Last night, Troy had homework in math and science. He spent 112 minutes altogether on his homework. He spent 3 times as long on science homework as on math homework.
How many minutes did Troy spend on his math homework?

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The dimensions of a horizontal cross-section will vary depending on the specific shape or object being considered.

To determine the dimensions of a horizontal cross-section, we need more specific information about the object or shape in question.

A horizontal cross-section refers to a slice or cut made parallel to the horizontal plane.

The dimensions of a horizontal cross-section will depend on the shape or object being sliced. For example, if we have a rectangular prism, a horizontal cross-section would result in a rectangle.

The dimensions of this rectangle would be equal to the dimensions of the corresponding face of the prism.

If we have a cylindrical object, a horizontal cross-section would result in a circle. The dimensions of this circle would be determined by the radius or diameter of the cylinder.

It is essential to provide more information about the shape or object to determine its corresponding horizontal cross-section dimensions.

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Answer:

f(g(x)) = 12x + 1

Step-by-step explanation:

Step 1: Define functions

f(x) = 3x - 2

g(x) = 4x + 1

Step 2: Find f(g(x))

f(g(x)) = 3(4x + 1) - 2

f(g(x)) = 12x + 3 - 2

f(g(x)) = 12x + 1

Work Shown:

IQR = Q3 - Q1

IQR = 70 - 48

IQR = 22

Note: Q1 and Q3 are the left and right edges of the box. The IQR is the width of the box.

The equation that provides the number of years since the car was purchased in terms of its value is (v/2000) - 8.5

In algebra questions, values that are ambiguous or subject to change are represented by letters or symbols.

When it comes to solving for an unknown variable, algebra becomes very useful.

For example, how much money will I save if item retailing for $20 is offered at a 10% discount?

Savings = Full Price * Discount = $20 * 10% = $2

or I spent $30 on items, with each item costing $5, how many items should I have?

Total = No. Items * Item Price

$30 = No. Items * $5

No. Items = Total / Item Price

No. Items = 6

Let the number of years = t

v = 17000 - 2000t

Value = 17000 by row/year

(v - 17000)/2000 = t

Therefore,

t = (v/2000) - 8.5

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the probability density function (PDF) of Z = X + Y is given by: fZ(z) = z, for 0 ≤ z ≤ 1 = 0, otherwise. This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

What is probability density function?

A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It is used to define the likelihood of a random variable taking on a specific value or falling within a certain range of values.

To determine the probability density function (PDF) of the random variable Z = X + Y, where X and Y are independent uniform random variables with range [0, 1], we can use the convolution of the PDFs of X and Y.

First, let's recall the PDF of a uniform random variable. A uniform random variable U with range [a, b] has a constant PDF given by:

fU(u) = 1 / (b - a), for a ≤ u ≤ b

= 0, otherwise

In this case, for X and Y with range [0, 1], the PDFs are:

fX(x) = 1, for 0 ≤ x ≤ 1

= 0, otherwise

fY(y) = 1, for 0 ≤ y ≤ 1

= 0, otherwise

Now, let's find the PDF fz of Z = X + Y by convolution:

fZ(z) = ∫ fX(x) * fY(z - x) dx

Since X and Y are independent, fY(z - x) = fY(z) since the range of Y is [0, 1].

fZ(z) = ∫ fX(x) * fY(z) dx

As the PDFs of X and Y are both 1 in the range [0, 1], the integral becomes:

fZ(z) = ∫ 1 * 1 dz

Since the integration bounds are not dependent on z, the integral evaluates to:

fZ(z) = ∫ 1 dz = z

Therefore, the probability density function (PDF) of Z = X + Y is given by:

fZ(z) = z, for 0 ≤ z ≤ 1

= 0, otherwise

This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

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(a) The shape of Jack's distribution of sample means is expected to be bell-shaped, with the mean being centered at the population mean of 50 and the standard deviation being much larger than the standard deviation of the population. This is because Jack is using larger sample sizes, which results in a more accurate estimate of the population mean.

The shape of Diane's distribution of sample means is expected to be similar to Jack's, but less pronounced. This is because Diane is using smaller sample sizes, which results in a less accurate estimate of the population mean.

(b) The mean of Jack's distribution of sample means is expected to be similar to the population mean of 50, but slightly larger due to the larger sample sizes. The mean of Diane's distribution of sample means is also expected to be similar to the population mean of 50, but again slightly larger due to the larger sample sizes.

(c) The standard deviation of Jack's distribution of sample means is expected to be smaller than the standard deviation of the population, because the larger sample sizes result in a more accurate estimate of the population mean. The standard deviation of Diane's distribution of sample means is also expected to be smaller than the standard deviation of the population, but again to a lesser extent due to the smaller sample sizes.

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Answer:

I believe it is a total of 73.188

The type of errors and number of errors depend on the experiment, that is how it is set up and the devices that one is using for measurement.

Assuming that we are using simple lab equipments and the experiment to be performed is - dropping a ball from a fixed height and measuring the time it takes for the ball to hit the ground. Let us also consider that the distance of the ball from the ground is already known. We can think of no such complex or non-measurable errors that can occur in this  experiment if performed with utmost care.

There can be two  possible errors that can occur in this simple experiment ( excluding errors from calculations)that are as follows :

1.If using a metre rule then there can occur systematic error.

2.Random errors can occur which are actually human errors, that is the stopwatch might not be started or stopped exactly when the ball is dropped or touched the ground respectively.

If we use a light gate, digital sensors and a computer software then the above errors are eliminated or at least gets significantly reduced.

Thus the measured value for g may not be the accepted value.

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Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

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Answer:

1. monomial

2. Binomial

3. polynomial

4.binomial

5 trinomial

6 binomial

Answer:

52

Step-by-step explanation:

arcsin 15/18

= 52

Answered by GAUTHMATH

a) The parameters in the second-order interaction terms & cross product interaction terms. b) The hypothesis of no curvature stated as the coefficients of these terms being equal to zero. c) To test the usefulness of an independent variable, its coefficient can be tested for significance.

a) The parameters involved in a test of the hypothesis that no curvature exists in the response surface are the second-order interaction terms between the three independent variables x1, x2, and x3, namely x1², x2², x3², as well as the cross-product interaction terms between any two of the three independent variables, namely x1x2, x1x3, and x2x3.

b) The null hypothesis for the test of no curvature in the response surface can be stated as H0: The coefficients of the second-order interaction terms (x1², x2², x3²) and cross-product interaction terms (x1x2, x1x3, and x2x3) are equal to zero, indicating that there is no curvature in the response surface.

c) To determine whether x is useful for the prediction of e(y), we can test the null hypothesis H0: β1 = 0, where β1 is the coefficient of the first independent variable x1 in the second-order model. If the null hypothesis is rejected, it would indicate that x1 is useful for the prediction of e(y).

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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To calculate the amount Travis should invest today to accumulate $190,000 for her retirement in 14 years, we can use the formula for compound interest:

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

Where:

A = the future value of the investment (desired amount of $190,000)

P = the principal amount (the amount Travis needs to invest today)

r = the annual interest rate (4.32% or 0.0432 as a decimal)

n = the number of times interest is compounded per year (semi-annually, so n = 2)

t = the number of years (14 years)

Substituting the given values into the formula:

190,000 = P(1 + 0.0432/2)^(2*14)

To solve for P, we can rearrange the formula:

P = 190,000 / [(1 + 0.0432/2)^(2*14)]

P = 190,000 / (1.0216)^28

P ≈ 190,000 / 1.850090

P ≈ 102,688.26

Therefore, Travis should invest approximately $102,688.26 today to accumulate $190,000 for her retirement in 14 years, assuming an annual interest rate of 4.32% compounded semi-annually.

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A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.

Using sample data, hypothesis testing is used to determine a hypothesis's credibility. It is represented as H0, and it is sometimes referred to as the "null."

Given; The average thickness and standard deviation of a sample of 50 eyeglass lens samples are 3.05 millimeters and.34 millimeters, respectively.

Such lenses should have a true average thickness of 3.20 mm. Utilizing a =.05

False hypothesis H0: Alternative hypothesis: mu1= mu2 HA: 'mu1' and 'ne'

Sample Size 50 Sample Mean 3.05 Sample Standard Deviation 0.34 Intermediate Calculations Standard Error of the Mean 0.0481 Degrees of Freedom 49 t Test Statistic -3.1196 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.0030 Reject the null hypothesis

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Answer:

24 minutes for 3 large arrangements

54 minutes for 9 small arrangements

6 minutes for each small arrangement

8 minutes for each large arrangement  

Step-by-step explanation:

hope this helps!

The asset's variance is approximately 0.0358, and its standard deviation is approximately 0.1891.

To calculate the variance and standard deviation of the asset's returns, we'll follow the steps mentioned earlier using the given probability distribution:

⇒ Calculate the expected return (μ):

μ = (0.27 * 0.25) + (0.18 * 0.25+) + (0.10 * 0.30) + (0.04 * 0.20+)

  = 0.0675 + 0.045 + 0.03 + 0.008

  = 0.1505

⇒ Calculate the variance (σ^2):

σ^2 = [(0.27 - μ)^2 * 0.25] + [(0.18 - μ)^2 * 0.25+] + [(0.10 - μ)^2 * 0.30] + [(0.04 - μ)^2 * 0.20+]

Substituting the values and simplifying:

σ^2 = [(0.27 - 0.1505)^2 * 0.25] + [(0.18 - 0.1505)^2 * 0.25+] + [(0.10 - 0.1505)^2 * 0.30] + [(0.04 - 0.1505)^2 * 0.20+]

    = [(0.1195)^2 * 0.25] + [(0.0295)^2 * 0.25+] + [(-0.0505)^2 * 0.30] + [(-0.1105)^2 * 0.20+]

    = 0.017972 + 0.00021617 + 0.0030309025 + 0.01459516

    = 0.0358141325

⇒ Calculate the standard deviation (σ):

σ = √(σ^2)

  = √(0.0358141325)

  ≈ 0.1891

Therefore, the asset's variance is approximately 0.0358 and the standard deviation is approximately 0.1891.

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Answer:

153

Step-by-step explanation:

discriminant = b² - 4ac

ax² + bx + c = 0

9x² - 3x - 4 = 0

a = 9

b = -3

c = -4

discriminant = (-3)² - 4(9)(-4) = 9 + 144 = 153

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

The frequency table shows that:

To construct frequency table with a range of 6 classes, we will determine range of the data which is difference between the largest and smallest value in the data set.

Data are: 42, 43, 46, 46, 47, 47, 48, 49, 49, 50, 51, 51, 51, 51, 51, 52, 52, 54, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 57, 57, 57, 57, 58, 60, 61, 61, 61, 62, 64, 64, 65, 68, 69

Age Interval     Frequency

40 - 45                    2  

46 - 51                    13

52 - 57                   31

58 - 63                    6

64 - 69                    5

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The probability that a face recognized as female is actually a male face is approximately 0.9608 or 96.08%.

To find the probability that a face recognized as female is actually a male face, we can use Bayes' theorem.

Let's define the following events:

A: The face is recognized as female.

B: The face is actually a male face.

We want to find the conditional probability P(B|A), which represents the probability that the face is male given that it is recognized as female.

According to Bayes' theorem:P(B|A) = (P(A|B) * P(B)) / P(A)

P(A|B) represents the probability of being recognized as female given that the face is actually male. From the given information, we know that the facial recognition tool correctly identifies the sex in 98% of cases, so P(A|B) = 0.98.

P(B) represents the probability that a randomly chosen face is male, which is given as 50% or 0.5.

P(A) represents the overall probability of being recognized as female. To calculate this, we need to consider both true positives and false positives . The probability of a false positive is given as 4%, so the probability of a true positive (correct identification) is 1 - 0.04 = 0.96. Since the gender distribution in the population is 50%, the overall probability of being recognized as female is:

P(A) = (P(A|B) * P(B)) + (P(A|not B) * P(not B))

= (0.98 * 0.5) + (0.04 * 0.5)

= 0.49 + 0.02

= 0.51

Now, we can substitute these values into Bayes' theorem to find P(B|A):

P(B|A) = (P(A|B) * P(B)) / P(A)

= (0.98 * 0.5) / 0.51

≈ 0.9608

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Answer:

156

Step-by-step explanation:

279 - 123 = 156

Answer:

156

Hope that this helps!

Thad would be 4 5/12 feet next year

Fractions are defined as the part of a whole number, a whole variable or a whole element.

In mathematics, there are different fractions,

These fractions are listed as;

From the information given, we have that;

Thad is  4 1/6 feet tall.

Next year he add 1/4 foot

Convert to improper fraction

25/6 + 1/4

Find the LCM, we have;

50 + 3/12

53/12

4 5/12 feet

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(a) The distance between the airport and the pilot's final landing point is 300 miles.

(b) the bearing from the airport to the pilot's final landing point is approximately 300.7684°.

(a) The distance between the airport and the pilot's final landing point can be calculated by finding the sum of the two distances traveled in the given directions.

First, let's calculate the distance traveled in the direction N 20° E for one hour at a speed of 200 mi/h. The formula to calculate distance is:

Distance = Speed × Time

Distance = 200 mi/h × 1 h = 200 miles

Next, let's calculate the distance traveled in the direction N 40° E for half an hour at the same speed. Since the time is given in hours, we need to convert half an hour to hours:

0.5 hours = 1/2 hours

Using the same formula, we can calculate the distance:

Distance = 200 mi/h × (1/2) h = 100 miles

To find the total distance, we add the two distances:

Total Distance = 200 miles + 100 miles = 300 miles

Therefore, the distance between the airport and the pilot's final landing point is 300 miles.

(b) To find the bearing from the airport to the pilot's final landing point, we can use trigonometry.

First, let's consider the triangle formed by the airport, the pilot's final landing point, and the point where the pilot made the course correction. The angle between the first leg (N 20° E) and the second leg (N 40° E) is 20°.

Using the Law of Cosines, we can find the angle between the first leg and the line connecting the airport and the final landing point:

cos(angle) = (a^2 + c^2 - b^2) / (2ac)

where a = 200 miles, b = 100 miles, and c is the distance between the airport and the final landing point (300 miles).

cos(angle) = (200^2 + 300^2 - 100^2) / (2 × 200 × 300)

Solving for angle, we find:

angle ≈ 39.2316°

The bearing from the airport to the final landing point is the angle measured clockwise from due north. Since the pilot initially flew in the direction N 20° E, we need to subtract 20° from the angle we calculated.

Bearing = 360° - 20° - angle

Bearing ≈ 360° - 20° - 39.2316° ≈ 300.7684°

Therefore, the bearing from the airport to the pilot's final landing point is approximately 300.7684°.

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The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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The impact of a high TER (tolerable error rate) and no prior year exceptions on the determination of sample size is dependent on the assessment of the auditor.

If the auditor determines that a high TER is acceptable and there were no prior year exceptions, the sample size can be smaller. However, if the auditor determines that a smaller sample size may not be sufficient to provide reasonable assurance, then the sample size should be larger. In some cases, a large TER may mean that the auditor can select less items for the sample, but this is dependent on the auditor's assessment of the situation.

Ultimately, the determination of sample size is based on the auditor's professional judgment and assessment of the risks and materiality involved in the audit. A high TER and no prior year exceptions may impact the determination of sample size, but the final decision should be based on the auditor's assessment of the situation.

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Answer:

Ans is y so find y by using formula for isoceles triangle that is 2 right triangles

Answer:

step 1-  (3x2 +  h) +  2c

step 2- 2.1    Factoring    3x2 + h + 2c

Also, Try to factor this multi-variable trinomial using trial.

Therefor the expresion is -1

Step-by-step explanation:

Hopefuly this helped! :)

Answer:

I would love to help you, but there are no photos nor links.

Step-by-step explanation:

Have a great day!