How do you look for a correlation using data points?

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

[tex]3x+2x+4=39 \\ \\ 5x+4=39 \\ \\ 5x=35 \\ \\ x=7[/tex]

the solutions of the following expressions are:

a) π/6

b) - π/6

c) - π/4

Trigonometry is the field of mathematics that deals with certain angles' functions and how to use such functions in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.

The lengths, heights, and angles of various triangles are studied in relation to one another in mathematics. The field was created around the third century BC as a result of the use of geometry in astronomical research.

a)

tan ⁻¹ (√3/3)

= tan ⁻¹ (1/√3)

= tan ⁻¹ (tan π/6)

= π/6

b)

tan ⁻¹ (-√3/3)

= tan ⁻¹ (-1/√3)

= tan ⁻¹ (tan - π/6)

= - π/6

c)

tan ⁻¹ (-1)

= tan ⁻¹ (tan - π/4)

= - π/4

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For the given question the two triangles are similar the length of side WX = XY.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two triangles XWZ and XZY are similar triangles based on ASA criteria.

Since, the two triangles are similar the length of side are also equal.

Hence, WX = XY.

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Answer:

3/4

Step-by-step explanation:

1 1/2 = 3/2

3/2 - x = 3/4

6/4 - x = 3/4

Hence,

x = 6/4 - 3/4 = 3/4

[tex]-8x+2 > 0[/tex]

Subtract 2 from both sides:

[tex]-8x+2-2 > 0-2[/tex]

[tex]-8x > -2[/tex]

Divide both sides by -8:

[tex]\dfrac{-8x}{-8} > \dfrac{-2}{-8}[/tex]

(Since we are dividing by a negative number, the sign will reverse)

[tex]x < \dfrac{1}{4} \texttt{ or }x < 0.25[/tex]

The system of inequalities to represent this real-world scenario is

[tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]

Given data :

Let  x be the number of adults and y be the number of campers.

There are rooms for 450 people, so

x+y≤450.

Each adult costs $7, then x adults cost $7x.

Each camper costs $4, then y campers cost $4y.

There is a maximum budget of $1,150, so

7x+4y≤1,150

Hence, you get the system of two inequalities:

 [tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]

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Podemos escribir "La diferencia de dos numeros mas otro numero" como:

(x - y) + z

Queremos escribir "La diferencia de dos numeros mas otro numero"

Pimero, recordar que la diferencia entre dos numeros se refiere a la resta entre dos numeros, entonces podemos empezar escribiendo:

(x - y)

Donde x e y son los dos numeros de los que tomamos la diferencia.

Y a esto le debemos sumar otro numero, que puede ser otra variable z, entonces obtendremos:

(x - y) + z

Esta es la expresion usando lenguaje algebraico.

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Subtract 90 from 180, which is 90 degrees.

Then you get the equation of 2x+56 = 90 for which the 2 represents the split between the 90 degrees and the +56 is the 56 degrees higher than the smaller angle.

Solving this gives you x = 17 degrees, which is the small angle.

For 17+56 = 73 = larger angle

17+73 = 90 plus the other 90 gives you 180 total.

Answer:

The smallest angle is 17°

Step-by-step explanation:

All the angles add up to 180°. Use this to write an equation.

x = smallest angle

x+56 = not the smallest angle

90 = the right angle

x + x+56 +90 =180

combine like terms

2x + 146 = 180

subtract 146

2x = 34

divide by 2

x = 17

The smallest angle is 17°.

see image.

The value of the equation is f ( 5 ) = 36

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( n ) = 8n - 4   be equation (1)

Now , when the value of n = 5 , we get

Substitute the value of n = 5 in the equation , we get

f ( 5 ) = 8 ( 5 ) - 4

On simplifying the equation , we get

f ( 5 ) = 40 - 4

f ( 5 ) = 36

Hence , the value of equation is f ( 5 ) = 36

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Answer:

Not always

Step-by-step explanation:

If you multiply

7894 times 5 it equals 39470

but,

if you multiply

1234 times times 5 it equals 6170

this is also true with multiplying the 4 digit number by 1.

Answer: C, y=|x+4|-2

Step-by-step explanation:

I have access to a Desmos Calculator.

The value of Sin(90) is equal to 1.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Sin(90) and to find the value using the unit circle

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.

The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

Hence, Sin (90) is equal to 1.

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The relation (0, 0), (2, 0), (2, 2), (3, 4) and (6, 6) is not function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

(0, 0), (2, 0), (2, 2), (3, 4) and (6, 6).

