84 - 9m = 54. Combining like terms, we get: -5m = -30 ;

m = 6.

To find the value of n, we can substitute m = 6 into either equation and solve for n. Using the second equation, we have: 3(6) + 2n = 28. Simplifying, we get: 18 + 2n = 28 ; n = 5.

To solve the system of equations 4m + 6n = 54 and 3m + 2n = 28, we used the method of substitution to solve for one variable in terms of the other, then substituted the expression into the other equation to solve for the first variable. We substituted the value of the first variable into one of the original equations to solve for the second variable.

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By angle sum property of triangle, the correct option is Option D: A=130°, b=4, a=7.

A triangle is a three-sided polygon, which is a closed figure with three straight sides and three interior angles.

According to the given information:

The correct answer is Option D: A=130°, b=4, a=7.

In a triangle, the sum of the measures of the interior angles is always 180 degrees. Therefore, if one angle of a triangle is given, the other two angles can be determined by subtracting the given angle from 180 degrees.

In Options A, B, and C, the given angle A is less than 90 degrees, which means that the triangle would be acute, and there is a unique triangle that can be formed using the given data. The given sides b and a are also of appropriate lengths to form a triangle based on the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

However, in Option D, the given angle A is 130 degrees, which is greater than 90 degrees. This would result in an obtuse triangle, where one angle of the triangle is greater than 90 degrees. In this case, the given sides b=4 and a=7 may not be of appropriate lengths to form a triangle, as they may not satisfy the triangle inequality theorem. Therefore, Option D does not determine a unique triangle, as the given data may not be able to form a valid triangle.

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The height of the cylinder is 17.00 inches, under the given condition that radius of the cylinder is 16 inches, volume is 13,665. 28 cubic inches  and have to round the answer to the nearest hundred.

Therefore, the volume of a cylinder is given by V = πr²h
Here,
V= volume of the cylinder,
r= radius of  the cylinder
h= height

Given that the radius of the cylinder is 16 inches and its volume is 13,665.28 cubic inches, then we can proceed to evaluate the height of the cylinder
V = πr²h
h = V / (πr²)
h = 13665.28 / (π(16)²)

h = 13665.28/ 3.14 x (256)

h = 13665.28/ 803.8

h = 17.00 inches

Then, the height of the cylinder is approximately 17.00 inches.

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Answer : Natural numbers include all the whole numbers excluding the number 0. In other words, all natural numbers are whole numbers, but all whole numbers are not natural numbers. Natural Numbers = {1,2,3,4,5,6,7,8,9,…..}

The average distance walked is  5 + 4/11 miles.

By using the graph we can see that:

So there are a total of:

5 + 9 + 3 + 5 = 22 girls.

And the average distance walked is:

A = (5*4 + 9*5 + 3*6 + 5*7)/22

A = 118/22 = 110/22 + 8/22 = 5 + 8/22 = 5 + 4/11

So the correct option is the first one.

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The 11-4 skills practice areas of regular polygons and composite figures involve finding the areas of different geometric shapes using specific formulas and methods.

To find the area of regular polygons, you can use the formula (1/2) x apothem x perimeter.

For composite figures, you can break the shape into smaller, more manageable shapes like rectangles, triangles, or circles, and then calculate the area of each component before adding them together.

Hence, The 11-4 skills practice areas of regular polygons and composite figures teach you to find areas using the appropriate formulas and methods, improving your geometry understanding and problem-solving abilities.

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Answer: it will take her 15 weeks.

Step-by-step explanation: first, you subtract 16 from 346, which you get 330. next, you divide 330 by 22 because gertrude saves $22 per week. in total, 330 / 22 is 15.

The value of

1. length BC = 4units

2. y = 44°

3. angle DAB = 56°

4. x = 2 units

A parallelogram is a quadrilateral with two pairs of parallel sides. The properties of parallelogram include:

1. The opposite sides of a parallelogram are equal in length

2. The opposite angles are equal in measure. 3. The interior angles on the same side of the transversal are supplementary.

Therefore , we can say that;

6-x = x +2

4 = 2x

x = 2

therefore line BC = 6-x

= 6-2= 4 units

Also, we can say that;

100-y = 12+y

2y = 100-12

2y = 88

y = 88/2 = 44°

Therefore angle DAB = 100-44

= 56°

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In a lottery daily game, a player picks three numbers from 0 to 9 (without repetition) there are 120 ways of choices that can be calculated with combinations.

A player picks three numbers from 0 to 9 in a lottery daily game without any repetition of digits). There is no specification of order.

Since we are not specified that there will be some order in selection of  digits (we can assume that there is no such order). Hence .

Therefore, we apply the formula of combinations as the order of items does not matter in case of combinations.

By applying the formula of combinations with no repetition we get,

Number of choices the player has in a lottery game is = nCr = n! /{( n - r)! r!}

where,  n is the total number of digits, that is n = 10

and r is the number of required digits, r = 3

Number of choices the player has in a lottery game is = 10 ! /{ ( 10-3)! 3!}

= 120

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The proof is not valid, nor does it prove that 4 is equal to 3

This evidence is not true.

The error occurs in the step involving factoring, where both sides of the equation are divided by (a + b - c).

The problem is that if (a + b - c) equals zero, it is not permissible to divide both sides of the equation by (a + b - c) because it is not defined to be divided by zero

Moreover, even if (a + b - c) is not equal to zero, dividing both sides by (a + b - c) does not result in an equation

In this particular case, the fact that 4(a + b - c) = 3(a + b - c) implies that (a + b - c) = 0 or 4 = 3. One valid conclusion only if 4 = 3 is false.

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The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The MAD indicates that the men's score spread is marginally less than the women's score spread.

The difference between a dataset's largest and lowest values is known as the range.

The range for the men's scores is: 75 - 65 = 10.

The range for the women's scores is 80 - 69 = 11.

The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The average distance between each data point and the dataset's mean is measured by the mean absolute deviation (MAD).

Find the mean first before calculating the MAD for the men's scores:

(65 + 68 + 70 + 72 + 73 + 75) / 6 = 70.5

The MAD indicates that the men's score spread is marginally less than the women's score spread.

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Therefore, the percent error is approximately 19.0% (rounded to the nearest tenth of a percent).

The percent error is a measure of the accuracy of a measurement or calculation. It is calculated by taking the absolute value of the difference between the measured or calculated value and the actual or accepted value, dividing that difference by the actual or accepted value, and then multiplying by 100 to express the result as a percentage.

The formula for percent error is:

% error = |(measured or calculated value - actual or accepted value) / actual or accepted value| x 100

The formula for percent error is:

(percent error) = [(|measured value - actual value|) / actual value] x 100%

Substituting the given values:

(percent error) = [(|1.7 - 2.1|) / 2.1] x 100%

(percent error) = [0.4 / 2.1] x 100%

(percent error) = 0.190476 x 100%

(percent error) = 19.0%

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Answer:

11

Step-by-step explanation:

The Pythagorean theorem states that in a right triangle, [tex]a^2+b^2 = c^2[/tex] , where c is the hypotenuse, and a and b are the legs. So to use the Pythagorean theorem, we let [tex]a=x-3,b=x+4[/tex] and [tex]c=x+6[/tex]. Expanding everything gives [tex]2x^2+2x+25=x^2+12x+36[/tex]

Moving everything to one side tells us

[tex]x^2-10x-11=0[/tex]

So

[tex](x-11)(x+1)=0[/tex]

This means that either x = 11 or x = -1. But looking back at our equation, x = -1 is a false solution, because sides of a triangle could not be negative in length, and x-3 = -4 when x =-1. Therefore x = 11.