**Answer:**

B

**Step-by-step explanation:**

1-cos2x=2sin²(x/2)

[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]

Watch the sign of the cosine function when using the cosign law. Cos 120 degrees for example, is in the second quadrant and therefore

Cos 120 is in the **second quadrant **and therefore is a negative **signed value**

What are quadrants in trigonometry?

A plane is divided into four sections, or **quadrants**, by an x-axis and a y-axis in a **rectangular coordinate system**. The letter O stands for the origin, which is the place where the two axes converge.

In the first quadrant, there are angles between 0 and 90.

In the **second quadrant**, there are angles between 90 and 180.

In the third quadrant, there are angles between 180 and 270.

In the fourth quadrant, there are angles between 270 and 360.

**Cos **is only positive in the first quadrant and in the 4th quadrant and always **negative **in the **second **and third quadrant

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Kathy is making party trays. yesterday she made 1 small tray and 4 large trays with 166 total pieces of fruit. today she made 4 small trays and 4 large trays with 232 pieces of fruit. how many pieces of fruit are on each size tray?

**Answer:**

We can start solving the problem by using a system of equations. Let x be the number of pieces of fruit on a small tray, and y be the number of pieces of fruit on a large tray.

From the information given, we know that:

Yesterday: x + 4y = 166 (1)

Today: 4x + 4y = 232 (2)

We have two equations and two unknowns, so we can use substitution to solve for one variable in terms of the other, and then substitute that back into the other equation.

From equation (1) we can solve for x:

x = 166 - 4y

Now we can substitute this into equation (2)

4(166 - 4y) + 4y = 232

Simplifying and solving for y:

-672 + 16y = 232

16y = 904

y = 56.5

This means that each large tray has 56.5 pieces of fruit.

Now we can substitute this value back into the first equation:

x + 4(56.5) = 166

x = 166 - 226

x = -60

This solution doesn't make sense, because the number of pieces of fruit can't be negative. This means that there is no solution to the system of equations, and it is impossible to determine the number of pieces of fruit on each size tray based on the information given.

**Step-by-step explanation:**

Which statement is only true for the t-test for dependent means rather than t-tests in general?

a)population variances are estimated from the information in the sample of scores actually studied

b)pretest

**Pretest-posttest** experimental designs are common is true for the t-test for dependent means rather than t-tests in general.

The correct answer is option B.

The use of pretest-posttest **designs **extends the posttest alone design with nonequivalent groups, one of the most fundamental methods for assessing the effectiveness of an intervention. One group in this two-group design undergoes therapy, and the final results are produced for the other group.

In conclusion, **quasi**-experimental design has long been a popular research methodology. An intervention that has been delivered to a group of study participants may be easily evaluated using pre-test and post-test designs, a sort of quasi-**experimental **research. A pretest is an assessment tool used by study participants before they get any form of therapy. Participants in a study are given a posttest, which is an evaluation tool, following their participation in the study.

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Use properties to evaluate (+)(-10).

OA. 2

OB. -2

C. 5

OD. -5

Try 2 I think it is correct

Solve -11/14x(-1/17)=?

The **solution **to the **expression **-11/14 x (-1/17) is 11/238

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

-11/14x(-1/17)

**Express **properly

So, we have the following representation

-11/14 x (-1/17)

Remove the **brackets**

This gives

-11/14 x (-1/17) = 11/14 * 1/17

So, we have

-11/14 x (-1/17) = 11/238

Hence, the **solution **is 11/238

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Please help me! Thank you so much!

The **mean **of the numbers, given the stem and leaf plot of the number of **classrooms **in each school in the city, is 84 classrooms

To find the mean of the **schools**, you first need to add up the number of **classrooms **in each school and then divided this sum by the number of schools that Evelyn used in the social studies project.

When using a **stem and leaf plot** in this instance, the stem is the tens figure and the leaf is the ones figure.

This means that a stem of 7 and lead of 7 means 77 classes.

The sum of the number of classrooms is therefore :

= 77 + 77 + 81 + 81 + 82 + 82 + 83 + 84 + 84 + 85 + 85 + 87 + 90 + 90 + 92

= 1, 260 classrooms

The **mean **is therefore :

= 1, 260 / 15 schools

= 84 classrooms

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can you help me find x and y

please and thank you!!!

and if you could explain that will be appreciated! :D

4x + y = 42 => y = 42 - 4x

3x - 2y = 26 => 3x - 2×(42 - 4x) = 26 => 3x - 84 + 8x = 26

=> 11x - 84 = 26 => 11x = 110 => x=10

y = 42 - 4x => y = 42 -4×10 => y= 42 - 40 => y= 2

**Answer:**

[tex]x = 10[/tex] and [tex]y = 2[/tex]

**Step-by-step explanation:**

That appears to be a parallelogram, so we can make the assumption that one side of the shape is equal to the side opposite to it because they are parallel lines.

With that assumption, we can set-up the equations, namely

[tex]42 = 4x+y[/tex] (eq. 1)

[tex]26 = 3x-2y[/tex] (eq. 2)

We can solve for x and y either through substitution or elimination, and it seems like elimination could be a faster way to do it.

Multiply eq. 1 by 2 and add it to eq. 2

[tex]84 = 8x+2y\\26 = 3x-2y[/tex]

-> [tex]110 = 11x[/tex]

[tex]x = 10[/tex]

And then we can substitute it back to any equation, and the result will be

[tex]y = 2[/tex].

Graph the line with slope - 1 passing through the point (4, 3).

**Answer: y = -x+7**

**Step-by-step explanation:**

Let's first set up it in slope-intercept form.

y = -x+b

We can find b using point (4,3).

Substitute 4 for x and 3 for y to get:

-3 + b = 4

b = 7

Therefore, the line is y = -x+7

Solve for t

4t = 20

t=?

4t=20

Divide both sides by 4

T=5

Divide both sides by 4

T=5

An industrial cleaning solution calls for 5 parts water to 2 parts concentrated cleaner. If a worker uses 15 more quarts of water than concentrated cleaner to make a solution.

A how much concentrated cleaner did she use ?

B how much water did she use ?

C how much solution did she make ?

**Answer: A. To find out how much concentrated cleaner the worker used, we can set up the equation: x + 15 = 5x/2, where x is the amount of concentrated cleaner used in quarts. Solving for x, we find that the worker used 15 quarts of concentrated cleaner.**

**B. Since we know that the worker used 15 more quarts of water than concentrated cleaner, we can find out how much water she used by adding 15 quarts to the amount of concentrated cleaner used. In this case, the worker used 15 quarts + 15 quarts = 30 quarts of water.**

**C. To find out how much solution the worker made, we add the amount of concentrated cleaner used and the amount of water used. In this case, the worker made 15 quarts + 30 quarts = 45 quarts of solution.**

**Step-by-step explanation:**

Cuando se calcula la potencia de un producto, que sucede con el exponente en los factores del producto, se.

Según el **álgebra de números reales**, la **potencia** del **producto** es el producto de las potencias.

¿Cómo determinar la potencia de un producto de dos números reales?

De acuerdo con la pregunta, tenemos el caso del **producto** de dos **números reales** a, b elevados a un **potencia** n, cuya descripción matemática se presenta a continuación:

(a · b)ⁿ

De acuerdo con el **álgebra de números reales**, este caso tiene la siguiente equivalencia:

(a · b)ⁿ = aⁿ · bⁿ

De modo, pues, que la potencia de un producto de dos **números reales** es igual al producto de las potencias de los números reales.

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which of the following would be examples of statistics? select all that apply. (check all that apply)

**Answer:**

0 votes

**Step-by-step explanation:**

When graphing a linear function in slope intercept form, why do you have to plot the y-intercept first? Why car't you use the slope first? Math

**Answer: Because the slope doesn't tell you any actual points on the line. It only tells you whether the line tilts up or down, and how steeply.**

**Step-by-step explanation:**

Which statement about the slope of the line is true? a It is fraction 1 over 6 throughout the line. b It is 6 throughout the line. c The slope from point O to point A is fraction 1 over 6 times the slope of the line from point A to point B. d The slope from point O to point A is six times the slope of the line from point A to point B.

The** slope** of the given line that passes through (4, 2) and (6, 3) is **m = 1/2**.

The general equation of a straight line is -

**y = mx + c**

{m} - slope.

{c} - intercept along the y - axis.

Given are the statements regarding the **slope** of the line as given.

The line passes through the points -

(4, 2) and (6, 3)

The **slope** of the line will be -

m = (3 - 2)/(6 - 4)

**m = 1/2**

Therefore, the** slope** of the given line that passes through (4, 2) and (6, 3) is **m = 1/2**.

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In matrix C, what is the value of c34 +c51

In **matrix **C** value **of c34 + c51 = 3 + 9 = 12

A matrix is a rectangular or square arrangement of numerical terms where the terms are arranged into **rows** and columns. Depending on the size of rows and columns, matrix are various types such as square, rectangular, upper triangular, lower triangular and so on.

**What is the value of c34+ c51?**

we are given a 5 × 5 matrix **square** matrix that means number of rows and number of columns is both 5.

the matrix is denoted by C.

C = 2 9 5 7 5

** **4 2 4 4 3

** **3 8 2 3 8

** **2 3 4 8 2

** **9 7 7 3 1

we know the formula for identify the elements of a matrix is given by

a₁₁ a₁₂ a₁₃ a₁₄ a₁₅

a₂₁ a₂₂ a₃ a₂₄ a₂₅

a₃₁ a₃₂ a₃₃ a₃₄ a₃₅

a₄₁ a₄₂₂ a₄₃ a₄₄ a₄₅

a₅₁ a₅₂ a₅₃ a₅₄ a₅₅

The above is a 5 x 5 square matrix in where the elements are identified by a.

If we compare the two matrices, we can determine that c34 is 3 and c51 is 9.

Therefore, c34 + c51 = 3+9 =12

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A train traveled 800 km in 8 hours. What is the speed at which the train traveled?

Speed = Distance / time

Speed = 800km / 8h

Speed = 800km/h

Speed = 800km / 8h

Speed = 800km/h

Use the properties of exponents to simplify the expression.

(y3/2 x -1/2)^4

**The properties of exponents used to simplify the expression are:**

**(a^m)^n = a^(m*n)**

**(a^m)^n = (a^n)^m**

**(a*b)^n = a^n * b^n**

**(a/b)^n = a^n / b^n**

**Using these properties, we can simplify the expression as follows:**

**(y3/2 x -1/2)^4**

**= (y^3/2 * x^-1/2)^4**

**= y^3/2 4 * x^-1/2 4**

**= y^(3/24) * x^(-1/24)**

**= y^6 * x^-2**

**So the simplified expression is: y^6 * x^-2**

Which equation represent the rule

**Answer:**

**y = 3x -8**

**Step-by-step explanation:**

8 times less means something will have to be (-8)

3 times the value of x is equal to (3x)

by looking at the answers we can deduct that our answer in fact is y = 3x -8

5

432-

1

--5-4-3-2-1 1

ENTY

-2

-3-

-4

Mark this and return

23

45x

Which function is represented by the graph?

Of(x)=-x-31 +4

Of(x) = -x + 3) +4

O f(x) = -x-41+3

Of(x) = -x +41 +3

Save and Exit

Next

4

27

Submit

On solving the provided question, we can say that the value of the **equation **here is f(2) = -29 and f(3) = -41

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A **mathematical statement **that establishes the equality of two mathematical **expressions** is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation here is

f(x)=-x-31 +4

f(2) = -29

f(x) = -x-41+3

f(3) = -41

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Evaluate the expression when n=-3. n^2-9n-6

**Answer: 30**

**Step-by-step explanation:**

n= -3

-3^2 = 9

9(-3) = -27

9-(-27)-6 = 30

Please help asap giving 50 points for it!!!

The system of **inequalities** which can be used to determine the number of dogs, d, and the number of **cats**, c, Nadia can house in the facility on any given day is:

A. 3.45c + 4.60d ≤ 200.

c + d ≤ 50.

How to write the required system of linear inequalities?In order to write a system of **linear inequalities** to describe this situation, we would assign variables to the number of **dogs** and number of cats respectively, and then translate the word problem into algebraic equation as follows:

Since the daily cost for her facility to house a cat is $3.45 and $4.60 for a **dog**, with a budget of $200, a linear inequality which represents this situation is given by;

3.45c + 4.60d ≤ 200.

Additionally, the facility has a total of 50 pens;

c + d ≤ 50.

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easy please help area of a trapezoid using decomposition

The **area** of the **trapezoid** is calculated as: D. 90 square units.

To find the **area** of the **trapezoid** that is shown in the image above, we can **decompose** the **trapezoid** into three shapes which are one rectangle and two identical triangles.

**Area** of triangle = 0.5 * base * height

**Area** of rectangle = length * width.

Given the following:

x = 8 units

y = 2 units

h = 9 units

**Area** of the 2 triangles = 2(0.5 * y * h) = 2(0.5 * 2 * 9) = 18 units²

**Area** of rectangle = x * h = 8 * 9 = 72 units²

**Area** of **trapezoid** = 18 + 72 = 90 units²

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What is the perimeter of the figure?

A. 65 in.

B. 140 in.

C. 64 in.

D. 180 in.

D

ok is the force that I have to go in and out for the June exam and the Zumba

Math on the Spot Lena wants

to put the elephant stickers in

an album. She says she will use

more pages if she puts 5 stickers

on a page instead of 10 stickers

on a page. Is she correct?

Explain.

Lena is not correct in her **statement **that she will use more pages if she puts 5 stickers on a page instead of 10 stickers on a **page**.

**Is it true that if you put 8 stickers on a page instead of 4, you will use less pages?**

Yes, it is true that if you put 8 **stickers **on a page instead of 4, you will use less pages. The total number of stickers divided by the number of stickers per page **determines **the number of pages needed. In general, the more stickers per page, the less **pages **will be needed to hold the same number of stickers.

If Lena puts 10 stickers on a page, she will need fewer pages than if she puts 5 stickers on a page.

For example, if she has 50 **elephant **stickers, she would need 5 pages if she put 10 stickers on a page, but she would need 10 pages if she put 5 stickers on a **page**.

This is because the total number of stickers **divided **by the number of stickers per page determines the number of pages needed. In general, the fewer stickers per page, the more pages will be needed to hold the same **number **of stickers.

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A vet tech uses ½ oz, ¾ oz, and 5/8 oz of solution to perform three urinary

analysis tests. How much total solution does she use?

**Answer:**[tex]\frac{15}{8}[/tex]** or **[tex]2 \frac{7}{8}[/tex]

**Step-by-step explanation:**

**Adding,**

[tex]\frac{1}{2}+\frac{3}{4}+\frac{5}{8} =\frac{4+6+5}{8} =\frac{15}{8}[/tex][tex]=2\frac{7}{8}[/tex]

DUE SOON! PLEASE HELP!

The evaluation of the **functions** in the question are as follows;

1. a) [tex]y = \dfrac{1}{x^2+5} -3[/tex]is not a **quadratic** function

b) The **function** is a quadratic function

c) The function is a quadratic function

d) The function is a quadratic function

2. Please find attached the graph of the function, *y* = -2·(x + 3)² + 4, created (for clarity) with MS Excel

a) The **axis of symmetry** is; x = -3

b) The **maximum** value is; (-3, 4)

c) The **x-intercepts** are; √2 - 3, and -√2 + 3

d) y-intercept is (0, -14)

e) The domain is the set of all real numbers

The range is (-∞, 4]

What is a function?A **function** is a **rule** that **maps** an input value unto an output, such that each input has exactly one output.

A **quadratic** function is a function of the form; y = a·x² + b·x + c

a) The function [tex]y = \dfrac{1}{x^2+5} -3[/tex], when simplified, we get;

[tex]y = \dfrac{1 - 3\cdot x^2 - 15}{x^2+5}[/tex], which is a **rational** polynomial.

Therefore, the function is not a quadratic function.

b) x² = y - 1

y = x² + 1

The above function is in the form; *y *= a·x² + b·x + c, where;

a = 1, b = 0, c = 1

c) y = 3·x - 7 + 4·x²

The above function is in the form *y *= a·x² + b·x + c, where;

a = 4, *b* = 3, and *c* = -7

d) The function *y* = 6·x - 3·√x can be expressed as; √x = z

Therefore; z² = x

Therefore; *y* = 6·x - 3·√x = 6·z² - 3·z

y = 6·z² - 3·z

The above function is a quadratic function, therefore, the function;

y = 6·x - 3·√3 is a quadratic function

2. The function *y* = -2·(x + 3)² + 4 is in the vertex form of the equation of a quadratic equation; y = a·(x - h)² + k

Where;

a = The leading coefficient

(h, k) = The coordinates of the vertex

Comparing the values, we get;

The vertex, (h, k) = (-3, 4)

a = -2

When *x* = 0, we get; *y* = -2·(0 + 3)² + 4 = -2 × 9 + 4 = -14

With a vertex of (-3, 4), we get;

When *x* = -6, *y* = -14

The graph can be obtained by drawing a parabola with vertex at (-3, 4), and passing through the points (0, -14), and (-6, -14)

Please find attached the graph of the function *y* = -2·(x + 3)² + 4, created with the points (0, -14), (-6, -14), and vertex point (-3, 4), created with MS Excel

a) The **axis of symmetry** is the line about which the graph is symmetrical

The axis of symmetry is the line *x* = -3

b) The maximum value is the vertex of the graph, which is the point (-3, 4)

c) The **x-intercept **are the point the graph intersects the x-axis, which are obtained by plugging in *y* = 0, as follows;

*y* = 0 = -2·(x + 3)² + 4

(x + 3)² = -4/(-2) = 2

x + 3 = ±√(2)

x = ±√(2) - 3

The x-intercepts are; *x* = √2 - 3, and -√2 - 3

d) The y-intercepts are the point the graph intersects the y-axis, which is the point where *x* = 0

Therefore, the y-intercept is the point (0, -14)

e) The domain is the set of possible input values or *x*-values

The domain of the function, as presented in the graph is the set of all real numbers

The domain is; (-∞, ∞)

The range is the set of the possible *y*-values

The graph of the function indicates that the maximum y-value is the point *y* = 4

Therefore, the range of the function is; -∞ < y ≤ 4, which is (-∞, 4]

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Find the value of each expression

0.5 exponent 4 + 1

**Answer:**

5

**Step-by-step explanation:**

adde it all upa and get the answer

WHiche quation represtents the line that hs a slope of 1/3 and an x-intercept of 5?

The correct option is B.

The **Equation** that represents the **line** that has a **slope** of 1/3 and an x-intercept of 5 is y-0 = 1/3(x-5)

The** slope** of a** line** is the measure of the **steepness **of a line and its **direction**. It can be used to predict whether the lines are parallel, perpendicular, or none.

The slope of any line can be calculated using any two distinct points lying on the line.

y -y1 = m(x-x1)

where y1 = 0

x1 = x-intercept = 5

y-0 = 1/3(x-5)

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Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. Determine the price of each bag of popcorn and the price of each drink.

The price of each bag of **popcorn** and the price of each **drink** is $7.5 and $4 respectively.

Let the **drinks** be represented as d.

Let the popcorn be represented as p.

From the information, **Xochitl** went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:

6p + 4d = 65

Alonso went into the same **movie** theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:

9p + 8d = 107.50

Equating the **equation**

6p + 4d = 65 ..... i

9p + 8d = 107.50 ..... ii

Multiply equation i by 8

Multiply equation ii by 4

48p + 32d = 520

36p + 32d = 430

12p = 90

**Divide**

p = 90/12

= 7.5

6p + 4d = 65 .

6(7.5) + 4d = 65

4d = 65 - 45

4d = 20

d = 20/4 = 5

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A large hospital has an average of 7 fatalities in a week. Using the Poisson model, what is the probability that this week it has 7fatalities? The probability that the hospital has 7 fatalities this week is

The **probability **that the **hospital **has 7 **fatalities **this week is approximately 0.0199

The **probability **that the hospital has 7 fatalities in a week, given an average of 7 **fatalities **per week, can be calculated using the **Poisson **distribution. The Poisson distribution is a **discrete **probability distribution that models the number of events (in this case, fatalities) that occur in a fixed interval of time (in this case, a week) with a certain average rate (in this case, 7 fatalities per week). The probability of k events happening in a given interval of time is given by the following formula:

P(k;λ) = (e^(-λ))*(λ^k)/k!

Where λ is the average number of events per interval of time and k is the number of events we are interested in.

In this case, we are looking for the probability that there are 7 fatalities this week, given that the average number of fatalities per week is 7. So we can plug in the values into the **equation**:

P(7;7) = (e^(-7))(7^7)/7! =0.149

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acceptance rejection method for standard normal distribution using standard laplace proposed
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in the neurotrauma unit, a teenager with a closed head injury related to an automobile accident is experiencing high intracranial pressure. T/F?
stimuli are carried to the brain from the periphery along the efferent neurologic tract.T/F
At the beginning of her speech, Elizabeth says the following regardinggiving women the right to vote: Had we a vote to give, might not the officeholders and seekers propose some change in woman's conditions?" Whatdoes she mean by this?
Please Help me solve for B
Compute |(x, t)|2 for the function (x, t) = (x)sin(t), where is a real constant. (Use the following as necessary: for (x), , t. Simplify your answer completely.)|(x, t)|2 =
Why was order important to the people of the medevil times?
Which function rule would help you find the values in the table n=2,4,6 m=-6,-12,-18
The New Democrats took control with the election of President Bill Clinton. Identify his ambitious agenda and evaluate the successes and failures that his agenda experienced. How is this an example of the polorized political actions we see today?
"alcoholics with Korsakoff's psychosis and memory loss often tell elaborate stories of imagined past trying to fool others into thinking they remember. What is this behavior called?(a) anterior communication(b) fuzzy trance memories(c) amnesia(d) confabulation"
A quadratic graph has equation y = (x-1)(x+7)Find the values of a, b and c.