Now, we now that any relation is said to be function if the every input value have their corresponding value and the input value should be distinct.

So, there is no two input values repeat.

Then, the given relation is not a function because in the relation the same input value 2 have output 0 and 2.

Hence, the relation is not function.

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By solving an algebraic equation we will see that Mike needs to use 30 pounds of the $5 jelly beans.

Mike wants to mix beans worth $5 per pound with 10 pounds of jelly beans worth $2 per pound to get a mixture that he can sell for $4.25 per pound

If he uses x pounds of the $5 beans, then we can write the equation:

x*$5 + 10*$2 = (10 + x)*$4.25

And now we can solve that equation for x.

$5*x + $20  = $42.50 + $4.25*x

$5*x - $4.25*x = $42.50 - $20

$0.75*x = $22.50

x = $22.50/$0.75

x = 30

So Mike needs to use 30 pounds of the $5 beans.

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Answer: There will be approximately 1154.6 people attending.

Step-by-step explanation:

To find out how many people will be attending in 4 years, we can use the formula:

Attendance(future) = Attendance(current) * (1 - rate)^time

Where:

Attendance(current) = 1200 people

Rate = 0.5% (as a decimal = 0.005)

Time = 4 years

So, Attendance(future) = 1200 * (1 - 0.005)^4

Attendance(future) = 1200 * 0.99^4 = 1200 * 0.9605 = 1154.6 people

So, in 4 years, there will be approximately 1154.6 people attending.

Three possible solution of this problem  are(x = 10, y = 0)(x = 6, y = 3),(x = 0, y = 6).

Inequality is the unequal distribution of resources, opportunities, and advantages among different people. It can be caused by a variety of factors, such as discrimination, unequal access to education, lack of economic opportunities, or social exclusion. Inequality has a negative effect on society, as it can lead to poverty, health issues, and a lack of economic growth. It is important to address inequality in order to create a more equitable society and ensure everyone has the same opportunities for success.

Linear Inequality: 10x + 20y ≤ 30,(x = 6, y = 3),

where x is the number of 10-minute appointments and y is the number of 20-minute appointments.

Graph:

The graph of the linear inequality 10x + 20y ≤ 30 is a half-plane, with a boundary line of 10x + 20y = 30 and a solution region of 10x + 20y ≤ 30.

Possible Solutions:

1) 10 10-minute appointments and 0 20-minute appointments (x = 10, y = 0)
2) 6 10-minute appointments and 3 20-minute appointments (x = 6, y = 3)
3) 0 10-minute appointments and 6 20-minute appointments (x = 0, y = 6).

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Answer:

The graphs of y = 3x + 4 and y = 3x + 7 are parallel because their slopes are the same (3).

The graphs of y = 2x - 5 and y = 5x - 5 are neither parallel nor perpendicular because their slopes are not the same (2 and 5).

The graphs of y = 3/5x - 3 and 5y = 3x - 10 are neither parallel nor perpendicular. The first equation is not in slope-intercept form, and the second equation is not in standard form.

The graphs of y = 7x + 2 and x + 7y = 8 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.

The graphs of y = -4x + 1 and 4y = x + 3 are perpendicular because the product of their slopes is -1.

The graphs of y = -1/3x + 2 and y = 3x - 5 are neither parallel nor perpendicular. The slopes are -1/3 and 3, which are not the same, so the lines are not parallel, and their product is not -1, so the lines are not perpendicular.

The graph of y = 4 is a horizontal line and the graph of 4y = 6 is not a function. So, they are neither parallel nor perpendicular.

The graphs of y = 5/6x - 6 and x + 5y = 4 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.

Step-by-step explanation:

A drop of water will reach the maximum height after 1.5s.

The velocity of the water is modeled by the linear equation:

v(t) = 48 - 32t

And the water reaches the maximum height when the velocity is zero.

Then we just need to solve the equation below:

48 - 32t = 0

48 = 32t

48/32 = t

1.5 = t

So it takes 1.5 seconds for a drop of water to reach its maximum height.

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Answer: The equation of a parabola is given by (y + 1/4) = 2*sqrt(10)x where the vertex is (0, -1/4) and the distance between the vertex and the focus is 2sqrt(10)

This equation is derived by using the standard form equation of a parabola and the given focus and directrix values.

