A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?

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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Answer:

A multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations

Step-by-step explanation:

T = 5200 = .2 ( E - 10600)

       5200 / .2 = E - 10600

            E = 5200/.2   + 10 600 = 36600 pounds

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.

Answer:3

Step-by-step explanation: 1/2 X 6 = 3

Answer:

6 x 1/2 = 3 full bottles

Step-by-step explanation:

The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²

where k is the proportionality constant.

In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.

In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:

Strength = k * width * depth² = k * x² * (d/2 - x)²

where x is the width and depth of the beam.

In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:

Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²

where θ is the angle at which the beam is cut from the log.

In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:

w = d sinθ

d = (d/2)cosθ

Then we can express the strength of the beam as:

Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²

Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.

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Complete question is:

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)

The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.

Option C is the correct answer.

Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.

where k and n are positive integers.

We have,

From the table,

From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.

So,

The vertex is (- 1, -3).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(-1, -3) = (h, k)

Make (- 2, 0) = (x, p(x))

0 = a (- 2 + 1)² + (-3)

0 = a x 1 - 3

a = 3

Thus, The vertex equation of p(x).

p(x) = 3(x + 1)² - 3

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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 point estimate of the population​ proportion, the margin of error for the following confidence​ interval, and the number of individuals in the sample are:

The point estimate of the population proportion:

= (lower bound + upper bound) / 2

= (0.640 + 0.910) / 2

= 0. 775

The margin of error for the confidence level :

= p - hat - lower bound

= 0. 775 - 0. 640

= 0. 135

The number of individuals in the sample with the specified characteristic (x ) :

= n x p - hat

= 1, 200 x 0. 775

= 930 people

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she needs to clean 15 uniforms to break even

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)

Answer:

2v-1

Step-by-step explanation:

9v+-3v+-4v-2+1

=9v-3v-4v-1

=6v-4v-1

=2v-1

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:)

Answer:
A and B

Step-by-step explanation:

-10/3= -3.33333333333

(- (-10))/(-3)= -10/3, (negative sign being erased)

=-3.33333333333

hope it helped:)

Answer:

the variance of X is 0.126.

Step-by-step explanation:

The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:

P(X = k) = (nCk)(N-nCk) / (NCk)

where C denotes the combination function.

(a) Expectation of X:

E(X) = np = nK/N = (4/20) * 4 = 0.8

Therefore, the expected number of white balls drawn is 0.8.

(b) Variance of X:

Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126

Therefore, the variance of X is 0.126.

Answer:

The expected number of white balls drawn is 0.4 and the variance of X is 0.24.

Step-by-step explanation:

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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Answer:

{-3, √3, -√3, 13/3}

Step-by-step explanation:

Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.

We can write the polynomial with these zeros as:

p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)

where a is some constant coefficient. Multiplying out the factors, we get:

p(x) = a(x + 3)(x^2 - 3)(x - 13/3)

To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:

a(x + 3)(x^2 - 3)(x - 13/3) = 0

This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:

(x + 3)(x^2 - 3)(x - 13/3) = 0

Expanding the quadratic factor, we get:

(x + 3)(x - √3)(x + √3)(x - 13/3) = 0

Canceling out the (x - √3) and (x + √3) factors, we get:

(x + 3)(x - 13/3) = 0

Solving for x, we get:

x = -3 or x = 13/3

Therefore, the other zeros are -3 and 13/3.

The complete set of zeros is {-3, √3, -√3, 13/3}.

Hope it helps^^

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:

60

Step-by-step explanation:

2$ times 30 luna bars at harmons is $60

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:

14/16 = 0.875

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

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:

A

Step-by-step explanation:

She earns $15 per poinsettia.

The expression that represents the total amount that Ignatio and his friends spent is 15t

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

After spending on t games, we have

f(t) = Rate * t

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

f(t) = 15 * t

Evaluate

f(t) = 15t

Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t

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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 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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The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.

In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:

Therefore, a system of linear equations to describe this situation can be written as follows;

x + y = 40      .....equation 1.

0.3x + 0.8y = 0.6(40)      .....equation 2.

From equation 2, we have the following:

0.3x + 0.8y = 24

0.3x + 0.8(x - 40) = 24

0.3x + 32 - 0.8x = 24

-0.5x = -8

x = -8/-0.5

x = 16 grams.

y = 40 - x

y = 40 - 16

y = 24 grams.

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Answer:

29

Step-by-step explanation:

she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.