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The height of the board up the side of the building is 7.5 feet.

An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 degrees.

The height of the board to the side of the building can be calculated as follows:

Therefore, the situation forms a right-angle triangle.

Using trigonometric ratios,

sin 70° = opposite / hypotenuse

sin 70° = x / 8

cross multiply

x = 8 sin 70°

x = 8 × 0.93969262078

x = 7.51754096629

Therefore,

distance of the board up the building  = 7.5 feet

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From probability of occurence of events the large box holds 180 hats.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows

Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Here we have 60 hats in the mall box.

And a large box holds 180% as many hats as the mall box is given.

So, 180/100 ×60 = 180

Therefore, from probability of occurence of events the large box holds 180 hats.

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There are eight perfect squares from 1 to 100 (i.e., except 1 and 100). They are represented as 4, 9, 16, 25, 36, 49, 64 and 81.

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, we can say that a perfect square is a number that can be expressed as the product of an integer by itself or as the second power of an integer. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then N can be represent as the product of x and x = x². So, the perfect square formula formula is , N = x². For example, If x = 3, and N = x². This means, N = 3× 3 = 3² = 9 . Here, 9 is a perfect square because it is equal to the square of a whole number, 3. We have to determine the number of perfect squares from 1 to 100.

1² = 1 ; 2² = 4 ; 3² = 9 ; 4² = 16 ; 5² = 25 ; 6² = 36 ; 7² = 49 ; 8² = 64 ; 9² = 81 ; 10² = 100

As we get, there are 10 perfect squares from 1 to 100. But, in actual manner they are only 8 perfect squares from 1 to 100 after excluding 1 and 100.

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To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.

The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.

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Answer:

There are 150 pounds of Candy Corn and 350 pounds of Candy Pumpkins in the mixture.

The conjecture for the relationship between the volume of the two spheres is "the volume of a sphere with radius 2y is 8 times greater than the volume of a sphere with radius y."

A conjecture is an educated guess or a hypothesis about a mathematical statement that has not yet been proven. It can be based on patterns or observations and can lead to further exploration and eventually a proof or disproof.

The formula for the volume of a sphere is given by (4/3)πr³, where r is the radius of the sphere. To compare the volumes of two spheres with different radii, we can substitute their respective radii into the formula.

If we let the radius of one sphere be y, then the volume of that sphere can be represented as (4/3)πy³. If we let the radius of the other sphere be 2y, then the volume of that sphere can be represented as (4/3)π(2y)³. Dividing the latter by the former, we get (4/3)π(2y)³ / (4/3)πy³ = (2y)³ / y³ = 8.

Thus, the volume of a sphere with a radius equal to 2y is 8 times greater than the volume of a sphere with a radius equal to y.

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The distance between the two points (-3, 2) and (3, 5) is approximately 6.71 units.

The distance between two points in a plane can be found using the distance formula. The distance formula is given by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

In this case, the points are (-3, 2) and (3, 5)

So, the distance between the two points is:

distance = √((3 - (-3))² + (5 - 2)²)

distance = √(6² + 3²)

distance = √(36 + 9)

distance = √(45)

distance = 6.7082039

So the distance between the points (-3,2) and (3,5) is approximately 6.71

It is worth mentioning that the distance formula is used to calculate the distance between two points in a 2D space, it is also called the Euclidean distance.

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The value of Angle ADB, which is the angle created while moving from A to D to B. Angle ABM is the angle created while moving from point A to point B to point M is [tex]41^{0}[/tex]

Due to the fact that angle ADB is an inscribed angle, its measure is halved compared to the angle of the arc that it intercepts. In other words, the angle is 40 degrees in length, which is equal to half of an 80 degree angle.

By adding up all of your balances at the end of each day for each eligible month, you may get your average daily balances (ADB) by dividing that amount by the number of days in that qualifying month.

3x - 16 = 9x + 4

4x = 20 x = 5 m

with BCE: 9 (5) + 4 = 49°

m with ADB = 41°

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The outside dimensions of the house are 11' 9" x 15' 11".

To determine the outside dimensions of the house, we need to take into account the thickness of the interior and exterior walls.First, we'll calculate the thickness of the interior walls. The interior walls are made of 2x4 (31/2") lumber with 1/2" drywall on both sides.

This means that each interior wall adds an additional 3 1/2" + 1/2" + 1/2" = 4 1/2" to the overall width and height of the house. Next, we'll calculate the thickness of the exterior walls. The exterior walls are made of 2x6 (51/2") lumber with 1/2" drywall on the interior and 7/16" siding with 35/8" brick on the exterior.

This means that each exterior wall adds an additional 5 1/2" + 1/2" + 7/16" + 3 5/8" = 8 11/16" to the overall width and height of the house. To calculate the outside dimension of the house, we will add the thickness of the interior and exterior walls to the dimensions of the interior rooms.

The outside dimension of the house will be:

Width = 11' 3" + 4 1/2" + 8 11/16" = 11' 9"

Height = 15' 7" + 4 1/2" + 8 11/16" = 15' 11"

So the outside dimensions of the house are 11' 9" x 15' 11".

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Question

The interior wall of a residence consists of a 2 × 4 (31/2") with 1/2" sheetrock on both sides. Exterior walls are 2 × 6 (51/2") construction with 1/2" sheetrock on the interior and 7/16" sheeting with 35/8" brick on the exterior. Determine the outside dimension of a house if there are two interior rooms with an interior wall. One room's dimensions I 11' 3", and Room 2 dimensions I 15' 7". How do I solve this?

Answer:

y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Since we are given x=1, we can plug that into the equation given:

-4y + [tex]\sqrt[3]{1}[/tex] = -6(1) + [tex]1^{2}[/tex]

-4y + 1 = -6 + 1

-4y = -6

y = [tex]\frac{-6}{-4}[/tex]

y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]

The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).

The given expression is 9x² - 12x + 4

By splitting the middle term, let us factor this polynomial.

To identify the factors we have to consider factors of 36 as (9 × 4)

9x²- 6x - 6x + 4

=3x(3x - 2) - 2(3x - 2)

=(3x - 2)(3x - 2)

Another example of a quadratic polynomial can be taken to demonstrate similar factorization:

x² + 9x + 20

= x² + 5x + 4x + 20

= x × (x + 5) + 4 × (x + 5)

= (x + 5)(x + 4)

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Translation, rotation, and reflection are three of the fundamental transformations.

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Solving the system of equations by the method of elimination we get

x = 7 and y = 7/3

Here we are given the system of equations:-

x - 3y = -2                                                         [1]

x + 3y = 16                                                        [2]

Since nothing is mentioned we will use the method of elimination for the question

Subtracting equation [2] rom [1] we get

-6y = -14

or, y = 14/6

or, y = 7/3

Now adding equation [1] and [2] gives us

2x = 14

or, x = 14/2

or, x = 7

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Complete Question

What is the solution to this system of linear equations

x - 3y = -2,

x + 3y = 16

Answer:

2x-2y

Step-by-step explanation:

1/3x + 2y + 5/3x - 4y

= 1/3x + 5/3x - 4y  + 2y

=6/3 x -2y

=2x-2y

The 5:3 (5 to 3) ratio of the number of Almond Joys candy to Kit kats candy, and the 40 Almond Joys candies stashed, indicates that the number of Kit kandies also received are 24 Kit Kats candies.

A ratio is an indication of the number of times one quantity is contained within another item.

The ratio of the Almond Joys to the Kit Kats = 5 : 3

The number of Almond Joys obtained = 40

The number of Kit Kats obtained can be found as follows;

The number of Almond Joys received for every 3 Kit Kats received = 5

Let x represent the total number of candies collected, we get;

[tex]\frac{5}{5+3} \times x = 40[/tex]

Therefore;

5·x = 40 × (5 + 3) = 320

x = 320 ÷ 5 = 64

The total number of candies collected = 64

The number of Kit Kats = The total number of candies collected - The number of Almonds Joys received

Therefore; The number of Kit Kats received = 64 - 40 = 24

The number of Kit Kats received = 24 Kit Kats

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You will have 24 Kit Kats based on the information given.

A ratio is defined as the comparison of two or more quantities that indicates their sizes in relation to each other.

From the information, after a long night of begging for candy, the person ended up having a decent stash of Almond Joys and Kit Kals in the ratio of 5:3.

Since Almond Joys and Kit Kats  are in the ratio of 5:3 and you had Almond Joys. Let K represent the number of Kit Kats. Then we have:

5 : 3 = 40 : K

5/3 = 40/K

5K = 3 × 40

5K = 120

K = 120/5

K = 24

Thus, you will have 24 Kit Kats

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The point that lies on the graph of the exponential function:

f(x) = 2^(x + 4) - 8

is (-2, -4)

Here we have the exponential function:

f(x) = 2^(x + 4) - 8

And we want to see which one of the given points lies on the graph of the exponential function.

To check that, we just need to replace the variable x by the first value of the ordered point and see if the function is equal to the second value.

For example, for the second point^(2, 12) we will get:

x = 2

f(2) = 2^(2 + 4)- 8

f(2) = 2^6 - 8 = 56

So we have the point (2, 56)

Now for the point (-2, -4) we will get:

f(-2) = 2^(-2 + 4) - 8

f(-2) = 2^2 - 8 = -4

So we have the point (-2, -4), this is the correct option.

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Applying the linear pair theorem, the measure of angle KJG is: 55°.

According to the linear pair theorem, if two angles lie on a straight line, they form a pair of angles whose sum is equal to 180 degrees.

In the image attached below, angles IJG and KLG are both angles on a straight line, and ate therefore equal to 180 degrees when added.

This:

Measure of angle IJG = 125°

m<KLG = 180 - m<IJG

m<KLG = 180 - 125

m<KLG = 55°

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Answer:

Image result for System with one solution 1 3 System with no solutions System with infinite number of solutions 2x 2y 8 and 3x 3y 12 3x 3y 12 and 5x 5y 10 y 4 x and y x 2

You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

Step-by-step explanation:

Answer:

1) 2x + 2y = -8 and 3x + 3y = - 12: Infinite: the lines are the same.

2) - 3x + 3y = 12 and 5x + 5y = 10: One solution (-3.10)

3) y +4 =-x and y = -x + 2: No solutions. Parallel

Step-by-step explanation:

See the attached worksheet. All three explanations are used to identify the three systems of equations. Some of the equations are equal to each other, apparent only when one rearranges the equations.

She did not find the correct solution. She graphed the bottom equation of the System incorrectly.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

According to the Problem

y = 3x - 3.....(1)

2x + 2y = 8........(2)

Substitute the value of y from equation 1 to equation 2

2x + 2(3x -3 ) = 8

2x + 6x -6 = 8

8x = 14

x = 1.75

Tus,

y = 3 * 1.75 - 3

y = 2.25

Therefore, she did not find the correct solution to the system of equations.

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The break - even point is 5.

C=15x + 150

R=45x

Here, C = R

15x + 150 = 45x

30x = 150

x = 5

The break - even point is 5

                                                 = 225

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Miguel takes 1.6 hours to cover the distance of 84.8 miles with the given speed of 53 miles per hour.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
In the question, we are given a speed = 53 miles per hour and the distance traveled with the given speed is 84.8 miles, we have to determine the time for the same distance.
We know that,
Speed = distance/time
Speed = 84.8 / 53
Speed = 1.6 hours

Thus, the required time evaluated is 1.6 hours.

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Answer:

Step-by-step explanation:

okay bc the inches is 26 so the answer is 88

bc if u subtract this 26 with this 1 its will. be 25 so add 50 to 25 it will be 88

Answer:

5%

Step-by-step explanation:

First, you do:

$2100/7 = $300

Then you do:

r x 6000 = $300

r = 300/6000 = 0.05

Finally, you do:

0.05 x 100 = 5%

So the interest rate is: 5%

The team Seahawk has a larger mean value of about 23 inches.

The three main methods for identifying the average value of a set of integers are mean, median, and mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.

The middle value in a list that is arranged from smallest to greatest is called the median.

The value that appears the most frequently on the list is the mode.

We know the mean of a data set is [tex]\frac{1}{n}\sum_{i=1}^{n} x_i[/tex].

So, The mean of Pelicans is, [tex]\frac{1}{15}\sum_{i=1}^{n} x_i[/tex].

= (1/15)×[20 + 20 + 22 + 21 + 22 + 23 + 22.5 + 24 + 21.5 + 22 + 23.5 + 22 + 23.5 + 22 + 24.5].

= (1/15)×[333.5].

= 22.23.

The mean of Seahawks is,

= (1/15)[21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23].

= 22.7.

So, Seahawks have a larger value of about 23 inches.

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The solution of the inequality is x < -50.

And we can use the substitution method to find the solution of the inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality 100 - 3x < -50.

Diego first solves the equation and sees that x = 50.

So, substituting the value of x to the inequality.

100 - 3(-50) < -50.

100 - 150 < -50

-50 < -50.

To find the solution of the inequality:

100 - 3x < -50.

-3x < -50 -100

x < - 50

Therefore, the solution of the inequality is x < -50.

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Rounded to the nearest foot, the height of the tree is 31 feet.

Height is a measurement of distance from the ground to the top of an object, such as a person, animal, or building. It is typically measured in centimeters (cm) or feet and inches. Height is an important measurement for medical professionals, as it can provide insight into a person's overall health and wellbeing.

Using the tangent formula in trigonometry, the height of the tree can be calculated as follows:
tan(angle of elevation) = Opposite/Adjacent
tan(angle of elevation) = 47/h
h = 47/tan(angle of elevation)
Therefore, the height of the tree is h = 47/tan(angle of elevation) = 47/tan(47°) = 47/1.53 = 30.78 feet
Rounded to the nearest foot, the height of the tree is 31 feet.

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Complete Question:
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is : height of the tree to the nearest foot. The height of the tree is feet. Round your answer to the nearest foot. with explanation. (And photo in question)

Answer:

s - 1 - t(s - 1)/(r + 1)

Step-by-step explanation:

x/(s - 1) + t/(r + 1) = 1

x/(s - 1) = 1 - t/(r + 1)

x = s - 1 - t(s - 1)/(r + 1)

Between these two integers the following surds lie

(1) √5 = 1-5

(2)√1 = 1-2

(3)√107 = 1-107

(4)√3​  = 1-3

There are two simple steps to surd simplification:

Split the number within the root into its prime factors. √50=√(5×5×2)

Based on the root write the prime factors, outside the root. In case of square root, write one factor outside the root, for every two similar factors within the root.

√18+√50.

Root of any whole number must always be greater than 1 as

√1 = 1

√2 = 1.41 > 1

Therefore, Between these two integers the following surds lie

(1) √5 = 1-5

(2)√1 = 1-2

(3)√107 = 1-107

(4)√3​  = 1-3

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No, the Sine law cannot be used directly on right triangles.

What is right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). The angle that measures 90 degrees is formed by two sides of the triangle, called the legs, and the third side, called the hypotenuse, is the side opposite the right angle. The legs of the right triangle are perpendicular to each other, meaning they form a 90 degree angle.

What is law of sines?

The sine law, also known as the "law of sines," is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

What is Pythagorean theorem ?

The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, can be used to solve for unknown side lengths in a right triangle. This theorem is particularly useful in trigonometry, geometry and navigation.

A right triangle is a special type of triangle that has one angle that measures exactly 90 degrees (a right angle). Since the sine law relates the lengths of the sides of a triangle to the angles, it can be used to solve for unknown side lengths or angles in a right triangle, as long as the other side lengths and angles are known.

However, it is important to note that the sine law is typically used to solve for unknowns in non-right triangles, where the angle measures are not known. In a right triangle, the Pythagorean theorem can be used instead, which relates the length of the hypotenuse to the lengths of the legs.

So, Sine law cannot be used directly on right triangles, but it can be used in solving triangles which includes right triangles as well.

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The graph that makes the increase in life expectancy from 1975-2000 appear to be relatively small is given by the following option:

b. A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.

The total increase is given as follows:

80 - 76.6 = 3.4 years.

Hence the higher the difference between the bounds of y, the smaller the difference will appear, meaning that the graph is given by option b.

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