express cos 0 as a ratio of given lengths of the right triangle shown

The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³

From the question, we are to determine the volume of the resulting block of wood.

From the given information,

The dimensions of the block of wood is 10 in. by 10 in. by 6 in.

First, we will calculate the original volume of the block of wood.

The original block of wood has a volume of

V = 10 x 10 x 6

V = 600 in³

Now, we will determine the volume og the hole that was cut through

The dimensions of the hole is 2 in. by 2 in. by 6 in.

Volume of the hole = 2 x 2 x 6

Volume of the hole = 24 in³

The resulting block would have a volume of

Volume of resulting block = 600 - 24

Volume of resulting block = 576 in³

Hence, the volume is 576 in³.

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Answer:

The percentage rate of change of a function f(t) is given by:

(Δf / f) x 100

where Δf is the change in f and f is the original value of the function.

To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:

(Δf / f) x 100 = 100

Simplifying, we get:

Δf / f = 1

This means that the change in f is equal to the original value of f.

So, we need to solve the equation:

f(t + Δt) - f(t) = f(t)

where Δt is the change in t.

Substituting the given function, we get:

[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2

Simplifying, we get:

-8tΔt + 8Δt^2 = 1

Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.

Ignoring the term Δt^2, we get:

-8tΔt = 1

Solving for Δt, we get:

Δt = -1 / (8t)

Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:

-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1

Simplifying, we get:

1 / t^2 = 1

Solving for t, we get:

t = 1

Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.

Answer:

To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.

First, we need to calculate the variable cost per hour of production:

Variable cost per hour = Direct labor / Hours of production

Variable cost per hour = $37,260 / 4,140 hours

Variable cost per hour = $9

Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:

Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs

Flexible budget = ($9 x 4,500 hours) + $43,370

Flexible budget = $40,500 + $43,370

Flexible budget = $83,870

Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.

Answer:

y = 4

x = 4√2 or 5.66

Step-by-step explanation:

If the △ is a right △ with 1 angle 45o, then the other angle is also 45o. This △ will be isosceles right triangle with y = 4

Pythagorean theorem: c^2 = a^2 + b^2

x^2 = y^2 + 4^2

x^2 = 4^2 + 4^2

x^2 = 32

x = √32 = 4√2 = 5.66

Step-by-step explanation:

For RIGHT  triangles the cos of an angle = adjacent LEG / hypotenuse

 so for THIS triangle   cos 55°  = x / 9.3

    re-arrange to    9.3 * cos 55° = x    

       use calculator to find x = ~ 5.3 units   (rounded)

Answer:

x = 5.3

Step-by-step explanation:

As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies \cos 55^{\circ}=\dfrac{x}{9.3}[/tex]

[tex]\implies x=9.3 \cos 55^{\circ}[/tex]

[tex]\implies x=5.3342608...[/tex]

[tex]\implies x=5.3\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 5.3 to the nearest tenth.

Answer:

Step-by-step explanation:

To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.

For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:

y1 = 2.9sqrt(49) + 20.1 = 42.7 inches

For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:

y2 = 2.9sqrt(16) + 20.1 = 28.9 inches

Therefore, the expected difference in height between the two children would be:

y1 - y2 = 42.7 - 28.9 = 13.8 inches

So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.

Answer:

Step-by-step explanation:

b-y=55

1) The system of inequalities that models this scenario will be:

6x + 3y ≤ 24

6x + 3y ≥ 4

2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.

3) The graph is attached accordingly.

a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.

Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:

6x + 3y ≤ 24 (budget constraint)

6x + 3y ≥ 4 (at least four snacks)

So the system of inequalities that models this scenario is:

6x + 3y ≤ 24

6x + 3y ≥ 4

b)

To solve for y in each inequality, we need to isolate y on one side of the inequality sign.

For the first inequality, we have:

x + y ≥ 3

Subtracting x from both sides, we get:

y ≥ 3 - x

So the solution for y is y ≥ 3 - x.

For the second inequality, we have:

6x + 3y ≤ 15

Dividing both sides by 3, we get:

2x + y ≤ 5

Subtracting 2x from both sides, we get:

y ≤ 5 - 2x

So the solution for y is y ≤ 5 - 2x.

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Answer:

Step-by-step explanation:

(9/4 * 8/7) - (3/8*4/1) =

(72/28) - (12/8)

18/7 - 3/2

36/14 - 21/14

15/14 = 1 1/14

Answer:

The graph of the function y = 100(1.05) is shown below.

b. Calculate the cost of the hotel per night after six years.

The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.

c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?

The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.

2 LEARNING RESOURCES

Discuss the advantages of using online learning resources for students.

One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.

Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs

The answer of the given question based on the compound interest is  the balance after 6 years is $14,162.62 (option a).

Amount refers to total value of something, usually in terms of a money. It can also be used in  context of a quantity of something, such as an amount of the  time or an amount of the material.

formula for the compound interest is :

A = P(1 + r/n)^(nt)

Where,

A = final amount

P = principal amount

r = annual interest rate

n = the number of times interest is to be compounded per year

t = time in years

In this case, we have:

P = $1,000

r = 3.75% = 0.0375 (annual interest rate as a decimal)

n = 12 (monthly compounding)

t = 6 years

Substituting the  values into  formula, we will get:

A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾

A = $1,4162.62

Therefore, the balance after 6 years is $14,162.62 (option a).

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Answer: y = 4/3x -3

Step-by-step explanation:

Using percentage, we can find:

1- 84600

2- 385400

3- 20811.6

4- 7576776

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the question,

Downpayment = 18% of 470000

= 84600

original amount financed =

470000-84600

= 385400

Monthly payment = 5.4% of 385400

= 20811.6

Total payment in 30 years = 7576776

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Answer:

the answer is c because every side of a triangle sides are he same so c is your answer

The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).

This can be calculated using the formula P(A|B) = P(A∩B) / P(B)

P(positive | disease) = P(positive ∩ disease) / P(disease)

                    = 141 / (141+16)

                    = 0.898

Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.

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-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.

Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).

The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.

Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

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Answer:

A or 420

Step-by-step explanation:

Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.

Answer:

-12 and 2

Step-by-step explanation:

1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.

2. Think of numbers that multiply to -144

3. Check and see if they add to -10

4. The only numbers that satisfy this are -12 and 2

Answer: 9.60

Step-by-step explanation:

Labeled price = $ 12

Discount = 20% of labeled price = 12 x 20%

= 12 x 2 / 10 = 24 / 10 = $ 2.4

Sale price = Labeled price - Discount.

Sale price = $ 12 - $ 2.40 = $ 9.60

Thus the sale price of the case of soda is 9.60 $

The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.

We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.

1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.

2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.

3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.

Based on the behavior of V(t), the following statement is supported:

As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.

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The data in the triangle is not sufficient to find the asked values in the question.

The relationship in between sides and angles for non-right (oblique) triangles is known as the Law of Sines. It simply asserts that for all sides and angles of a given triangle, the ratio of the length of a side to the sine angle opposite this side is the same.

You must know between two angles but one side of the triangle (AAS or ASA) either two sides and an angle opposing one of them in order to employ the Law of Sines (SSA).

g/sinG = h/sinH = f/sinF

Where G, H and F are the angles and g, h and f are the angles' opposing sides.

Put the values:

g/sin136 = 13/sinH = 7/sinF

The three pairs of expression are-

HF/sin136 = 13/sinH ;   13/sinH = 7/sinF and g/sin136 = 7/sinF.

HF = 13*sin136/sinH

HF = 10.97/SinH

From the found 3 expression, each has two missing value.

Thus, the angles F and H is not possible to find.

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Answer:

in absolute value you consider both the positive and negative side of the expression in the absolute bar.

After addressing the issue at hand, we can state that Therefore, function  g(-2) = 0 and g(4) = -4.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

When x = -2, g(x) = 0.

When x = 4, g(x) = -4.

Therefore, g(-2) = 0 and g(4) = -4.

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The width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

The region contained inside the rectangle's perimeter is referred to as the area of the rectangle. In other terms, the area of a rectangle is the whole area that a rectangle encloses. Depending on the provided dimensions, this may be determined using the area of rectangle formula and a number of other techniques.

Let us suppose the width = x.

Then, length is given as:

l = x + 7

The area of the rectangle is:

A = lw

Substituting the values:

A = (x + 7)x

The perimeter of the rectangle is:

P = 2(l + w)

P = 2(x + 7 + x)

P = 2(2x + 7)

P = 4x + 14

Also, we have:

A = 2P

Substituting the values of area and perimeter:

4x + 14 = (x + 7)x

Simplifying the expression:

x^2 + 7x = 8x + 30

x^2 - x - 30 = 0

(x-6)(x+5) = 0

Since, width cannot be negative value we have:

x = 6.

l = 7 + 6 = 13 inches.

Hence, the width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

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Answer:

Gold ring = 6180

Step-by-step explanation:

Gold ring = ?

I = prt

= 19000 x 6% x 2

= 2180

Amount to be paid= 19000 + 2180

= 21180

gold ring = 21180 - 15000

= 6180

The sum of the infinite geometric series is: ²/₅

The formula for the sum of an infinite geometric series is;

[tex]S_{\infty} = \frac{a}{1 - r}[/tex]

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

Answer:

See below.

Step-by-step explanation:

For this problem, we are asked to find x, the hypotenuse.

There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.

Represented as;

[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]

We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.

Substitute:

[tex]40^2+42^2=c^2[/tex]

[tex]3364 = c^2[/tex]

Square Root the Equation:

[tex]\sqrt{3364} = \sqrt{c^2}[/tex]

[tex]c = 58.[/tex]

The Hypotenuse is 58. Our final answer is Letter D.

That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.

In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).

In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).

The answer is option d.

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Answer:

154%

Step-by-step explanation:

First, we need to calculate the increase in size of the privately owned farm:

increase = new value - old value

increase = 432 - 170

increase = 262

Next, we can use the formula to calculate the percent increase:

percent increase = (262 / 170) x 100%

percent increase = 1.54 x 100%

percent increase = 154%

Therefore, the percent increase in the size of privately owned farms in the country is 154%.

Answer:

To multiply polynomials, you can follow these steps:

Distribute each term of the first polynomial to each term of the second polynomial.

Combine like terms.

Simplify the resulting expression.

Here is an example:

(2x + 3)(x - 4)

Distribute:

2x(x - 4) + 3(x - 4)

Combine like terms:

2x^2 - 8x + 3x - 12

Simplify:

2x^2 - 5x - 12

So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.

Step-by-step explanation: