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The measure of angle ∠B in triangle ABC will be 35.89°.

Given that:

Sides, AC = 23 miles and AB = 22 miles

Angle, ∠A = 110°

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

23 / sin C = BC / sin 110° = 23 / sin B

The value of BC is calculated as,

BC² = AB² + AC² - 2 AB·AC cos A

BC² = 22² + 23² - 2 x 22 x 23 x cos 110°

BC² = 1359.124

BC = 36.87 miles

The value of angle B is calculated as,

36.87 / sin 110° = 23 / sin B

sin B = 0.586

∠B = 35.89°

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4,396 flowers are needed to surrond the circular garden.

We know that the circumference of a circle of radius R is:

C = 2*3.14*R

Here the radius is 175ft, then the circumference is:

C = 2*3.14*175ft = 1,099ft

And we know that:

1ft = 12in

Then the circumference in inches is:

1,009*12 in = 13,188 in

If each flower is separated by 3 inches, the number needed is:

13,188 in/3in = 4,396 flowers.

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Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

Complementary angles are defined as two angles whose sum is 90 degrees.

Complementary angles sum up to 90 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Therefore, the sum of the angles is 180 degrees.

Let's find the angles that are supplementary or complementary to the highlighted angles.

Therefore,

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

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So the measure of angle HLK is 45 degrees.

In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.

Here,

Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.

By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,

measure of angle HLK = 1/2 * measure of arc HK

= 1/2 * 90°

= 45°

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The number of hours it will take to complete the resurfacing project is:

51 hours

We are told that the department of  transportation is resurfacing 12. 75 miles of roadways in Collin County.

Now, we are also given that:

Number of miles completed each hour = 1/4 mile in section = 0.25 mile per hour

Thus, the number of hours it will take to complete the resurfacing project is:

That would be 12.75 divided by 0.25 hours

= 12.75/0.25

= 51 hours

Thus, we conclude that is the total time it will take to complete the project

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a) The fraction of all the meal combinations which have at least one vegan option is 1/8.

b) There are 168 different three-course meal combinations available.

A fraction is a way of representing a part or a ratio of a whole, using a numerator and a denominator separated by a slash ("/") or a horizontal line. The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts that make up the whole.

According to the given information:

a) To work out the fraction of all the meal combinations which have at least one vegan option, we need to count the total number of meal combinations with at least one vegan option, and then divide it by the total number of meal combinations.

The vegan options in the table are:

Mozzarella salad (V)

Cheese pizza (V)

Aubergine curry (V)

There are a total of 4 salads (including the vegan salads) and 6 mains (including the vegan mains). So the total number of meal combinations without any restriction is 4 x 6 = 24.

Now, we can calculate the total number of meal combinations without any vegan option, which is 24 - 3 = 21 (since 3 options are vegan).

So, the fraction of all the meal combinations which have at least one vegan option is (total meal combinations - meal combinations without any vegan option) divided by total meal combinations:

= (24 - 21) / 24

= 3 / 24

= 1 / 8

Therefore, the fraction of all the meal combinations which have at least one vegan option is 1/8.

b) If diners also choose one of 7 dessert options, we can simply multiply the total number of meal combinations (24) by the number of dessert options (7) to get the total number of three-course meal combinations available:

24 x 7 = 168

So, there are 168 different three-course meal combinations available.

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Answer:

Step-by-step explanation:

A cuz if we do 7-9=1 and he has one pound of each

The length of the radius of the cylinder with a volume of 490π cubic inches and a height of 10 inches is 7 inches.

The formula for the volume of a cylinder is V = πr²h,in which r= radius , h= cylinder height. Now we can rearrange formula by equating for r which gives the following formula:

V = πr²h

r² = V/(πh)

r = √(V/(πh))

By putting the values in the formula we can get:

r = √(490π/(π*10))

r = √49

r = 7

Therefore, the length of the radius is 7 inches.

Cylinder's volume can be viewed as the area that it takes up. It is computed by dividing the cylinder's height by the base's area, which is a circle. In this instance, we are informed that the height is 10 inches and the capacity is 490 cubic inches.

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The initial exercise time is 30 minutes, so the y-intercept of the line is 30. The athlete increases their exercise time by 3 minutes each day, which means the slope of the line is 3. The correct answer is option: A.

We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the first day's exercise time as our point, we get (1, 30) as our (x1, y1) values. Substituting these values into the point-slope form and simplifying, we get y - 30 = 3(x - 1), that  is option A. Hence option A is correct.

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The circumferences and areas of the circles are listed below:

Case 2: s = 54.689 cm

Case 3: 16257.980 ft²

Case 4: 26.999 mm

In this problem we need to determine the circumference and the area of the circle, whose equations are introduced below:

Circumference

s = 2π · R

Area

A = π · R²

Where:

Case 2 (A = 238 cm²)

R = √[(238 cm²) / π]

R = 8.704 cm

s = 2π · (8.704 cm)

s = 54.689 cm

Case 3 (s = 452 ft)

R = (452 ft) / 2π

R = 71.938 ft

A = π · (71.938 ft)²

A = 16257.980 ft²

Case 4 (A = 58 mm²)

R = √[(58 mm²) / π]

R = 4.297 mm

s = 2π · (4.297 mm)

s = 26.999 mm

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Based on the information we can infer that the area of the figure is 464 ² units.

To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:

Now we must find the area of the non-grid regions and subtract them from the area we found previously:

576 - 112 = 464 units ²

According to the above, the area of the figure is 464 units ²

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On solving the provided query we have Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

The facts (3) ABCD and AB are insufficient to demonstrate that ABCD is a parallelogram.

The diagonals are bisected by each other, which is a characteristic of parallelograms, according to statement (1).

According to statement (2), opposing sides of a parallelogram are congruent and parallel, which is another characteristic of parallelograms.

Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

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Answer:

(-13.82, ∞)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable X on one side of the equation. First, we can subtract 3.8 from both sides of the inequality, which gives us:

X > -10.02 - 3.8

Simplifying this expression, we get:

X > -13.82

Therefore, the solution set for this inequality is all the values of X that are greater than -13.82. In interval notation, we can write the solution set as (-13.82, ∞).

Answer:

An equivalent equation would be 2x = 4.

Step-by-step explanation:

Expanding the brackets and simplifying, we get:

8x + 4 - 3x + 6 = 20

Combining like terms, we get:

5x + 10 = 20

Subtracting 10 from both sides, we get:

5x = 10

Dividing both sides by 5, we get:

x = 2

So an equivalent equation would be 2x = 4.

Answer:

The equivalent equation to 4(2x+1)-3(x-2)=20 is 5x+11=20

Step-by-step explanation:

Hence, the  equivalent expression  of 8(m + 4) is 8 m + 32.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Two  expressions are equivalent  if they can be simplified to the same  third expression or if one of the expressions can be written like the other. In  addition, you can also determine if two expressions are equivalent when values are substituted in for  the variable and both arrive at the same answer.

we  know  that,  the  distributive  property of multiplication over addition,

that  is  a(b + c) = ab + ac.

So, apply  this  property in  8(m + 4),

than we get:

8(m + 4) = 8 m + 8(4)

8(m + 4) = 8 m + 32

Therefore,  the  equivalent  expression  for 8(m + 4) is 8 m + 32.

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Answer: Im gonna guess and say its c

Step-by-step explanation:

The calculated value of the logarithmic expression log(a⁵b⁵/c⁸) is 69

From the question, we have the following parameters that can be used in our computation:

log a = 9

log b = -8

log c = -6

The expression to calculate is given as

log(a⁵b⁵/c⁸)

When the expression is expanded using product and quotient rules, we have

log(a⁵b⁵/c⁸) = loga⁵ + logb⁵ - logc⁸

Apply the power rule of logarithm to rewrite as

log(a⁵b⁵/c⁸) = 5loga + 5logb - 8logc

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

log(a⁵b⁵/c⁸) = 5 * 9 + 5 * -8 - 8 * -8

Evaluate

log(a⁵b⁵/c⁸) = 69

Hence, the value of the logarithmic expression log(a⁵b⁵/c⁸) is 69

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Answer:

Step-by-step explanation:

This graph represents the line of best fit for some dataset.

It is reduced to a linear function in this instance with a constant slope, where x represents the independent variable and y, the dependent variable. This shows us quiz score is supposedly directly proportional to the time spent on homework per week in hours.

To find the amount of time someone should expect to study to get a 96% on their quiz you need to resolve the linear function modeled by y=mx+b which is in slope-intercept form. where m is the slope and b is the y-intercept. the y-intercept can be found when x = 0  which is shown in the graph to be 63, to solve for slope you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] which is rise/ run. then plug in any 2 points I will use (1,69) and (2,75) [tex]\frac{75-69 }{2-1 }[/tex] or 6 which means m = 6, therefore, our equation is y = 6x + 63 and because we know that y must be 96 for this question, we can solve for x using inverse operations. 96 = 6x + 63 subtract 63 from both sides and 6x = 33 then divide by 6 and 33/6 = 5.5 so a person should expect to study 5.5 hours to get a quiz score of 96%

Answer:  

Distant with current is 30, distance against current is 24.

Rate with current is 6, rate against current is 4.

Time with current is 8 hours, time against current is 14

Step-by-step explanation:  

2nd question answer: 24 - 6x = 8.

Answer:0.00000221

Step-by-step explanation:

Move the decimal place 6 times

Answer: Symbol max-min and answer 10-4

Step-by-step explanation:

The length of ZW is 45 inches.

A parallelogram is a member of quadrilateral which has a pair of opposite sides to be equal, and a pair of slant opposite sides.

In the given information, we have;

WX = YZ (a pair of opposite side of a parallelogram are equal)

2x + 15 = 4x - 21

collect like terms,

21 + 15 = 4x - 2x

36 = 2x

x = 36/2

x = 18

So that;

WX = 2x + 15

      = 2(18) + 15

WX = 36 + 15

      = 51

XY = x + 27

     = 18 + 27

     = 45

Therefore,

ZW = XY  (a pair of opposite sides are equal)

ZW = 45

The length of ZW is 45 inches.

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Answer:

 92.5°

Step-by-step explanation:

You want the angle where chords cross, given that they intercept arcs of 55° and 130°.

The angle x° is the average of the measures of the intercepted arcs:

  x° = (55° +130°)/2

  x° = 92.5°

We can expand 12.907.054 as 1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1.

To expand a decimal number by showing each digit by value, we need to break it down into its place values. For example, in the number 12.907.054, the first digit to the left of the decimal point is in the billions place, the second digit is in the hundred millions place, and so on.

So, we can expand 12.907.054 as follows:

1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1

This means that 12.907.054 can be written as the sum of its place values. The first digit to the left of the decimal point is worth 10 billion, the second digit is worth 1 billion, and so on until we reach the ones place.

Expanding a decimal number by showing each digit by value is a way to better understand the place values of each digit and to break down the number into smaller parts for easier analysis.

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The water property that explains why the air temperature significantly changed but the water temperature stayed relatively the same is the property of specific heat.

Water's high specific heat capacity allows it to absorb and retain heat energy without much change in temperature, explaining why its temperature did not shift despite significant changes in the air temperature. Air has low specific heat capacity, while water has high.

Therefore, This caused the stream water temperature to remain stable despite environmental changes. Air temps change quickly due to its lower heat capacity.

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The side length of the juice box is given as follows:

5 cm³.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

The total volume of the box in this problem is given as follows:

55 + 40 + 30 = 125 cm³.

Hence the side length of the juice box is given as follows:

a³ = 125

a³ = 5³

a = 5 cm.

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The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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Answer: y - 2 = 2(x - -3)

The slope is 2 is you find the intercept.

Step-by-step explanation:

:)

Answer:

a maybe

Step-by-step explanation: