Using Trig to Find a Side

Answer:

the price of each lemon bought by Encik Halim is RM1.45.

Step-by-step explanation:

Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.

Let's assume that the cost of each lemon bought by Encik Halim is x RM.

The total cost of 108 lemons would then be 108x RM.

Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.

We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:

Total cost = Total revenue - Profit

Total cost = RM244.80 - RM88.20

Total cost = RM156.60

We know that Encik Halim bought 108 lemons, so we can write:

Total cost = Number of lemons bought x Cost per lemon

RM156.60 = 108x

Therefore, the cost per lemon bought by Encik Halim is:

x = RM156.60/108

x = RM1.45

So the price of each lemon bought by Encik Halim is RM1.45.

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

From the given information, the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

We are to carry out the operation

Add -4(row 1) to row 3

This means we should multiply row 1 by -4

-4 × [ 1     2    1   | -5

       -4   -8   -4  | 20

Now, we will add the result to row 3

4    -1     6  |  -8

-4   -8   -4  | 20

------------------------

0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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Applying the triangle sum theorem, the measure of angle x is calculated as: m<x = 72 degrees.

In a triangle, when all of its interior angles are added together, the triangle sum theorem states that we will get a sum of 180 degrees.

Therefore, we have:

m<AHI = 63 degrees [based on the corresponding angles theorem]

Considering triangle AHI, applying the triangle sum theorem, we will have the following:

m<x + m<AHI + m<A = 180°

Substitute:

m<x + 63 + 45 = 180°

m<x + 108 = 180°

m<x = 180 - 108 [subtraction property of equality]

m<x = 72 degrees.

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The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.

To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.

Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.

To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.

The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.

Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.

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The complete question is:

An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?

The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. In this case, we can find the GCF of 75 and 3 by listing their factors and finding the largest one they have in common. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 3 are 1 and 3. The largest factor they have in common is 3. Therefore, the GCF of 75 and 3 is 3.

We can use the GCF to factor the expression 75 - 3x by dividing each term by the GCF and writing the expression as a product. In this case, we can divide both terms by 3 to get 75/3 - (3x)/3, which simplifies to 25 - x. We can then write the original expression as a product by multiplying this simplified expression by the GCF: 3(25 - x).

Therefore, the factored form of 75 - 3x using the GCF is 3(25 - x).

Answer:

3(25-x)

Step-by-step explanation:

First we find the GCF of 75 and -3x, which is 3

3 is the highest number we can divide both 75 and -3

Hence, the answer is 3(25-x)

The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.

In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).

We have to find the equivalent-expression for (3x-1)-2(x+2);

⇒ (3x-1)-2(x+2),

⇒ (3x - 1) - 2x - 4,

Combing the like-terms together in the above expression,

We get,

⇒ 3x - 2x -1 - 4,

⇒ x - 5,

Therefore, the correct equivalent expression is Option (c).

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The given question is incomplete, the complete question is

Which of the following expression is equivalent to (3x-1)-2(x+2)?

(a) x+3

(b) x+1

(c) x-5

(d) x-3

The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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Based on the above, the width of the field is 62 meters.

Based on the question, Let's say that the width of the field is  denoted with 'w'.

Note that the formula for the perimeter (P) of a rectangle is:

P = 2(l + w)

where"

l = length

w =  width.

Fixing the values into the equation, it will be:

300 = 2(88 + w)

So, Divide both sides by 2:

150 = 88 + w

Subtract 88 from both sides:

w = 150 - 88

w = 62

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Se text below

The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?

Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.

Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.

Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,

P(|X - μ| ≥ kσ) ≤ 1/k²,

where μ and σ are the mean and standard deviation of X, respectively.

Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.

Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,

P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,

where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,

P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².

To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.

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The reference angle of given angles are -6π/13 and -5π / 6

To get coterminal angles, you simply have to add or subtract 2π.

a) 32π/13 =

= -32π/13 + 2π

= -32π + 26π / 13

= -6π/13

b) -17π/6 + 2π =

= -17π + 12π / 6

= -5π / 6

Hence the reference angle of given angles are -6π/13 and -5π / 6

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A passenger can travel 6.875 miles for $20 using the given taxi fare function.

To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.

The equation we need to solve is:

2.56x + 2.40 = 20

To solve for x, we can start by subtracting 2.40 from both sides of the equation:

2.56x = 17.60

Next, we can divide both sides by 2.56:

x = 6.875

This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.

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Answer:

14/16 = 0.875

Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.

The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:

(x - 9) ÷ 3 = 43

x = 43 x 3 + 9

x = 138

With the certain number, x = 138, the correct mathematical operations can be performed as follows:

(138 - 3) ÷ 9

135 ÷ 9

= 15

Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.

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Answer:

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)= 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = -\dfrac{1}{0}[/tex]   is not defined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac {1}{0}\\[/tex]  is not defined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) =\:0[/tex]

Step-by-step explanation:

[tex]\text{Values of trig functions for $-\dfrac{\pi}{2}$ are: }\\\\[/tex]

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = - sin\left(\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)=\cos \left(\dfrac{\pi }{2}\right) = 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = \dfrac{sin\left(-\dfrac{\pi}{2}\right)}{cos\left(-\dfrac{\pi}{2}\right) } = \dfrac{-1}{0}[/tex]
This is undefined since division by zero is undefined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{sin\left(-\dfrac{\pi }{2}\right)} = \dfrac{1}{-1} =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{\cos\left(-\dfrac{\pi }{2}\right)} = \dfrac {1}{0}[/tex]
This is undefined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) = \dfrac{cos\left(-\dfrac{\pi }{2}\right)}{sin\left(-\dfrac{\pi }{2}\right)}\:=\:\dfrac{0}{-1\:}=\:0[/tex]

The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.

z = (x - μ) / (σ/√n)

where x is the sample mean.

Substituting the values, we get:

z = (242.4 - 246) / (89.7/√158) ≈ -0.670

We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.

P(z > -0.670) ≈ 0.751

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Answer:

the number is even

Step-by-step explanation:

an even number plus an even number will aalways be even. adding 6 to an odd number will never be even. Therefore the number will be even

Answer:

t = time in years

p(t) = population at time t

[tex]p(t) = 500000( {1.043}^{t} )[/tex]

[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]

Answer:

A

Step-by-step explanation:

She earns $15 per poinsettia.

Answer:

[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]

hope it helps:)

The null and the alternate hypothesis are:

In hypothesis testing, we take the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is the opposite of the claim , while the alternative hypothesis states  the claim.

In this case, the null hypothesis is that a majority of adults would not erase their personal information online if they could (i.e., 50% or less of them would do so). The alternative hypothesis is that a majority of adults would erase their personal information online if they could (i.e., more than 50% of them would do so). In symbolic form:

H₀: p ≤ 0.5

H₁: p > 0.5

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Answer:

2:35

Step-by-step explanation:

it takes 2 hours to get to Muar so 9:45

he spends 1 hour 40 in muar so 11:35

he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35

The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.

Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:

AC/CE = BC/CD

Given the following:

AC = 7.2 units

CE = 2.4 units

CD = 4.2 units

BC = ?

Plug in the values:

7.2/2.4 = BC/4.2

Cross multiply:

BC = 7.2 * 4.2 / 2.4

BC = 12.6 cm

Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.

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The likelihood that the first question will be true is equally likely and unlikely.

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

The teacher gave a true and false quiz where P(true) = 0.5 for each question.

This means that

P(true) = 0.5

As a percentage,, we have

P(true) = 50%

When the probability of an event is 50%, then the event is equally likely and unlikely.

Hence, the liikelihood is (c) qually likely and unlikely.

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Answer:

  $640

Step-by-step explanation:

You want to know the income tax reduction resulting from investing $3200 in a defined-contribution account when the marginal tax rate is 20%.

The money invested in a defined-contribution account is not subject to income taxes when it is invested. The tax savings is ...

  20% × $3200 = $640

Jermaine lowered his taxes by $640.

she needs to clean 15 uniforms to break even

Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.

An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:

ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.

The given situation can be expressed in the form f(x) = mx + b.

Where,

f(x) = the total cost for detailing the car.

x = the number of minutes it takes to detail the car.

m = The cost per minute for the detailing in car.

b = the flat fee for detailing the car.

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