(0)
Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.) 5 sin2(x) − 8 sin(x) − 4

As per the given 4 x 5 matrix, the reduced row echelon form of A is \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

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The two consecutive positive integers are 5 and 6.

Let the two consecutive positive integers be x and x + 1. We are given that the product of these integers is 3 less than three times their sum. This can be expressed as:
\(x(x + 1) = 3(x + x + 1) - 3\)
Now we can solve for x:
\(x^2 + x = 6x + 3 - 3\)
\(x^2 + x = 6x\)
\(x^2 - 5x = 0\)
Factoring the left side of the equation, we get:
\(x(x - 5) = 0\)
From this equation, x can be 0 or 5.

However, since the question asks for positive integers, we can't use x = 0. Therefore, x = 5.

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App inventor's random integer block test is sufficient for app inventor's prng . but to increase our confidence in app inventor's prng we can do other tests like random fraction test and random set speed test.

The Coin Flip Experiment app allows you to run experiments aimed at determining how "good" the App Inventor PRNGs are. The app allows the user to "flip a coin" her N times and the results are displayed. They should record and count the results and calculate the average head percentage. The expectation of should reach 50% on average as N increases.

To properly test an App Inventor PRNG, you must test both the Random Integer and Random Fraction blocks along with the Random Fraction and Random set speed to blocks. Create dice simulations to get better than 50/50 predictions and reuse dice simulators for all combinations of different App Inventor random blocks. If such a combination yields the same results, then you can be confident that her PRNG in App Inventor provides a good model of randomness from all angles.

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Ana will take 100 ml on the first day and 5 ml less each day for 20 days, requiring a total of 1050 ml; the prescribed amount of 960 ml is not enough, resulting in a shortage of 90 ml, which will last for 18 days.

Ana will take the syrup for 20 days, and on each day, she will take 5 ml less than the previous day. To calculate the total amount of syrup Ana will need for the 20 days, we can use the formula for the sum of an arithmetic series,

S = (n/2) x (a₁ + aₙ), In this case, n = 20, a1 = 100 ml, and an = 100 ml - (19 x 5 ml) = 5 ml. Plugging in the values, we get,

S = (20/2) x (100 ml + 5 ml) = 1050 ml

So Ana will need a total of 1050 ml of syrup for the 20 days. The doctor prescribed 3 bottles of 320 ml each, which is a total of 960 ml. This is not enough to cover the full 20 days of treatment, as Ana will need 1050 ml. Therefore, there is a shortage of 90 ml of syrup. To calculate how many days Ana will lack syrup for, we need to divide the shortage by the daily reduction in dose,

90 ml/5 ml per day = 18 days

So Ana will have enough syrup for the first 2 days, but she will lack syrup for the next 18 days.

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Complete question - Ana has to take a syrup for 20 days, the doctor has prescribed 3 bottles of 320 ml each, she has to take the syrup in such a way that each day that passes she takes 5 ml less than the day before. If you start taking a 100 ml dose, how many ml will you take on the last day? Was the amount of syrup prescribed by the doctor enough? How much syrup is left over or lacking? if he lacked syrup, for how many days would he lack?

Answer:

y = 10.5

Step-by-step explanation:

Δ MOP and Δ MNQ are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{OP}{NQ}\) = \(\frac{MO}{MN}\) ( substitute values )

\(\frac{y}{7}\) = \(\frac{8+4}{8}\) = \(\frac{12}{8}\) ( cross- multiply )

8y = 84 ( divide both sides by 8 )

y = 10.5

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

10x-1=10x+4

10x-10x=4+1

x=5

Question

In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?

• one half the area of circle L

• one third the area of circle L

• one half the circumference of circle L • one third the circumference of circle L

Answer:

• one third the circumference of circle L

Step-by-step explanation:

In the question, we are told that:

In circle L, arc MNOP is 120° and the radius is 5 units.

We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L

Step 1

Find the Area of circle

Area of a circle = πr²

r = 5 units

Area of a circle = π × 5²

Area of a circle = π × 25

Area of a circle = 78.53981634 square units

Step 2

Find the arc length of a circle

Arc length = 2πr × θ /360

r = 5 units

θ = 120°

Arc length = 2 × π × r × 120/360

Arc length = 2 × π × r × (1/3)

Arc length = 2 × π × 5 × (1/3)

Arc length = 10.47198 units

Step 3

Circumference of a circle = 2πr

= 2 × π × 5

= 31.415926536 units

Since the Circumference of a circle = 2πr

Arc length of the circle for the above calculation, = 2πr × 1/3

Therefore, the statement that best describes the arc length MNOP of Circle L is:

" the arc length MNOP is one third the circumference of circle L"

Answer:

the arc length MNOP is one third the circumference of circle L

Step-by-step explanation:

i fishie yupo

Answer:

yes

Step-by-step explanation:

the y grows by 15 for every 1 the x grows by

Answer:

D

Step-by-step explanation:

Answer:

1. -3/1

2.negative

3.$18

Step-by-step explanation:

since the graph is going down, it is negative, and look at the ending points on the x and y-axis. 18/6 is 3. so the slop is -3 :)

Answer:

1. -3

2. negative

3. $18

Step-by-step explanation:

1. slope is rise/run so...

-3/1=-3

2. because run was a change of 3 DOWN the y axis we and run is a change of 1 to the right on x axis we have a negative slope. -3

3. she borrowed $18. Vertical intercept means the point where our line crosses the vertical axis. (Vertical axis is Y axis.)

The approximately 99.38% of the data falls between the values 120 and 280.

To find the percentage of data that falls between the values 120 and 280, we need to find the standard scores (z-scores) that correspond to these values and use a standard normal table to find the proportion of data within this range.

First, we'll find the z-score for 120:

z = (120 - 200) / 40 = -2.5

Similarly, the z-score for 280 is:

z = (280 - 200) / 40 = 2.5

Now we can use a standard normal table to find the proportion of data between -2.5 and 2.5 standard deviations from the mean. This proportion is approximately 0.9938 or 99.38%.

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The false statement is "Assumption A4 is violated because heteroskedasticity is inherent for binary outcome variables."

Assumption A4 in linear regression assumes homoskedasticity, which means the variability of the errors (ε) is constant across all levels of the independent variables. However, in the given regression model, the statement falsely claims that heteroskedasticity is inherent for binary outcome variables.

In reality, heteroskedasticity is not a necessary consequence of binary outcome variables. The violation of homoskedasticity typically arises due to the relationship between the independent variables and the variability of the errors, rather than the nature of the outcome variable itself.

In this particular model, the assumption violated is A6, which states that the errors should be normally distributed. Since the outcome variable, attendcol, is binary (taking values of 0 or 1), the assumption of normal distribution for the errors is not appropriate. Binary outcome variables follow a discrete probability distribution, such as the Bernoulli distribution.

Assumption A2, which involves the inclusion of both faminc and \(faminc^2\) in the model, is not inherently violated. Including both linear and squared terms of faminc allows for a nonlinear relationship between family income and the probability of attending college

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The reflective properties of conic sections can be exploited in various applications, such as focusing light or radio waves, enhancing signal reception, and designing optical systems. Each conic section exhibits unique reflective characteristics based on the arrangement of its foci and the shape of the curve.

Let's discuss the reflective properties of the three conic sections: parabola, ellipse, and hyperbola.

Parabola:

Reflective Property: A parabola has a single focus point, located either above or below the vertex. Any ray of light parallel to the axis of symmetry of the parabola will reflect off the curve and pass through the focus point.

Application: This property of the parabola makes it useful in designing reflective surfaces, such as satellite dishes or car headlights, where incoming parallel light rays are focused at a single point.

Ellipse:

Reflective Property: An ellipse has two foci, located at the two foci points on the major axis. When a ray of light enters the ellipse, it reflects off the inner surface of the curve, obeying the law of reflection. The angle of incidence is equal to the angle of reflection.

Application: The reflective property of the ellipse is utilized in applications such as astronomy, where elliptical mirrors are used in telescopes to focus light from distant celestial objects onto a focal point.

Hyperbola:

Reflective Property: A hyperbola has two foci, one on each branch of the curve. When a ray of light enters one branch of the hyperbola, it reflects off the inner surface of the curve, obeying the law of reflection. The angle of incidence is equal to the angle of reflection.

Application: The reflective property of the hyperbola finds applications in antenna design, specifically in satellite dishes and radio telescopes. The hyperbolic shape allows incoming waves to be focused or directed towards a specific point or receiver.

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The correct number line that can be used to find the distance between the given points (4, -1) and (8, -1) is a number line going from negative 2 to positive 8 in increments of 1, with the points at 4 and 8.Option (A)

The reason for this is that the two points have the same y-coordinate, which means they lie on a horizontal line. To find the distance between them, we simply need to measure the difference between their x-coordinates, which is 8 - 4 = 4. On the given number line, the distance between points 4 and 8 is also 4 units, so we can directly read off the distance as 4 units.

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Answer: x = 16 or if it is x+2/3 (two thirds), then 5 1/3

Step-by-step explanation: 16+2 divided by 3 = 6. 5 1/3 + 2/3 = 6.

Answer:

5 1/3

Step-by-step explanation:

Step 1:

6 = x + 2/3        Equation

Step 2:

6 - 2/3 = x       Subtract 2/3 on both sides

Answer:

5 1/3 = x          Subtract

Hope This Helps :)

Answer:

Step-by-step explanation:

L=−25t+200

The expression to represents the given situation will be;

⇒ L = $25t + $50

Where, L represent the total amount borrowed by Nevaeh.

And, t is represent the number of weeks.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Neveah borrowed money from her friend and agreed to pay $25 per week.

After 6 weeks, Nevaeh still owed her friend $50.

Now,

Let L represent the total money borrowed by Nevaeh.

And, t is the number of weeks for pay $25 per weeks.

Then, We can formulate;

⇒ L = $25t + $50

Therefore, The expression to represents the given situation will be;

⇒ L = $25t + $50

Where, L represent the total amount borrowed by Nevaeh.

And, t is represent the number of weeks.

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Answer:

No 1

Here,

Let X be age of daughter

and 3X be age of father

Now,x+17+3 = 20 age

and 3x+43-20 = 7point9x

Step-by-step explanation:

So,

20÷7point9 = 2point8 years ago

Hence,

age of father = 48÷2point8 = 21point5 years

age of daughter = 20÷2point8 = 10 years

so, before 2point8 years ago father was as old as his daughter

Answer:

x=-2

Step-by-step explanation:

Answer:

1/3x - 3.3 = -4

         +3.3   +3.3

                  1/3x = -0.7

                    /1/3     /1/3

         x = -2.1

check: 1/3(-2.1) - 3.3

                    -0.7 - 3.3

                       -4 = -4

correct!

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

LM=JK

3x+1=13

3x=12

x=4

The three-period weighted moving average for july is 145.4.

A weighted moving average technique is one of several methods for forecasting a given month's value or attribute. Other techniques for forecasting from historical data include the evenly weighted moving average method, a regression analysis method, and so on.

Now, according to the question;

The weighted moving average strategy forecast for month of July is given by:

= (Weight for May * Sales for May) + (Weight for April * Sales for April) + (Weight for June * Sales for June)

= (0.5 * 148) + (0.3 * 142) + (0.2* 144)

= 145.4

Therefore, the three-period weighted moving average for july is 145.4.

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The complete question is -

13. Given the following historical data and weights of .5, .3, and .2, what is the three-period weighted moving average forecast for period 5?

Period Value

1 - 138 (march)

2 - 142 (april)

3 - 148 (may)

4 - 144 (june)

Answer:

To get the circumference, multiply the diameter by pi.  You have the diameter in meters, and you were given an approximate value of pi.  Multiply these 2 numbers, and get the circumference in meters.

Step-by-step explanation:

Answer:

144π or about 452.39

Step-by-step explanation:

Diameter = 24 meters

Radius = diameter/2 = 12 meters

Area of a circle = π*radius*radius = π*radius^2

Area = π*12^2 = 144π = 452.39

The highest frequency of any score in the histogram would be 5/20 = 0.25.

The score that has the highest frequency is 8. This is determined by counting the number of bars corresponding to each score. In this histogram, there are 5 bars corresponding to the score 8, which is the highest number compared to any other score.

Formulaically, we can calculate the frequency for each score by dividing the number of observations for that score by the total number of observations. For the score 8, this would be 5/20 = 0.25. This is the highest frequency of any score in the histogram.

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The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".

This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,

collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.

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Option E is correct. People who are not registered to vote may bias the sample results is not a legitimate concern about the procedure being used.

People who are not registered to vote may bias the sample results is not a legitimate concern about the procedure being used because the polling firm is specifically interested in surveying a representative sample of registered voters in the United States.

The procedure targets registered voters by calling random phone numbers within the United States.

Since the focus is on registered voters, people who are not registered to vote are not part of the target population for this survey.

Therefore, their presence or absence in the sample does not affect the representativeness of the sample for registered voters. Option E is correct.

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Complete question:

A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed. - If there is no response or if an answering machine is reached, another number is automatically called. - If a person answers, a survey worker verifies that the person is at least 18 years of age. - If the person is not at least 18 years of age, no response is recorded, and another number is called. - If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used? (A) Registered voters with children under the age of 18 years may be underrepresented in the sample. (B) Registered voters with unlisted telephone numbers may be underrepresented in the sample. (C) Registered voters who have more than one telephone number may be overrepresented in the sample. (D) Registered voters who live in households consisting of more than one voter may be underrepresented. (E) People who are not registered to vote may bias the sample results.

Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

Step 1: Multiply both sides of the equation by de:

a/b * de = bc/ef * de

Step 2: Simplify the left side of the equation:

ade = bcde

Step 3: Divide both sides of the equation by ad:

a/d = b/e

Step 4: Multiply both sides of the equation by be:

ab/d = be/e

Step 5: Simplify the left side of the equation:

ab = be

Step 6: Divide both sides of the equation by be:

a/b = 1/e

Step 7: Multiply both sides of the equation by ef:

a/b * ef = 1/e * ef

Step 8: Simplify the left side of the equation:

aef = ef

Step 9: Divide both sides of the equation by ef:

a/b = 1/e

Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

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Answer:

perpendicular

b and e

congruent

Answer:

23 is 31/100

Step-by-step explanation:

not sure about the rest sorry :(

Answer:

16. Garret

17. 0

18. 4140

19. 2,3

20. 29/69

21. 3 1/3

22. choice  A

23. 31/100

24. 7

The number of pounds of apples that are in his supply is 16 pounds

Let's represent the total supply of apples by "x" pounds.

Mitch uses 1/4 of his supply of apples for apple crisp, so he uses 1/4x pounds of apples for apple crisp.

Mitch uses 3/8 of his supply of apples for pies, so he uses 3/8x pounds of apples for pies.

According to the problem, Mitch uses a total of 10 pounds of apples, so we can set up the following equation:

1/4x + 3/8x = 10

To solve for x, we can first find a common denominator for 1/4 and 3/8, which is 8:

5/8x = 10

So, we have

x = 10 * 8/5

Evaluate

x = 16

Therefore, there are 16 pounds of apples in Mitch's supply.

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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Answer:

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

Given x-values in the table.

Use the equation of the function to find the corresponding y-values:

When x = - 27:

When x = 0:

When x = 27:

So the missing numbers are: - 3, 0 and 3.

The matching choice is B.