can u please help me before it kicks me out of the tutoring.Solve the linear system of equations.

Answer:

  60°

Step-by-step explanation:

The definition of cosine tells you ...

  cos(β) = 3/6 = 1/2

  β = arccos(1/2) . . . . use the inverse cosine function to find the angle

  β = 60°

_____

The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...

  1 : √3 : 2

The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.

Answer:

Graph A

Step-by-step explanation:

We can plug the function into a graphing calculator and check to see which graph matches up.

The question's single element is divided into

A composite shape is a geometrical figure formed from two or multiple elementary shapes layered and intermixed.

These simpler elements may comprise of

As the base forms are overlapped or mixed to create an entirely new shape, they form a composite figure with a combined outline more intricate than any single component.

The single element in the question is separated to form

Learn more about geometric figure at

https://brainly.com/question/26741034

#SPJ1

Answer:

No

Step-by-step explanation:

the graph fails the vertical line test

Answer:

a

  \(P(E \ n\  Z) =  0.0196\)

b

\(P(E \ n\  Z \ n \ Y) =  0.0027\)

Step-by-step explanation:

From the question we are told that

The probability of that a person is being called for jury duty in any given year is \(P(J) = 0.14\)

Let P(E) be the probability a person being selected in the first year, Let P(Z) be the probability a person being selected in the second year

and Let P(Y) be the probability a person being selected in the third year

Generally the probability that a particular eligible person in this city is selected in both of the next 2 years is mathematically represented as

\(P(E \ n\ Z) = P(E) * P(Z) = P(J)^2\)

=>      \(P(E \ n\  Z) =  0.14^2\)

=>      \(P(E \ n\  Z) =  0.0196\)

Generally the  probability that a particular eligible person in this city is selected in both of the next 3 years is mathematically represented as

     \(P(E \ n\  Z \ n \ Y) =  P(E) * P(Z)  * P(Y) =  P(J)^3\)

=> \(P(E \ n\  Z \ n \ Y) =  0.14^3\)

=>  \(P(E \ n\  Z \ n \ Y) =  0.0027\)

This multiplication of each probabilities is valid because each probability is independent of one another

Answer:

a13

Step-by-step explanation:

a^9 × a^4 = a(9 + 4)

= a13

Answer:

the 19%

Step-by-step explanation:

we can convert each to a percentage, decimal, or fraction to solve. i used decimals:

1/5 = 2/10 = 0.2

0.22 is a decimal

19% = 19/100 = .19

then we compare

.22 > .2 > .19

The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

To know more about equation,

https://brainly.com/question/2228446

#SPJ1

Answer:

The first part is 5

The maximum it can be is 200

Step-by-step explanation:

Because I said So

Sofie will not make a profit if she sells her scarves for $5 or less.

The maximum profit Sofie can make is $200.

A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

According to the given problem,

y = (x - 5)(50 - 2x)

⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)

⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)

⇒ y - (x - 5)(-2x + 50) = 0

⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0

⇒ y - ( -2x² + 50x + 10x - 250) = 0

⇒ y - ( - 2x² + 60x - 250 ) = 0

⇒ y + 2x² - 60x + 250 = 0

⇒ 2x² -60x + y + 250 = 0

⇒ ( 2x² - 60x ) + y + 250 = 0

⇒ 2 ( x² - \(\frac{60}{2}\)x) + y + 250 = 0

⇒ 2 ( x² - \(\frac{2^{2} *3*5}{2}\)x) + y + 250 = 0

⇒ 2 ( x² - 30x ) + y + 250 = 0

⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0

⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0

⇒ 2( x - 15 )² + y = -2(-225) - 250

⇒ 2( x - 15 )² + y = 450 - 250

⇒ 2( x - 15 )² + y = 200

⇒ y = -2( x - 15 )² + 200

This equation is in the form of y =  a(x - h)² + k where the vertex of the parabola is (h , k).

Therefore the vertex of the parabola is at (15 , 200)

Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.

Learn more about parabola here:

https://brainly.com/question/5527217

#SPJ2

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


Learn more about graphs at:

https://brainly.com/question/17267403

#SPJ1

Based on the result shown in the table below, a statement which is true include the following: A. exactly 1/5 of the students chose pizza as their favorite food.

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. In order to determine the true statement, we would evaluate them as follows;

"Exactly 1/5 of the students chose pizza as their favorite food."

Total number of students that chose pizza = 6 + 4

Total number of students that chose pizza = 10 students.

Total number of students = 26 + 24

Total number of students = 50 students.

Therefore, the fraction of students that chose pizza as their favorite food is given by:

Fraction = 10/50

Fraction = 1/5.

Read more on fraction here: brainly.com/question/2194108

#SPJ1

Complete Question:

Two classes were asked what was their favorite food at a local restaurant. The results are shown in the table below.

Which statement is true?

Exactly 1/5 of the students chose pizza as their favorite food.

Less than 25% of students chose tacos as their favorite food.

More students prefer French fries than prefer tacos.

Exactly 1/2 of students prefer either pizza or hamburgers.

Answer:

(7, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

4x + 3y = 37

y = x - 4

Step 2: Solve for x

Substitution

Step 3: Solve for y

The correct option is (b) i.e. The cosecant of an angle is defined as the length of the hypotenuse over the length of the side opposite.

What is Trigonometric ratio?

Trigonometric ratios are mathematical functions used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles. The three main trigonometric ratios are sine, cosine, and tangent

All statements contain some sort of mistake except the statement (b).

The statements should be corrected as given below:

A). The cosine of an angle is defined as the length of the side adjacent over the length of the hypotenuse.

C). The cotangent function is defined as the length of the side adjacent over the length of the side opposite.

D). The sine function is defined as the length of the side opposite over the length of the hypotenuse.

To learn more about Trigonometric ratio, visit the link:

https://brainly.com/question/25618616

#SPJ1

F(-10) means the x value in the equation is -10.

Replace x with -10 and solve:

4(-10) -12 = -40 - 12 = -52

F(-10) = -52

Answer: -52

How to: Use the given functions to set up and simplify f ( − 10 ) .

Have a great day and stay safe ! sorry if im wrong

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

Know more about the domain here:
https://brainly.com/question/30096754

#SPJ8

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

The length of side KL is approximately 4.8 cm.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Using the Law of Sines, we can set up the following proportion:

l/sin(L) = m/sin(M)

Where l is the length of side KL, L is the measure of angle KLM (which is 72 degrees), m is the length of side LM, and M is the measure of angle KML (which we can find by subtracting L from 180 degrees).

M = 180 - L

= 180 - 72

= 108 degrees

Now we can substitute the given values into the proportion and solve for l:

l/sin(72) = 5.9/sin(108)

l = sin(72) * (5.9/sin(108))

≈ 4.8 cm (rounded to the nearest 10th of a centimeter)

For more question on length click on

https://brainly.com/question/28322552

#SPJ11

Answer:

4

9

Step-by-step explanation:

If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.

If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.

Answer:

4

9

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

For such more questions on amount

https://brainly.com/question/24644930

#SPJ8

Answer:

A

Step-by-step explanation:

Point R is (1, 5).

The transformation (x + 1, y - 1) denotes a translation of one unit to the right and one unit downwards.

Simply add one to the x-coordinate and subtract one to the y-coordinate of R. Hence:

\(R'=((1)+1, (5) -1)=(2, 4)\)

Next, we want to dilate RUST by a scale factor of three. Since the dilation is centered on the origin, we can simply multiply each coordinate by three. This yields:

\(R'=(3(2), 3(4))=(6, 12)\)

Our answer is A.

the required standard error is 6.9 for the sampling distribution.

The standard error of the sampling distribution is given by the formula SE = sqrt( (SD1² / n1) + (SD2² / n2) )

As per the question, we are given that samples of size 51 are drawn from population A with a standard deviation of 5.49, and samples of size 76 are drawn from population B with a standard deviation of 5.06.

Substituting these values into the formula, we get:

SE = √( (5.49² / 51) + (5.06² / 76) )

SE = √( (30.11) + (17.93) )

SE = √(48.04)

SE = 6.9

Therefore, the required standard error is 6.9 for the sampling distribution.

Learn more about the standard deviation here:

https://brainly.com/question/16555520

#SPJ1

Answer:15

Step-by-step explanation:

Check the picture below.

\(243=9(r)(r)(r)\implies 243=9r^3\implies \cfrac{243}{9}=r^3\implies \sqrt[3]{\cfrac{243}{9}}=r\implies \boxed{3=r} \\\\[-0.35em] ~\dotfill\)

\(n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{5}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{3} \end{cases}\qquad \implies a_5=a_1\cdot 3^{5-1} \\\\\\ 243=a_1\cdot 3^{5-1}\implies 243=a_1\cdot 3^4\implies 243=a_1\cdot 81 \\\\\\ \cfrac{243}{81}=a_1\implies \boxed{3=a_1}\hspace{12em} {\Large \begin{array}{llll} a_n=3(3^{n-1}) \end{array}}\)

Answer:

The null hypothesis is   \(H_o : \mu_A - \mu_B = 0\)

The alternative hypothesis is  \(H_a : \mu_A - \mu_B > 3\)  

Step-by-step explanation:

From the question we are told that

  The mean of method A is \(\mu_A = 46.31\)

  The standard deviation of method A is  \(\sigma = 6.44\)

   The  mean of method B is  \(\mu_B = 42.79\)

   The standard deviation of  method B  is  \(\sigma_B = 7.52\)

An appropriate set of null and alternative hypothesis to determine whether Method A increases students points by more than 3 points is

The null hypothesis is   \(H_o : \mu_A - \mu_B = 0\)

The alternative hypothesis is  \(H_a : \mu_A - \mu_B > 3\)  

The volume of the rectangular prism is 4.84 cm cube.

A rectangular prism is filled exactly with 605 cubes. Each cube has edge

length 1 / 5 cm. Therefore, the volume of the rectangular prism can be

calculated as follows:

volume of each cube = l³

volume of each cube = (1 / 5)³

volume of each cube = 1 / 125 cm³

Therefore,

volume of the rectangular prism = 605 × 1 / 125

volume of the rectangular prism = 605 / 125

volume of the rectangular prism = 4.84 cm³

learn more on rectangular prism here: https://brainly.com/question/29175503

#SPJ9

Answer:

18.84

Step-by-step explanation:

You multiply 3 by 2 and then 6 by 3.14

Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the number. The the difference of the number and 7 is (x-7). We are told that twice that is -22, so we can write ...

  2(x -7) = -22 . . . . written using math symbols

__

To solve this, we can divide by 2:

  x -7 = -11

and add 7:

  x = -4

The number is -4.

For the given integers and equations -

(a) The proposition is true.

(b) The proposition is false.

(b) The proposition is true.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

(a) There exist integers x and y such that 4x + 6y = 2.

This proposition is true.

We can solve the equation 4x + 6y = 2 for integers x and y by subtracting 4x from both sides and then dividing by 2 -

4x + 6y = 2

6y = 2 - 4x

y = (2 - 4x) / 6

y = (1 - 2x/3)

Since x and y are integers, y must be an integer as well.

We can see that y is an integer when x is odd, so we can choose any odd integer for x and then find the corresponding value of y using the equation above.

Therefore, the statement is true.

(b) There exist integers x and y such that 6x + 15y = 2.

This proposition is false.

We can try to solve the equation 6x + 15y = 2 for integers x and y by dividing both sides by 3 -

2 = 6x + 15y

2/3 = 2x + 5y

Since 2/3 is not an integer, it is impossible to find integer values of x and y that satisfy this equation.

Therefore, the statement is false.

(c) There exist integers x and y such that 6x + 15y = 9.

This proposition is true.

We can solve the equation 6x + 15y = 9 for integers x and y by dividing both sides by 3 -

2x + 5y = 3

We can see that we can choose x = 1 and y = 1 as a solution to this equation, and since x and y are integers,

Therefore, the statement is true.

To learn more about equation from the given link

https://brainly.com/question/28871326

#SPJ1