Write the logarithmic expression as a single logarithm.
1/2(log₂x + log ₂y) - 5 log ₂(x+6)

The three internal angles of the triangle are α = 21.3°, β = 139.7°, and θ = 88.9°.

We can use the Law of Cosines to solve for the angles of the triangle:

cos(α) = (b² + c² - a²) / (2bc)

cos(β) = (a² + c² - b²) / (2ac)

cos(θ) = (a² + b² - c²) / (2ab)

Substituting the values given in the problem, we get:

cos(α) = (12.2² + 50.6² - 18.5²) / (2 x 12.2 x 50.6) = 0.929

α = cos⁻¹(0.929) = 21.3°

cos(β) = (18.5² + 50.6² - 12.2²) / (2 x 18.5 x 50.6) = -0.777 (note the negative value)

β = cos⁻¹(-0.777) = 139.7°

cos(θ) = (18.5² + 12.2² - 50.6²) / (2 x 18.5 x 12.2) = 0.056

θ = cos⁻¹(0.056) = 88.9°

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Answer:

127.5

Step-by-step explanation:

you arrange the numbers from least to greatest then divide by 2 If the amount of numbers you have are iuneven add 1 to it for example the first 9 prime numbers. 9 isn't and even number so you add 1 then divide by

The bucket of fish are the sea otters fed each day is 2 buckets or 3/2 bucket(in fractions).

What is fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written as a number (the numerator) over another number (the denominator), separated by a horizontal line. The denominator indicates the number of equal parts into which the whole is divided, while the numerator indicates how many of those parts are being considered.

Explanation:

The sea otters are fed 1/4 as much fish as the dolphins, which means they are fed:

(1/4) x 6 = 6/4 = 3/2 buckets of fish each day.

However, we cannot have half a bucket of fish, so we need to round this up to the nearest whole number. Therefore, the sea otters are fed:

2 buckets of fish each day.

So the answer is: 2 buckets.

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The given statement is false.

You can compare two marginal distributions to see if the corresponding two variables are related - False.

Comparing marginal distributions can only disclose information about the distribution of each variable individually, not whether the variables are connected or not.

To see if two variables are connected, we must look at their joint distribution or conditional distribution. To examine the degree and direction of a link between two variables, statistical approaches such as correlation analysis or regression analysis can be utilised.

As a result, comparing marginal distributions is insufficient to tell whether two variables are connected or not.

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A linear equation can be solved in four steps. First, simplify; next, use the properties of addition and subtraction; then, use the properties of multiplication and division; and last, check your work.

Any equation whose variables' highest powers are all equal to one is said to be a linear equation. This results in a graph with a straight line and is typically written as Ax+By=C. Here, x and y are the variables; A and B are their respective coefficients; and C is a constant.

The steps to solve a linear equation are given by

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The null space of A is spanned by the vector x = (t, -t, -t, -t), where t is a real number

Vectors are an important mathematical tool for representing data, equations, and other mathematical objects. In this problem, we are given a matrix A and asked to find a non-zero vector x in the null space of A.

The matrix A = | | 1-1-1-1 | can be reduced to row-echelon form using row operations. The resulting matrix is A = | | 1 0 0 0 | , which has a single non-zero row, indicating that the null space of A is one-dimensional.

Therefore, the non-zero vector x in the null space of A can be written as x = (t, -t, -t, -t), where t is a real number.

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Answer:

21x + 7

Step-by-step explanation:

See picture below :)

Answer: Part A: Option C) 7.5x≥60

Part B: 8 hours

Step-by-step explanation:

Part A: To represent the situation in terms of x hours, we can use the formula:

Distance driven ≤ distance the car can travel per hour × hours the car is charged

Since Eva needs to drive at least 60 miles and the car can travel 7.5 miles per hour of charging, we can write the inequality as:

60 ≤ 7.5x

The correct answer is (C) 7.5x ≥ 60.

Part B: To find the least amount of time that Eva will need to charge her car, we can solve the inequality from Part A as follows:

7.5x ≥ 60

x ≥ 8

This means that Eva will need to charge her car for at least 8 hours to be able to drive at least 60 miles.

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The closed shapes with four sides are called quadrilaterals.

Therefore, the four sides closed shape is known as quadrilateral.

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Answer:

114.3

Step-by-step explanation:

multiple the length value by 2.54

10 feet to meters can be find out by simply dividing the 10 feet by 3.081 so the  value will be 3.048 meters.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

One foot is equal to 0.3048 metres, or 3048/10000 metres. So, you multiply 10 by either 0.3048 or 3048/10000 to convert 10 feet to metres.

For the decimal answer, we use 0.3048, and for the fractional answer, we use 3048/10000. The math, formulas, and conversions from 10 feet to metres are shown below.

0.3048 metres divided by feet

10 feet = 3.048 metres, or 10 divided by 0.3048.

metres equal 3048/10000 feet.

10 × (3048/10000) = 3 6/125

10 feet equals 36/125 metres.

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There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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Standard conversions state that 375 cm is equivalent to 147.6 inches.

A fixed magnitude of a quantity that serves as a reference point for measuring other quantities of the same sort is referred to as a unit of measurement. Convention or legislation establish and adopt it. Every other amount of that sort can be expressed as a multiple of the unit of measurement.

One inch is 2.54 cm long.

We can compose,

2.54 cm equals one inch.

1 cm equals 0.54"

Thus, 375 cm will be equal to 375/2.54 inch.

175 cm = 147.6 in.

So, 375 cm equals 147.6 inches in inches.

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Complete question - what is 375cm in inches?

Or you could pick any integer larger than this.

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

Work Shown:

23% = 0.23 in decimal form

x = some positive number

1/x < 0.23

1 < 0.23x .... see note below

0.23x > 1

x > 1/0.23

x > 4.347826 approximately

If x is an integer, then the smallest it can get is x = 5

Check:

Note: The inequality sign does not flip in the 2nd step shown above because x is positive. The sign only flips if we multiplied both sides by a negative value.

The illustration of 10 sided polygon is attached below.

Polygons are closed geometric figures made up of line segments that are connected end-to-end. The number of sides of a polygon determines the polygon's name.

In mathematical terms, a decagon is a 10-sided polygon with 10 vertices and 10 angles.

To draw a decagon, we need to start by drawing a circle. We can use a compass to draw a circle of any size we want. The radius of the circle will determine the size of the decagon.

Next, we need to draw a horizontal line through the center of the circle. This line will be the base of the decagon, and it will divide the circle into two equal halves.

Since a decagon has 10 sides, we need to divide the circle into 10 equal parts.

We can then use these lines as guides to draw the sides of the decagon. We start at one of the points where the lines intersect the circle, and draw a line segment to the next point.

We can label the vertices of the decagon with numbers, starting with 1 and going clockwise, as shown in the diagram.

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To discover the coordinates of a polar point, you need to recognize its distance from the origin (the polar axis) and the perspective it makes with the superb x-axis.

The space is commonly denoted via the image r, and the angle is denoted by means of the image θ. To devise a polar point, you start by locating the foundation and drawing a line alongside the polar axis.

Subsequently, you measure the angle θ from the fine x-axis, shifting counterclockwise.

In the end, your degree the distance r from the starting place and plot the factor on the corresponding location.

To find the coordinates of a polar point, you can use the subsequent formulas:

x = r cos(θ)

y = r sin(θ)

Right here, x and y constitute the rectangular coordinates of the factor, while r and θ constitute the polar coordinates.

Those formulas let you convert between polar and rectangular coordinates, which can be useful for graphing and solving problems in diverse branches of mathematics and physics.

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Uncontrollable factors can have an effect on the result of a scenario or experiment. Here are a few strategies for dealing with such factors:

Recognize the variables, Reduce the impact, Randomization, Statistical analysis, Concentrate on what you can control.

Recognize the variables: The first stage is to identify the uncontrollable elements and acknowledge their possible effect on the result. This allows you to plan for unexpected events and alter your expectations accordingly.

Reduce the impact: Even if you can't control the circumstances, you can reduce their influence by taking particular activities. For example, if weather conditions may have an impact on the result of an outdoor event, you may want to arrange it during a more favourable time of year.

Randomization: When dealing with uncontrolled elements in a scientific experiment, randomization can assist in evenly distributing the impact of these factors among multiple groups.

Statistical analysis: In data analysis, statistical analysis can help to account for the impact of uncontrollable factors. Statistical models can provide more accurate estimates of the influence of a given variable by controlling for other variables and accounting for the variability produced by uncontrolled factors.

Concentrate on what you can control: In many circumstances, it is more productive to focus on what you can control than than fretting about what you can't. You may be able to mitigate the effects of uncontrollable elements to some extent by recognising and maximising the controllable factors.

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1. a. No, points A, C, and E are NOT coplanar.

This is because A and E are outside the plane)

b. The three lines are AE, CD, BC

c. The three collinear points are; A,B,E

d. The intersection of line AB and line CD is BE

A coplanar point is a point that lies in the same plane as one or more other points.

In three-dimensional space, a plane can be defined by at least three non-collinear points. Any additional point that lies on this plane is considered coplanar with those points.

In simpler terms, if you imagine a flat surface like a piece of paper, and you place some points on it, any additional point that you place on that same flat surface will be coplanar with the original points.

It's worth noting that coplanar points do not necessarily have to be in a straight line, as long as they all lie on the same plane.

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Answer:

here is how to solve the math problems with sales tax and discount:

a) To find the total bill, we need to add the purchase price and the sales tax. To find the sales tax, we need to multiply the purchase price by the sales tax rate. The purchase price is the sum of the prices of the two pairs of shoes, which is $37 + $42 = $79. The sales tax rate is 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 79 = $5.53. The total bill is 79 + 5.53 = $84.53.

b) To find the discounted price, we need to subtract the discount from the original price. To find the discount, we need to multiply the original price by the discount rate. The original price is the same as the purchase price in part a, which is $79. The discount rate is 25%, which as a decimal is 0.25. So, the discount is 0.25 x 79 = $19.75. The discounted price is 79 - 19.75 = $59.25. To find the total bill with the coupon, we need to add the sales tax to the discounted price. The sales tax rate is still 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 59.25 = $4.15. The total bill with the coupon is 59.25 + 4.15 = $63.40.

I hope this helps!

Step-by-step explanation:

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 12 = 24

Then the value of x will be,

→ 2x + 12 = 24

→ 2x = 24 - 12

→ 2x = 12

→ x = 12 ÷ 2

→ [ x = 6 ]

Hence, option (d) is correct.

The expression can be written as ⁴√y. The solution has been obtained by solving the radical expressions.

What are radical expressions?

A square root-containing expression is referred to as a radical expression. When a root other than a square root is being represented, the radical sign's 'V'-shaped component will have a superscript number.

We are given expression as y to the three fourths power, all over y to the one half power. This can be written as

[tex]\frac{y^{3/4}}{y^{1/2} }[/tex]

We know that

cᵃ ÷ cᵇ = cᵃ⁻ᵇ

So, using this we get

[tex]y^{3/4 - 1/2[/tex]

[tex]y^{1/4[/tex]

Since, we have to represent this in the radical form, we know that

b[tex]^{1/a}[/tex] = ᵃ√b

So, using this we get

[tex]y^{1/4[/tex] = ⁴√y

Hence, the expression can be written as ⁴√y.

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We can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

What is Division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse operation of multiplication and is represented using the division symbol ÷ or the forward slash /.

Solution:

To estimate how many more megawatt hours were generated from wind in 2020 than in 2016, we need to make some assumptions and approximations since the problem only provides data for 2009 and 2017.

Assuming that the wind energy generation continued to increase at the same constant rate between 2017 and 2020, we can estimate the amount of wind energy generated in 2020 as follows:

1. From 2009 to 2017, the wind energy generation increased by 254 million - 74 million = 180 million megawatt hours.

2. The time period between 2009 and 2017 is 8 years, so the average annual increase in wind energy generation is 180 million / 8 years = 22.5 million megawatt hours per year.

3. Therefore, we can estimate the wind energy generation in 2020 as 254 million + 3 years x 22.5 million = 322.5 million megawatt hours.

4. Similarly, we can estimate the wind energy generation in 2016 as 74 million + 7 years x 22.5 million = 224.5 million megawatt hours.

5. The difference in wind energy generation between 2020 and 2016 is then:

322.5 million - 224.5 million = 98 million megawatt hours.

Therefore, we can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

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90 kilograms(kg) are about equivalent to 198.416 lbs (pounds).

To convert 90 kilograms to pounds, you may use the conversion factor of 2.20462 pounds per kilogram. 90 divided by 2.20462 results in:

90 kg x 2.20462 pounds per kilogram = 198.416 pounds (rounded to three decimal places)

= 198.416 lbs

Kilogram (kg) and pound (lbs) are units of mass or weight. The kilogram is the base unit of mass in the International System of Units (SI), while the pound is a commonly used unit of mass or weight in the imperial system of measurement.

One kilograms is equivalent to 2.20462 pounds. Conversely, one pound is approximately equal to 0.453592 kilograms. To convert from kilograms to pounds, you can multiply the number of kilograms by 2.20462, and to convert from pounds to kilograms, you can divide the number of pounds by 2.20462.

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The rate of change of the area is equal to -3 * 8^2 = -12.694 in2/min.

The rate of change of the area is the rate at which the area is increasing or decreasing over a given period of time. It is calculated by taking the difference between the initial and final area values and dividing it by the amount of time it took for the change to occur.

For example, if the area of a square increases from 10 square meters to 12 square meters over a period of two days, then the rate of change of the area would be (12-10)/2 = 1 square meter per day.

The rate of change of the area of a circle is equal to the negative of the product of the rate of change of the radius and the square of the radius. The rate of change of the radius is given as -3 inches per minute, and the radius is given as 8 inches. So, the rate of change of the area is equal to -3 * 8^2 = -12.694 in2/min.

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To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.

Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.

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Answer:

they’re both negative to -4.5 is the answer

Step-by-step explanation:

Answer: They’re both negative to -4.5 is the answer

Step-by-step explanation:

The heart-shaped curve traced around a point on the circumference of a circle rolling completely around an equal fixed circle is called a "Cardioid."

A cardioid is a mathematical curve that is formed by tracing a point on a circle that rolls around another fixed circle. The term "cardioid" is derived from the Greek word "kardia," which means heart, as the curve resembles the shape of a heart. The cardioid curve has several interesting properties, including symmetry about a line called the "polar axis." The curve also has a "cusp" at the bottom point of the heart shape, where the curve changes direction abruptly. The length of the curve is four times the diameter of the rolling circle. Cardioids have applications in a variety of fields, including mathematics, physics, and engineering. They are used in the design of certain types of antennas, in the analysis of fluid flow, and in the study of planetary motion. They also have applications in the creation of heart-shaped designs in art and decoration. In summary, a cardioid is a heart-shaped curve that is formed by tracing a point on the circumference of a circle that rolls completely around an equal fixed circle. It has unique properties and applications in a variety of fields.

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The converted value in the standard form using grams to pounds representing the mass is given by 400 grams = (0.881849 ) pounds.

Standard form  to relates these two given quantities of mass grams and pounds is equal to  :

One gram is equivalent 0.00220462 pounds.

Now, substitutes the standard relation between the grams and the pounds to calculate the required value,

1 gram = 0.00220462 pounds

⇒ 400 grams = ( 400 ) × ( 0.00220462 ) pounds

⇒ 400 grams = ( 0.881849 ) pounds

Therefore, the converted value of 400 grams into the pounds as per standard norms is written as  ( 0.881849 ) pounds.

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The value of f(-7) in the given function, f(x) = -x^2 + 2x + 6, is -57

From the question, we are to determine the value of f(-7) in the given function

The given function is

f(x) = -x^2 + 2x + 6

To find the value of f(-7) in the given function,

We will substitute -7 for x in the expression for f(x) and evaluate the resulting expression

That is,

f(x) = -x^2 + 2x + 6

f(-7) = -(-7)^2 + 2(-7) + 6

Simplifying this expression gives:

f(-7) = -49 - 14 + 6

f(-7)= -57

Hence, the value of f(-7) is -57

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The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A fraction is a mathematical concept that represents a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator over a denominator, separated by a horizontal line, such as 1/2, 3/4, or 7/8.

Given that the volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively.

Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock = [tex]\pi r^2_ch_c[/tex]

Volume of Ptolemy's clock = [tex]\pi r^2_ph_p[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock.

We are given that after 2 hours of draining, both clocks have the same water height.

Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

hc/hp = [tex](r_p/r_c)^2 * (5/4)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]r^2_ch_c/2 = r^2_ph_p[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]h_c - (3/4)h_c = (1/4)h_c[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]h_p - (3/5)h_p = (2/5)h_p[/tex]

hp= 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

hp/hc = 1/10/(1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

hc/(2/5)hp = (1/4)/(2/5)(1/10)

= 5/4.

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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