Step-by-step explanation: A parabola can be defined by the set of points that are equidistant to the focus (F) and the directrix (d). The standard form equation of a parabola is (y - k) = 4p(x - h) where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix. In the given scenario, the focus is (-3, -5/4) and the directrix is y = -3/4. By using these values we can find the distance between the vertex and the focus which is 2sqrt(10) and the vertex is (0, -1/4). Then we can substitute these values into the standard form equation to get the equation of the parabola (y + 1/4) = 2sqrt(10)*x.

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95.99% probability that the company will find 2 or fewer defective products in this batch and 0.66% probability that 4 or more defective products are found in this batch.

It is a branch of mathematics that deals with the occurrence of a random event.

The binomial probability is the probability of exactly x successes on n repeated trials.

[tex]P(X=x)=C_{n,x} .p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} =\frac{n!}{x!(n-x)!}[/tex]

And p is the probability of a success on a single trial.

24 products means that n=24

3.2% are defective, thus p=0.032

The probability that 2 or fewer are defective is:

P(X≤2)=P(X=0)+P(X=1)+P(X=2)

In which P(X=0)=0.4582

P(X=1)=0.3635

P(X=2)=0.1382

0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.

The probability that 4 or more are defective is:

P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

=0.4582+0.3635+0.1382+0.0335

P(X≥4)=1-P(X<4)

=1-0.9934

=0.0066

0.0066 = 0.66% probability that 4 or more defective products are found in this batch.

Hence, 95.99% probability that the company will find 2 or fewer defective products in this batch and 0.66% probability that 4 or more defective products are found in this batch.

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Answer:

[tex]2.48\times 10^{-2}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\left(1.24 \times 10^2\right)\left(3.6 \times 10^{-3}\right)}{1.8 \times 10}[/tex]

Remove the parentheses in the numerator:

[tex]\implies \dfrac{1.24 \times 10^2 \times 3.6 \times 10^{-3}}{1.8 \times 10}[/tex]

Collect like terms in the numerator:

[tex]\implies \dfrac{1.24 \times 3.6 \times 10^2 \times 10^{-3}}{1.8 \times 10}[/tex]

Multiply the numbers 1.24 and 3.6:

[tex]\implies \dfrac{4.464 \times 10^2 \times 10^{-3}}{1.8 \times 10}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{4.464 \times 10^{2-3}}{1.8 \times 10}[/tex]

[tex]\implies \dfrac{4.464 \times 10^{-1}}{1.8 \times 10}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a \times b}{c \times d}=\dfrac{a}{c} \times \dfrac{b}{d}:[/tex]

[tex]\implies \dfrac{4.464}{1.8} \times \dfrac{10^{-1}}{10}[/tex]

Divide the numbers 4.464 and 1.8:

[tex]\implies 2.48\times \dfrac{10^{-1}}{10}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 2.48\times 10^{-1-1}[/tex]

[tex]\implies 2.48\times 10^{-2}[/tex]

Answer:

x = 8

y = 30

Step-by-step explanation:

10x + 6y = 260

5x + 7y = 250

we can use the elimination method by multiplying the second equation by -2 to get:

-10x - 14y = -500

now we can add them together:

10x + 6y = 260

-10x - 14y = -500

the 'x' will be eliminated and we have -8y = -240

y = 30

plug 30 into either equation to solve for 'x':

10x + 6(30) = 260

10x + 180 = 260

10x = 80

x = 8

Answer:23.45

Step-by-step explanation:

Answer:

103/140

or

0.74

Step-by-step explanation:

9/28 +29/70

taking L.C.M of 29 and 70

= (9×5 + 29×2)/140

= (45 + 58)/140

= 103/140

= 0.74

1)

You tutor for 9 hours.

2)

You tutor for 4 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the tap diagram,

1)

You have three parts.

A friend has one part.

This means,

4 parts = 12 hours

1 part = 3 hours

Now,

You = 3 parts = 3 x 3 = 9 hours.

2)

You have two parts.

A friend has four parts.

This means,

6 parts = 12 hours

1 part = 2 hours

Now,

You = 2 parts = 2 x 2 = 4 hours.

Thus,

You tutor for 9 hours.

You tutor for 4 hours.

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The diagram showing parallel lines and the related angles is used to fill the information

d Nail salon

c Community Center

g Library

e Gas Station

a Clothing Store

f Pet Store

h Restaurant

b Park

Two angles that are inside (between) the two lines, more especially on the same side of the transversal, are referred to as same side inside angles.

Vertical angels are the angles that are the opposite angles formed when two lines cross. They are equal to each other.

Angles with the same size that are found on opposing sides of the transversal line are known as alternate angles. Angles that alternate are equal:

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Answer:first option

Step-by-step explanation: