Using logarithmic properties, what is the solution to log4(y - 9) + log43 = log481? Show all necessary steps.

Answer:

324

Step-by-step explanation:

To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.

To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324

Answer:

Shortage

Step-by-step explanation:

If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

Answer:

Planes

Step-by-step explanation:

You can think of a plane as a sheet of paper that goes on in all directions.

Answer:

B. planes

Step-by-step explanation:

The grammer makes sense

Answer:

the answer is 25c²

Step-by-step explanation:

(5c-3d)²-9d²

5²c²+3²d²-9d²

25c²+9d²-9d²

25c²

Answer:

= 25c² - 30cd

Step-by-step explanation:

(5c-3d)²-9d²

[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]

Answer:

2.016, 2.16, 2.1682, 2.2

How to put anything from least to greatest?

The decimals that you have put are the following:

2.16

2.1682

2.2

2.016

How to do it:

If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.

We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.

Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.

So now here are the decimals from least to greatest:

2.016, 2.16, 2.1682, 2.2

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The solution is;

 a. (2, 10) is not a solution to y < 12- x.

 b. (3, 13) is a solution to y ≤ 15 - x

 c. (4, 19) is a solution to y > 19 - x

 d. (5, 13) is not a solution to y ≥ 12 - x

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

A Set of such values is called a solution set to the considered equation or inequality.

Substitute the values where the variables are, and simplify to the point where you can tell whether the statement is true.

Each ordered pair is (x, y), thus the first value gets substituted for x; the second value gets substituted for y.

a. (2, 10)

 11 < 13 -2 = 11

no

b.(3, 13)

 8 ≤ 16 -3 = 13

yes

c. (4, 19)

 20 > 18 -4 = 14

yes

d. (5, 13)

 9 ≥ 15 -5 = 10

no

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A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.

B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.

C. Using the Lagrange method, the optimum combination of goods can be determined as follows:

Let L(X,Y) be the Lagrangian of this problem:

L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)

Where λ is the Lagrange multiplier.

The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.

∂L/∂X = 0 -> X = 11.85

∂L/∂Y = 0 -> Y = 8.57

Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.

D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.

==========================================================

Explanation:

Let's go through each answer choice to see which are true and which are false.

A.

The fractions for advertising and rent are 1/6 and 7/12 respectively. The LCD is 12, so let's get 1/6 to have a denominator of 12. Multiply top and bottom by 2 to get 1/6 = 2/12.

Now we can compare the fractions 2/12 (aka 1/6) and 7/12. Clearly 7/12 is larger. It's like saying "having 7 slices of pizza is more than 2 slices of pizza". Therefore, the claim that more was spent on advertising compared to rent is false.

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

B.

1/4 = 3/12 when multiplying top and bottom by 3

3/12 was spent on supplies and 2/12 was spent on advertising

We see that more was spent on supplies, so claim B is true

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

C.

This claim is false because it contradicts claim B.

Another way to see why it's false is to use a calculator to get these decimal values

Since 0.17 is not larger than 0.25, this means 1/6 is not larger than 1/4.

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

D.

We could use any of the methods mentioned in the previous sections, but I'll go another route.

For now assume that the fractions for supplies and rent (1/4 and 7/12 respectively) are equal.

Let's use cross multiplication to say the following:

1/4 = 7/12

1*12 = 4*7

12 = 28

Clearly the two sides are different so the original fractions aren't equal. To fix this error, replace each equal sign with a "less than" sign like so

1/4 < 7/12

1*12 < 4*7

12 < 28

Think of it like working backward up the chain. Start with 12 < 28 which is clearly true, and you can work backwards to end up with 1/4 < 7/12.

The fact we end up with 1/4 < 7/12 shows the claim "The bookstore spends more on supplies than rent" is false. It's the other way around: the bookstore spent more on rent compared to supplies.

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

Summary: We found only choice B to be true. The other statements were false.

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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Answer:

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean speed is 70 mph and the standard deviation is 3 mph. So, we can estimate the percent of vehicles whose speeds are between 64 mph and 76 mph as follows:

64 mph = 70 mph - 3 mph * 1

76 mph = 70 mph + 3 mph * 1

Since the speeds are within one standard deviation of the mean, we can use the Empirical Rule to estimate that approximately 68% of the vehicles have speeds between 64 mph and 76 mph.

So, the answer is approximately 68%.

Step-by-step explanation:

A=4πr²

A = 4× 22/7 ×8²

A = 4 ×22\7×64

A=804.6m²

The y-coordinate for the solution to the system of equations is y = -3.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.

The system of equation is given as:

y = 1/2x - 4

y = -2x + 1

Substituting the value of y in equation 1 we have:

-2x + 1 = 1/2x - 4

-2x + 1 = x - 8 / 2

(-2x + 1)(2) = x - 8

-4x + 2 = x - 8

2 + 8 = x + 4x

10 = 5x

x = 2

Substituting the value of x in the second equation:

y = -2(2) + 1

y = -4 + 1

y = -3

Hence, the y-coordinate for the solution to the system of equations is y = -3.

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Answer:

b. -1.

Step-by-step explanation:

The cosine function is periodic with period 2π, and for angles in the range [-90°, 90°], it takes on values in the range [-1, 1].

For the angle θ = -90°, the cosine is given by:

cos(-90°) = cos(270°) = -1

the answer is b. -1.

Answer: Scalene Right

Step-by-step explanation:

None of the side lengths are equal and there's a 90 degree angle

Answer:

Step-by-step explanation:

Here's a step by step solution with more details:

Let's call the length of the two equal sides of the triangle as x.

The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.

The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 1 1/3) = 5 2/5

Simplifying the equation:

2x + 1 1/3 = 5 2/5

Subtracting 1 1/3 from both sides:

2x = 4 1/5

Dividing both sides by 2:

x = 2 2/5

So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.

Answer:

One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm

Step-by-step explanation:

This is describing an isosceles triangle

1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

Let

x = one of the two equal sides of the triangle

∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]

Perimeter of a triangle = Sum of all three sides:

[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]

Expand the parenthesis using the Distributive Law and bring all the like terms together:

[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]

[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]

[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]

The two denominators of the two fractions have to be manipulated to be made the same:

[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]

[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]

[tex]= \frac{81 - 20}{15} = 3x[/tex]

[tex]= \frac{61}{15} = 3x[/tex]

Cross-multiplication is added:

[tex]= (61)(1) = (15)(3x)[/tex]

[tex]= 61 = 45x[/tex]

Isolate x and make it the subject of the formula:

x = [tex]\frac{61}{45}[/tex]

x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm

∴Third side:

= [tex]\frac{61}{45} + \frac{4}{3}[/tex]

= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]

= [tex]\frac{61}{45} + \frac{60}{45}[/tex]

= [tex]\frac{61 + 60}{45}[/tex]

= [tex]\frac{121}{45}[/tex]

= [tex]2\frac{31}{45}[/tex]cm

Step-by-step explanation:

The slashes through the lines indicate they're of the same length, which means this is an equilateral triangle. Therefore all three angles are 60 degrees.

The lines being parallel mean that angle x shares the same angle as the triangle in the bottom-right corner.

The parallel lines intersecting with the line segment that is consistent throughout the triangle makes the angle the same.

Step-by-step explanation:

We can see that the triangle in the picture is an equilateral triangle, because its sides are all marked with one dash, meaning they are equal lengths. We note that all the angles in an equilateral triangle are each 60°.

The little arrows on the top and bottom lines in the figure indicate that they are parallel, which means that the diagonal line between them creates a set of alternate angles (I've attached a pic of what alternate angles generally look like to make this clearer).

Alternate angles are equal, which means x is equal to the angle at the bottom right of the triangle, which is 60°.

Answer:

19 < x < 53

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

36 - 17 < x < 36 + 17

19 < x < 53

Answer:

Step-by-step explanation:

First you identify your variable, for our sake lets use x:

x= number in question

Next you write the equation given in the question:

2(x-5)= x+25

Next you use the distributive property and multiply 2 by both x and negative 5 to get:

2x-10=x+25

Now you want to get all of the x's to one side so you subtract the x on the right, fro the one on the left giving you:

x-10=25

Then you simply add 10 to 25 giving you the answer of x=35

The quantity of cholesterol in an egg is 272 mg

The quantity of cholesterol in a cupcake is 18 mg

The quantity of cholesterol in a slice of pizza is 9 mg

Let the amount of egg be e

Let the amount of cupcake be c

Let the amount of pizza be p

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol

e + c + p = 299

The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol

3c + 4p = 90

By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol

3e + c = 834

e + c + p = 299

3c + 4p = 90

3e + c = 834

solving the simultaneous equation gives

e = 270

c = 18

p = 9

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Answer:c

Step-by-step explanation:

The Ohio Lottery has been based on the probability deriving with the correct derivation of the number with the highest chances.

Probability has been defined as the mathematical description of learning the chances of an event to occur. The probability ranges from 0 to 1, with 1 being complete probability, and 0 means no chances of event to occur.

The Ohio lottery has been given as the game of lottery operated by the  Ohio Lottery Commission. The purpose initiated by the Ohio Lottery has been to raise the funds for the education.

The lottery has been based on the probability of the common outcomes that delivers the formation of the numbers with the highest chances of getting resulted.

The games such as Bucket 5, Super Lotto, Ohio Lotto has been based on the probability of the drawing the numbers, and the correct probability won the lottery.

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Your question is probably incomplete, and most probably the complete question is:

Create a Math Essay on probability of the Ohio lottery.

The unknown in the similar triangles are as follows;

x = 15 units

x = 16 units

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional to each other.

Let's solve for x in the triangles as follows:

using the proportion,

2.

9 / x = x / 25

cross multiply

25 × 9 = x²

x² = 225

x = √225

x = 15 units

3.

x / 12 = 12 / 9

cross multiply

9x = 144

x = 144 / 9

x = 16 units

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Answer: the answer is 5/12

The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

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The equation and solution that represents the number of bags of cans of aluminum cans for recycling that Sara collects, given that Miri collects 3x cans as Sara, is x = 123/3, which is 41.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

Mathematical expressions contain variables, constants, numbers, and values using mathematical operands.

Equations differ from mathematical expressions based on the use of the equation symbol (=).

The number of bags of aluminum cans collected by Sara = x

The number of bags of aluminum cans collected by Miri = 3x

3x = 123 bags

The equation representing the number of bags of cans Sara collects x = 123/3

x = 41 (123/3)

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The total value of $6800 compounded quarterly at 6% for 3 years is $8,123

From the question, we have

A = final amount

P = principal amount (initial investment) = $6800

r = annual interest rate = 0.06 ie. 6%

n = number of times interest is compounded per year = 4

t = time (in years) = 3

The total value is calculated as:

A = P(1 + r/n)^(nt)

substitute the known values in the above equation, so, we have the following representation

A = 6800(1 + 0.06/4)^(4*3)

Evaluate

A = 8130.2

Hence,, the value is $8130.2

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The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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