Find the angle of elevation of the sun from the ground, when a tree that is 11yrds tall casts a shadow 10yrds long

The statements which are correct about the equation 3(x - a) = 3x - 6 are;

According to the task content; the equation which is to be considered is;

3(x - a) = 3x - 6

Therefore, it follows from the distributive property that we have;

3x - 3a = 3x - 6

Therefore

On this note, the true statements are as indicated above.

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The team attempted 30 three-point shots.

Let x be the number of three-point shots the team attempted.

We know that the team attempted 50% more two-point shots than three-point shots, so the number of two-point shots is 1.5x.

We also know that 50% of the two-point shots were successful and 40% of the three-point shots were successful, so we can set up the following equation:

(1.5x)(0.5) + (x)(0.4) = 54

Solving for x yields x = 30.

Therefore, the team attempted 30 three-point shots.

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let's firstly get its equation and then find the x-intercept, keeping in mind that the x-intercept occurs when y = 0.

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 2}(x-\stackrel{x_1}{3}) \qquad \implies\quad \stackrel{\textit{setting y = 0}}{0-4=-2(x-3)} \\\\\\ -4=-2x+6\implies -10=-2x\implies \cfrac{-10}{-2}=x\implies 5=x~\hfill \boxed{\stackrel{x-intercept}{(5~~,~~0)}}[/tex]

Answer:

Each soccer ball cost $12.20

Step-by-step explanation:

183/15 = 12.20

The logarithmic function  [tex]f(x)=\log _{x} b[/tex] is the inverse of the exponential function [tex]g(x)= b^{x}[/tex].

The logarithm function is of the form [tex]f(x)=\log _{x} b[/tex] where [tex]x[/tex] is the base and [tex]b > 0[/tex].
The exponential function is of the form [tex]g(x)= b^{x}[/tex] where [tex]x[/tex] represents variable and [tex]b[/tex] represents constant. [tex]b[/tex] is also called the base of the function and must be greater than 0.
The inverse of a function exists if and only if the function is one-one and onto function. When the function has inversed the range of the function changes to the domain of the inversed function and the domain of the function changes to the range of the inverse function.

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Step-by-step explanation:

7(4n−6)=6+4(4+3n)

Step 1: Simplify both sides of the equation.

7(4n−6)=6+4(4+3n)

(7)(4n)+(7)(−6)=6+(4)(4)+(4)(3n) (Distribute)

28n+−42=6+16+12n

28n−42=(12n)+(6+16) (Combine Like Terms)

28n−42=12n+22

Step 2: Subtract 12n from both sides.

28n−42−12n=12n+22−12n

16n−42=22

Step 3: Add 42 to both sides.

16n−42+42=22+42

16n=64

Step 4: Divide both sides by 16.

[tex]\frac{16n}{16} = \frac{64}{16}[/tex]

n=4

Answer: 48°

Step-by-step explanation:

       We know that the angles of a triangle are equal to 180 degrees when added together. Using this logic, we will create an equation to solve for x. Then we will substitute this value of x back into the expression for angle F.

   Given:

E + D + F = 180°

   Substitue:

(8x - 18)° + (6x - 4)° + (5x - 7)° = 180°

   Reorder and combine like terms:

8x° + 6x° + 5x° - 18° - 4° - 7° = 180°

19x° - 29° = 180°

   Add 29 to both sides of the equation:

19x° = 209°

   Divide both sides of the equation by 19:

x = 11

   Substitute this value of x into the expression for angle F:

(5x - 7)°

(5(11) - 7)°

(55 - 7)°

48°

1) The next number in the series 99, 33, 11, 11/3, 11/9, . . . is 11/27

The correct answer is an option (c)

2)  In the given group the smallest amount is .18

1.

We have been given a sequence of numbers 99, 33, 11, 11/3, 11/9,. . .

We need to find the next number in given sequence .

We can observe that given series is geometric sequence with the first term a₁ = 99 and the common ratio r = 1/3

We know that the formula for the n-th term of gemetric sequence is:

an = a₁ × r^(n - 1)

For n = 6,

a₆ = 99 × (1/3)⁽⁶ ⁻ ¹⁾

a₆ = 99 × (1/3)⁵

a₆ = 11/27

Hence, the next number in the series is 11/27

2.

If we arrange the numbers in ascending order then it would be,

0.18, 0.59, 0.7, 3, 6, 15

So, the smallest amount is .18

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The leaf representation is given as

              14 l

              15 l 1447

              16 l 56

              17 l 8

              18 l 366

The 10th means that after the decimal, So the foundation must be the 15.1. This will be the 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

In order to help visualize the shape of a distribution, a stem-and-leaf display or stem-and-leaf plot is a tool for presenting quantitative data in a graphical manner, comparable to a histogram.

The adoption of monospaced (typewriter) typestyles during that period contributed to their appeal since they made it simple for then-current computer technology to create the images. The improved graphic capabilities of modern computers have reduced the employment of these techniques.

While a stemplot is another name for a stem-and-leaf plot, it frequently refers to a different kind of chart. The term "simple stem plot" may refer to the mapping of a matrix of y values to a common x axis, along with the identification of the common x value by a vertical line and the individual y values by symbols on the line.

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Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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The other side length is √20 after applying the Pythagoras and other two sides are 2 and 2√3.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

One side length = 2

Other side length = 2√3

Apply Pythagoras

x^2 = 2^2 + (2√3)^2

x^2 = 4 + 12

x = √20

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Implementing a new system into an organization module by module is called a​ phased approach.

A phased approach is one of two common methods used to develop an ERP system solution. In this strategy, the system's functionalities are introduced in a certain order, gradually replacing previous systems and processes.

This frequently indicates that a business starts off with core functionality that is given top attention, and then other applications are gradually added in stages over time. An alternative implementation strategy, however, uses an all-at-once model in which the system and all apps "Go Live" simultaneously.

The optimal implementation plan for your firm will depend on the needs, goals, and strategies you have for it. This might involve a hybrid strategy where crucial functionality is added to the core ERP programs first, and then desirable features are added later on in a staged implementation. By considering all of your options, your firm can decide which will serve its interests the most effectively.

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Answer: The meaning of the statement “ x vary inversely as y “ is “x is inversely proportional to y".

Final Answer // x=5yx is equal to 5 over y

Step-by-step explanation:

The scale of the map is 1 dm : 25 km

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

Mathematical statement

The mathematical statement is given as

50 km in real distance is 2dm on a map

The scale is then calculated as

Scale = Map distance :  Actual distance

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

Scale = 2 dm : 50 km

Divide by 2

Scale = 1 dm : 25 km

Hence, the scale is 1 dm : 25 km

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Answer:

Step-by-step explanation:

Here are a few tips for quickly dividing large numbers and decimals:

Use estimation: Estimate the quotient by rounding the dividend and divisor to easy numbers. This can save time and give you a rough idea of the answer.

Use long division: This method can be used to divide larger numbers, and it involves breaking down the dividend into smaller parts, dividing each part by the divisor, and then combining the results.

Use a calculator: A calculator can quickly divide large numbers and decimals, and it eliminates the need for long division or estimation.

Use the reciprocal: Dividing by a number is the same as multiplying by its reciprocal, so if you know the reciprocal of the divisor, you can use it to quickly divide any number.

Use mental math: If you are comfortable with mental math and good at it, you can use it to quickly divide numbers. This can help you to quickly divide large numbers and decimals.

Use the method of repeated subtraction or shifting the decimal point: Instead of dividing by repeatedly subtracting the divisor from the dividend or shifting the decimal point, this method can also be used to divide large numbers and decimals.

Practice: The more you practice dividing large numbers and decimals, the better and faster you will get at it.

Answer:

calculator. the one I usually use is the casio fx-97SGX

Answer:

b = 2sqrt(5)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

4^2 + b^2 = 6^2

16+b^2 = 36

b^2 = 36-16

b^2 = 20

Taking the square root of each side

sqrt(b^2) = sqrt(20)

b = sqrt(20)

b = sqrt(4*5)

b = sqrt(4) sqrt(5)

b = 2sqrt(5)

b = 2sqrt(5)

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

4^2 + b^2 = 6^2

16+b^2 = 36

b^2 = 36-16

b^2 = 20

Taking the square root of each side

sqrt(b^2) = sqrt(20)

b = sqrt(20)

b = sqrt(4*5)

b = sqrt(4) sqrt(5)

b = 2sqrt(5)

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The x-intercept of the line 18x – 5y = 12 is 2/3

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

A linear equation

The linear equation is represented as

18x–5y=12

Express properly

So, we have the following representation

18x – 5y = 12

Set y to 0 to determine the x-intercept of the line

So, we have the following representation

18x – 5 * 0 = 12

Evaluate the products

18x = 12

Divide by 18

So, we have

x = 12/18

Simplify

x = 2/3

Hence, the intercept is 2/3

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The larger side of the rectangle is 70 cm and the area is 3150 cm²

A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also, opposite sides are parallel and of equal length.

Given that, the sides of a rectangle are in the proportion 9:14 and the perimeter of the rectangle is 230 cm

Let the smaller side of the rectangle be 9x and larger side be 14x

We know that the perimeter of a rectangle = 2(l+w)

Therefore, perimeter = 2(9x+14x)

2(9x+14x) = 230

2×23x = 230

2x = 10

x = 5

Therefore, the smaller side of the rectangle is 45 cm and larger side is 70 cm

Area of a rectangle = (l×w)

Area = 70×45 = 3150 cm²

Hence, required answers are 70 cm and 3150 cm²

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On solving the provided question, we can say that  let the equation be  X =   4ª - 4(2) (-8) => X = -15

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let the equation be

X =   4ª - 4(2) (-8)

here, a = 0

X = 1 - 8-8

X = -15

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The given triangles are congruent due to the congruent postulate AAS.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given figure,

In ΔCDE and ΔABF has :

m∠C = m∠A

m∠D = m∠B

side DC = side AB

According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Hence, ΔCDE ≅ ΔABF

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Answer:

my answer is one

Step-by-step explanation:

I don't know why but when i ask it in my brother he is an engineer so he know that

a.

The image shows the pattern with 7 dots and 10 lines. The dots are arranged in a square, with 3 dots on each side.

b. The complete table is seen below

ci.  the expression for the number of dots in Pattern n is n + 1.\

cii.  the expression for the number of lines in Pattern n is n + 2.

d.   the 76th pattern has 77 dots and 78 lines.

(a)

b.

Pattern Number of dots Number of lines

1st                            2                   4

2nd                            3                  5

3rd                              5                 7

4th                               7        10

5th                             9                13

6th                            11                16

7th                           13               19

8th                           15             22

9th                          17              25

10th                           19              28

(c)

(i) The pattern of dots in Pattern n can be found by adding 1 to the number of lines in Pattern n - 1 and  the expression for the number of dots in Pattern n is n + 1.

(ii) The number of lines in Pattern n can be found by adding 2 to the number of lines in Pattern n - 1 and  the expression for the number of lines in Pattern n is n + 2.

(d)

If a pattern has 76 lines, then it is the 76th pattern in the sequence. So, n = 76.

The number of dots in the 76th pattern is 76 + 1 = 77.

The number of lines in the 76th pattern is 76 + 2 = 78.

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Domain of the given graph is {x/-4≤x≤4}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain of a function or relation is the set of all possible independent values the relation can take.

The graph is passing through the points (4, 0)(-4, 0)(0, 1) and (0, -1)

Four comma zero, minus four comma zero, zero comma one and zero comma minus one.

The x is between -4 and 4

The domain of the given graph is {x/-4≤x≤4}

Hence, domain of the given graph is {x/-4≤x≤4}

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A cylindrical basin is 2 feet tall and has a diameter of 5 feet, as shown. If the basin is completely filled with water, how much water will it hold? Round the answer to the nearest tenth of a foot.

The basin holds 39.3 cubic feet of water.

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc. Let us see the formula used to calculate the volume of a cylinder. We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr2. Thus, the volume (V) of a right circular cylinder, using the above formula, is,

V = πr²h

Here,

⇒ 'r' is the radius of the base (circle) of the cylinder

⇒ 'h' is the height of the cylinder

⇒ π is a constant whose value is either 22/7 (or) 3.142.

Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.

