Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer: IS easy you only need to put your answer that you got when you multiply the numbers:)

Step-by-step explanation:

Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Product of an Equation:

In mathematics, a product is a number or quantity obtained by multiplying two or more numbers. Example: 4 × 7 = 28, where the number 28 is said to be the product of 4 and 7. Another example: 6 times 4 is 24, so 6 multiplied by 4 is 24. The product of two positive numbers is a positive number, as if the product of two negative numbers is also positive (e.g., -6 × -4 = 24).

Now,

(A) We need to find the product of two given expressions.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] ×  [tex]5x^{2} -2x +6[/tex]

To multiply two given expressions, first multiply the first term in the first parenthesis by the entire expression in the second term, then do the same for the second term in the first parentheses.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]

⇒ [tex]\frac{1}{2x} * [5x^{2} -2x +6] - \frac{1}{4} * [5x^2 - 2x +6][/tex]

⇒ [[tex]\frac{1}{2x} * 5x^2[/tex] - [tex]\frac{1}{2x} *2x[/tex] + [tex]\frac{1}{2x}* 6[/tex] ] - [ [tex]\frac{1}{4} * 5x^2 + \frac{1}{4} * 2x - \frac{1}{4}*6[/tex]]

Now, simplify the equation:

[tex]\frac{5x}{2} -1 + \frac{3}{x} - \frac{5x^2}{4} +\frac{x}{2} +\frac{3}{2}[/tex]

Rearranging the equation:

[tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

Thus, the product of the two expressions is [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex].

(B) To compare the two expressions we will find the value of the two given expressions,

[tex]\frac{1}{2x} -\frac{1}{4} * 5x^{2} -2x +6[/tex] = [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

For the value of:

[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

simplifying the equation:

    [tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

⇒ [tex][\frac{1}{4x} * (5x^{2} -2x +6)] - [\frac{1}{2} * (5x^{2} -2x +6)][/tex]

⇒ [tex]-\frac{5x^2}{2} + \frac{9x}{4} + 3.5 +\frac{3}{2x}[/tex]

As you can see, the result of the product of the two expressions is different.

Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Complete Question:

What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form.

(A) show your work.

(B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer

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Answer:

8.2%

Step-by-step explanation:

To find the sales tax percentage, we need to determine how much of the total price was due to sales tax. To do this, we can subtract the price of the cupboard from the total price:

$92.82 - $85.78 = $7.04

So the sales tax was $7.04. We can then divide the sales tax by the price of the cupboard and multiply by 100% to find the sales tax rate as a percentage:

$7.04 / $85.78 * 100% = 8.2%

Rounding to the nearest tenth, the sales tax rate was 8.2%.

Answer:

8.2% (rounded to the nearest tenth)

Step-by-step explanation:

$92.82-$85.78= $7.04

100%= $85.78

1%= $85.78÷100

= $0.8578

$7.04÷$0.8578= 8.2% (rounded to the nearest tenth)

Answer:

a. x= –10

b. x= 7

Step-by-step explanation:

a. 2(x+3)=x–4

2x+6=x–4

C.L.T

2x–x= –6–4

x= –10

b.4(5x–2)=2(9x+3)

20x–8=18x+6

C.L.T

20x–18x=6+8

2x=14

divide both sides by 2

x= 7

The most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C 12, 4), D(5,2) is A. parallelogram.

The most precise name for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C (8, 8), D (8,5) is A. kite

Since the lengths of all sides are equal and the opposite sides are parallel, because the slopes of two parallel lines are equal. Therefore, ABCD is a parallelogram because opposite sides are parallel and congruent.

Also, since, the two disjoint pairs of consecutive sides are congruent as AB=DA and BC=CD. Thus, by definition of kite, that Two disjoint pairs of consecutive sides are congruent, the given quadrilateral is a kite.

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The answer to the quadratic equation is x=1±√33/4.

In mathematics, a quadratic equation is one of degree 2, which means that its maximum exponent is 2. A quadratic has the formula y = ax2 + bx + c, where a, b, and c are all integers and a cannot be zero.

Use the quadratic formula to find the solutions.

−b±√b²−4(ac)/2a

Substitute the values a=2, b=−1, and c=−4 into the quadratic formula and solve for x.

1±√(−1)²−4⋅(2⋅−4)/2⋅2

Simplify.

Simplify the numerator

Raise −1 to the power of 2.

x=1±√1−4⋅2⋅−4/2⋅2

Multiply −4⋅2⋅−4.

Multiply −4 by 2.

x=1±√1−8⋅−4/2⋅2

Multiply −8 by −4.

x=1±√1+32/2⋅2

Add 1 and 32.

x=1±√33/2⋅2

Multiply 2 by 2.

x=1±√33/4

The result can be shown in multiple forms.

x=1±√33/4

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The ball is 7 feet high when it leaves the child’s hand

Given that

h(x) = -x^2 + 6x + 7

When it leaves his hand, we have

x = 0

This gives

h(0) = -(0)^2 + 6(0) + 7

Evaluate

h(0) = 7

Here, we have

h(x) = -x^2 + 6x + 7

Differentiate and set to 0

-2x + 6 = 0

So, we have

x = 3

The maximum height is

hmax = -3^2 + 6(3) + 7

hmax = 16

This means that h(x) = 0

So, we have

-x^2 + 6x + 7 = 0

This gives

x^2 - 6x - 7 = 0

Expand

x^2 + x - 7x - 7 = 0

Factor

x(x + 1) -7(x + 1) = 0

So, we have

(x - 7)(x + 1) = 0

Solve for x

x = 7 or x = -1

Hence, the distance is 7 feet

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The height, in inches, of the entertainment center is 32 inches while other dimensions are 16 inches.

The volume of the unit will be the product of length, depth and height. Now the depth will be 2x. Based on this, performing the calculation to find the value of x.

Volume = length × depth × height

8192 = x × x × 2x

Performing multiplication on Right Hand Side of the equation

8192 = 2x³

Rewriting the equation according to x

x³ = 8192/2

Performing division on Right Hand Side of the equation

x³ = 4096

Taking cube root on Right Hand Side of the equation

x = [tex] \sqrt[3]{4096} [/tex]

x = 16 inches

Height = 2×16

Performing multiplication on Right Hand Side of the equation

Height = 32 inches

Thus, length and depth are 16 inches and height is 32 inches.

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Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x)

Volumes and their variations, mathematics and supporting structures, types and their placements, and locations where they can be collected are all included in the study of mathematics. This same relationship between a group of inputs, each of which produces going support, is referred to as a "function.". Every function has a territory and a codomain, usually known as a scope. F is typically used to denote operations (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one operations, several more functions, within functions, and also on functions.

given

According to the table, the function's value at x = 10 is:

h(10) is not defined.

the values of the function change as x exceeds x = 10 to:

h(x+) = 18.5......

When roughly speaking, we have:

h(x+) = 18.5

Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x) .

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The complete question :-

What is Limit of h (x) as x approaches 10 plus?

If the equation be x + 2(51 - x) = 83 then the value of x be 19.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.

Let x be the number of 1 point shots.

51 - x be the number of 2 point shots

Let the equation be x + 2(51 - x) = 83

Expanding the above equation as

x + 2(51 - x) = -x + 102

simplifying the above equation, we get

-x + 102 = 83

-x = -19

Divide both sides by -1

[tex]$\frac{-x}{-1}=\frac{-19}{-1}[/tex]

x = 19

Therefore, the value of x be 19.

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Domain and range of the composite function (gof)(x) formed by given f(x) and g(x) is equal to all positive real numbers and y > 6 , y ∈R  respectively.

Function f(x ) is :

f(x) = e^x

Function g(x) is :

g(x) = x + 6

To find the range of composite function (gof)(x) simplify the function .

(gof)(x)

= g ( f(x))

Substitute f(x) = e^x we get

= g ( e^x )

Replace x by e^x in g(x) we get,

= e^x + 6

Domain of the composite function is given by all the value based on e^x that is all positive real numbers.

Range is translated by 6.

y > 6 , y∈ R ( positive real numbers)

Therefore, the domain and range of  composite function (gof)(x) is all positive real numbers and y > 6 , y∈ R ( positive real numbers) respectively.

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The measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

For the tangent of X equal, we can make x the subject by finding the tan inverse of opposite divided by the adjacent side as follows:

tan X = 8/10 {opposite/adjacent}

X = tan⁻¹(0.8)

X = 38.6598

Therefore, the measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.

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Answer:

Trinomial

Step-by-step explanation:

A trinomial is an algebraic expression with three, unlike terms.

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The solution of the inequality is x < 5

Inequalities are defined as unequal comparison between two expressions, numbers or equations on the basis of their sizes on the number line.

From the information given, we have that;

-8<4(8-2x)

expand the bracket

-8 < 32 - 8x

collect like terms

-8 - 32 < -8x

subtract the like terms

-40 < - 8x

Make 'x' the subject of formula, we have to divide both sides by the coefficient of x, we get;

-40/-8 < -8x/-8

Divide the values

x < 5

Hence, the value is x < 5

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Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. The expected value of his or her total winnings for the four spins is $800.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again.

We have to determine the expected value of his or her total winnings for the four spins.

Total winning depends on the fourth term.

Outcome              Skunk        100        200        500

Probability              1/4            1/4          1/4          1/4

Total Winning          0             900       1000       1300

Expected Total Winning = 1/4 (0 + 900 + 1000 + 1300)

Expected Total Winning = 1/4 × 3200

Expected Total Winning = 800

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The complete question is:

Contestants on a game show spin a wheel like the one shown in the figure above. Each of the four outcomes on this wheel is equally likely and outcomes are independent from one spin to the next.

The contestant spins the wheel.

If the result is a skunk, no money is won and the contestant's turn is finished.

If the result is a number, the corresponding amount in dollars is won.

The contestant can then stop with those winnings or can choose to spin again, and his or her turn continues.

If the contestant spins again and the result is a skunk, all of the money earned on that turn is lost and the turn ends.

The contestant may continue adding to his or her winnings until he or she chooses to stop or until a spin results in a skunk.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. What is the expected value of his or her total winnings for the four spins?

Answer:

2900

Step-by-step explanation:

16/25+24/30+3/4

=25*30*4=2900

The inequality of the statement is x <= 5

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

The data plan on your family's cell phone costs more if your family uses more than 5 GB in a month

Represent the data plan with x

This means that the inequality is

x <= 5

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Answer:

  (c)  x = 18/5

Step-by-step explanation:

You want the solution to -(-2 -5x) +(-2) = 18.

Eliminating parentheses, we have ...

  2 +5x -2 = 18

  5x = 18 . . . . . . . simplify

  x = 18/5 . . . . . . divide by 5

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{x}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 2 }\implies \cfrac{10}{x-3}=2\implies 10=2x-6 \\\\\\ 16=2x\implies \cfrac{16}{2}=x\implies \boxed{8=x}[/tex]

Answer:

Step-by-step explanation:

Since the balls are drawn with replacement, the probability of drawing a black ball on any single draw is 7/15. The probability of drawing 6 black balls in succession is the product of the probabilities of each individual draw being a black ball. Therefore, the probability is:

(7/15)^6 ≈ 0.019

Rounding to three decimal places, the probability is 0.019.

Answer:

0.003

Step-by-step explanation:

The probability of drawing a black ball on any given draw is 7/15, since there are 7 black balls and 15 total balls in the urn. Because the balls are replaced after each draw, the probability of drawing a black ball on each of the 6 successive draws is (7/15) x (7/15) x (7/15) x (7/15) x (7/15) x (7/15) = (7/15)^6.

Therefore, the probability of drawing 6 black balls in succession is:(7/15)^6 = 0.0028 (rounded to three decimal places)

So the probability that all 6 balls drawn from the urn are black is approximately 0.003.

The distance apart is given as 1/3 inches

Since the original scale was 2 inches = 45 miles, the highway length on the original map was 8 inches * 45 miles/2 inches = 180 miles.

So, each of the 17 rest stops was spaced 180 miles / (17 - 1) = 10 miles apart on the highway.

With the new scale of 1 inch = 30 miles, each inch on the map represents 30 miles on the highway.

Thus, each rest stop on the new map is 10 miles / 30 miles/inch = 10/30 inches = 1/3 inch apart.

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When x = 6, the value of y is:

y = -5x

y = -5(6)

y = -30

Therefore, when x = 6, y is equal to -30.

Answer:

-30

Step-by-step explanation:

given,

y = -5x

x = 6

Now,

y = -5x

or, y = -5(6)

therefore, y = -30

Answer: 11

Step-by-step explanation:

410 * 65 = 26,650 sq ft

26,650/2500 = 10.66 bags

Answer:

11 bags.

Step-by-step explanation:

We know that the area is 410 x 65 = 26650

Now, we need to divide to find how many bags is needed.

26240/2500 = 10.66, which we round up cause we can't have a half bag.

The number of questions on the math quiz, given the points per question and the total points, in the quiz, was 15 questions.

To find the number of questions in the quiz, you can use the formula :

= Number of total points in the quiz / Number of points per question

Number of total points in the quiz = 45 points

Number of points per question

The number of questions given in the quiz by Mr. Thurgood is:

= 45 / 3

= 15 questions

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The full question is:

Mr. Thurgood gave his students a math quiz last Friday. Each question on the quiz was worth 3 points, and the quiz was worth 45 points in all. How many questions were in the quiz?

The probability that a randomly selected woman does not have red/green colorblindness is 0.98 (98%).

The probability of not having red/green colorblindness is the inverse of the probability of having colorblindness. The probability of having red/green colorblindness is given as 0.92%. To calculate the probability of not having red/green colorblindness, subtract the probability of having colorblindness from 1. 1 - 0.92 = 0.08. This means that the probability of not having red/green colorblindness is 0.08, or 8%. To convert this to a percentage, multiply by 100. 0.08 x 100 = 8%. The probability of not having red/green colorblindness is 8%. This can also be written as 0.98 (98%).

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Answer: The tip is 20% of the cost including tax. Thus .20 * X=3.50.Divide both sides of the equation by .20..20 divided into .20 = 1, so “X” = 1.And 3.50 divided by .20 = 17.50 So X = 17.50, cost of the meal plus the tax.The tax is .07, so we know that 100% of the meal cost PLUS 7% of the meal cost is 107% of the meal cost. That is 1.07 * Meal without tax = 17.50. Divide 17.50 by 1.07 and you get 16.355. Round up to 16.36.Is that right? Let’s see:7% tax on meal at 16.36 is 16.36 * .07 = 1.1452. Round up to 1.15.$1.15 + 16.36 = 17.51.And 20% (the tip) of 17.51 is .20 * 17.51 = 3.50Cost of the whole meal; food, tax and tip is 16.36+1.15+3.50 = 21.01. 

Step-by-step explanation: my big brain

The wavelength of red light is exactly the same as the wavelength of violet light, so it is not longer or shorter.

1. First, we need to identify the wavelengths of red light and violet light.

2. Red light has a wavelength of 8x10 to the -7 power meters and violet light has a wavelength of 8x10 to the -7 power meters.

3. Since both wavelengths are the same, the wavelength of red light is not longer or shorter than the wavelength of violet light.

The wavelength of light is measured in meters, and the wavelength of red light is 8x10 to the -7 power meters, while the wavelength of violet light is 8x10 to the -7 power meters. This means that both the wavelengths are exactly the same and the wavelength of red light is not longer or shorter than the wavelength of violet light. This is because the wavelength of light is a fundamental property that determines the color of light and the wavelength of red light and violet light are both the same.-

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It is better to buy 2-64 oz bottles of liquid dish soap for $8.39.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, the store sells 2-64 oz bottles of liquid dish soap for $8.39 or 3 - 40 oz bottles at $7.20.

2 pounds = 32 oz

So, 32+64=96 oz

Now, 8.39/96

= $0.087 per oz

Here, 3 - 40 oz = 88 oz

Unit rate = 7.20/88

= $0.081 per oz

Therefore, it is better to buy 2-64 oz bottles of liquid dish soap for $8.39.

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Answer:

-3x -4

Step-by-step explanation:

(-7x +1) + (4x-5)
= -7x +1 + 4x-5 (brackets are unnecessary due to the commutative law of addition)
= -3x -4