We are given that the height of the basin h = 2 ft and the diameter = d = 5 ft.

So, radius r = d/2 = 5/2 = 2.5 ft

The amount of water the basin holds is equal to the volume of cylindrical basin.

Volume =πr²h

=3.1416×2.5²×2

=39.27 cubic feet

= 39.3 cubic feet

Thus, the basin holds 39.3 cubic feet of water.

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Answer:

3rd option ==> 5/4

Step-by-step explanation:

5x/4 means that for every time x increases by 1, y increases by 5/4.

5/4 is the coefficient for x.

Answer:

[tex]\dfrac{5}{4}[/tex]

Step-by-step explanation:

The general slope-intercept form of a line equation is

[tex]y = mx + b[/tex]

where m is the slope and b the y-intercept

The given line has the equation:
[tex]y = \dfrac{5}{4}x - \dfrac{7}{4}[/tex]

Comparing the general equation to this equation tells us that the slope

[tex]\textr{m } = \dfrac{5}{4}[/tex]

and y-intercept

[tex]b = -\dfrac{7}{4}[/tex]

We have depicted the function f(x).

If the function is stretched vertically by a factor of 5 -> 5f(x).

If the function is shrunk horizontally by a factor of 5 ->  f(5x).

If the function is shifted to the right five units -> f(x) - 5

If the function is shifted to the down five units -> f(x - 5)

If the function is shifted to the up five units -> f(x) + 5

If the function is shifted to the right five units -> f(x + 5)

What is a function?

A function is a mathematical relationship between a set of inputs, known as the domain, and a set of outputs, known as the range. In other words, it's a rule that assigns a unique output to each input.

If the function is stretched vertically by a factor of 5 -> 5f(x).

If the function is shrunk horizontally by a factor of 5 ->  f(5x).

If the function is shifted to the right five units -> f(x) - 5

If the function is shifted to the down five units -> f(x - 5)

If the function is shifted to the up five units -> f(x) + 5

If the function is shifted to the right five units -> f(x + 5)

Hence, we have depicted the function f(x).

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In a regression analysis, the error term ε is a random variable with a mean or expected value of zero. The correct option is a.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Given:

Analysis is a regression analysis.

And the error term in regression analysis:

The error term, which refers to the total of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

ε = Epsilon or error term.

The variation in the dependent variable that the independent factors do not explain is taken into account by the error term.

The values of the error term should be determined by random chance.

The average value of the error term must be equal to zero in order for your model to be impartial.

Therefore, error term is zero.

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McCandless weighed a hundred and forty pounds when he died.

It was apparent that McCandless had been deceased for nineteen days based on a mysterious journal that was discovered among his belongings.

According to a driver's license that was granted eight months before he passed away, he was 24 years old and weighed 140 pounds. After being taken out of the woods, his body underwent an autopsy, which found that it weighed only 66.7 pounds and had no subcutaneous fat that could be seen.

The coroner's findings said that malnutrition was the death's most likely cause.

Thus, McCandless weighed a hundred and forty pounds when he died.

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McCandless weigh when he died is at the amount of sixty-seven pounds.

The term weigh in math is defined as the measure of the force of gravity on an object and the mass of an object will never change, but the weight of an item can change based on its location.

Here we have know that the driver's license issued eight months before he perished indicated that he was twenty-four years old and weighed a hundred and forty pounds. Therefore his body was flown out of the wilderness, and at the time of autopsy determined that it weighed sixty-seven pounds and lacked discernible subcutaneous fat and the cause of death was officially reported as starvation.

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The multiplication of the fraction 6 2/3 × 3 6/7 is 25 5/7 as a mixed number in simplest form.

Fraction refers to a number which consists of a numerator and a denominator. A numerator is the upper value of a fraction while a denominator is the lower value of a fraction.

6 2/3 × 3 6/7

= 20/3 × 27/7

= (20 × 27) / (3 × 7)

Multiply the numerator and denominator respectively.

= 540 / 21

= 25 15/21

It can also be written in simplest form as;

= 25 5/7

Therefore, 25 5/7 is the result of the multiplication of the fraction 6 2/3 × 3 6/7 in its simplest form

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Answer:

-18.66666666666667

Step-by-step explanation: