The picture shows angles A and B. Explain why sin(B) = sin(A) and why cos(B) = -cos(A).
​

The value of the obtuse angle by applying sine rule for the attached diagram is equal to x° = 38.2°.

As given in the question,

Diagram of the obtuse angle triangle is attached.

In the given triangle,

Name the vertex of angle x as 'C' and side opposite to angle x as AB.

Draw a perpendicular from point A to BC at point D such that AD = z .

Given m ∠ACB = x°

AB = 2y

AC = y

m ∠ABC = 18°

In ΔADB,

sinB = AD / AB

⇒ sin 18° = z / 2y __(1)

In ΔACD,

sin ACD = AD / AC

⇒ sin ( 180 - x )° = z  / y  __(2)

Divide (1) by (2) we get,

sin18° / sin ( 180 - x )° = ( z / 2y ) / ( z / y )

⇒ sin 18° / sinx° = 1 / 2

⇒ sinx° = 2sin18°

⇒ sinx° = 2 (0.309 )

⇒ x° = sin⁻¹( 0.618)

⇒x° =  38.2°

Therefore, the obtuse angle for the given attached diagram using sine rule is equal to 38.2°.

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The slope of a line perpendicular to the line y = -4x + 12 is 4.

Slope is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. Since we only have one point, we cannot calculate the slope. The slope of the original line is -4.

To find the slope of the line perpendicular to it, we take the negative reciprocal of the original slope.

Therefore, the slope of the perpendicular line is 4.

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Therefore ,we  reject H₀   Percentage of type A blood  donations differs from 40% (percentage of population having type A blood)

According to the scientific method, a theory cannot be regarded as scientific unless it has been tested. The majority of scientific hypotheses are based on observations from the past that cannot be adequately explained by the state of knowledge at the time.

Here,

We are going to develop a proportion test.

Information we have:

Proportion   P₀   =  40 %      P₀   =  0,4  (percentage of population having type A blood)

Sample size    n   =   150

Sample  mean   P  =  82/ 150      P  = 0,5466

As  P₀  =   0,4      Q₀  =  0,6     P₀*Q₀   =  0,24

1.-Test Hypothesis:

H₀    null hypothesis                            P₀   =   0.4

Hₐ   alternative hypothesis                 P₀   ≠   0.4

2.- signficance level

    a  )   α  =  0.01    we have a two tail-test      α/2    =   0.005  

    b  )   α  =  0.05                                               α/2    =   0.025

Then  from t-student table we get t(c)   n  = 150    df =  149

    a  )   α/2    =   0.005             t(c)    =  2.581

    b  )   α/2    =   0.025             t(c)    =  1.962

3.-Compute t(s)

t(s)   =   (  P  -  P₀ )  / √P₀Q₀/n  

Plugging  in known values  

t(s)   =[ ( 0.5466 -  0,4  )*√150 ] / √0.24

t(s)   = 0,1466 * 12.25 / 0.4899

t(s)   =  3.6657

Compare t(s)  and  t(c)

t(s)  >  t(c)       3.6657  >  2.581      

Then  t(s) is out of the acceptance region  we reject  H₀.

Simple inspection led us see that for

α/2    =   0.025             t(c)    =  1.962

The situation is the same

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240240 many different possible rankings are there.

What is combination?

In mathematics, a choice is made from a set of various elements whenever the order of a choices is unimportant (unlike permutations). For instance, there really are three possible combinations of the two fruits, an apple and a pear, if three fruits are provided, like an apple, a tangerine, and a pear. Formally speaking, a set S's k distinctive components make up a subset known as a k-combination. In other words, 2 combinations are identical only if all of their members are the same. (How the people are arranged in each set is irrelevant.) how many k-combinations there are for a set of n components

The formula below calculates how many ways there are to make an ordered list of "unique components chosen from a set of 'n' elements, in accordance with the arrangement principle:

P(N,R)=  [tex]\frac{n!}{n-r!}[/tex]

p(14,5)= 14!/9!

=14*13*12*11*10

=240240

Hence, 240240  many different possible rankings are there.

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Answer:

Step-by-step explanation:

1.75+ 14.50+ 3.25= 19.5

8.25% of  19.5= 1.60875

19.5 + 1.60875= 19.7 rounded

19.7+ 17%= 19.87

$19.87 is the total

I rounded so the closest to this might be the answer

Answer:

y = [tex]\frac{1}{2}[/tex]x + 2

Step-by-step explanation:

Parallel lines have the same gradient, so

y = [tex]\frac{1}{2}[/tex]x + c

Put in your point (2,3):

(3) = [tex]\frac{1}{2}[/tex](2) + c

3 = 1 + c

3 - 1 = c

2 = c

So

y = [tex]\frac{1}{2}[/tex]x + 2

If you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

What is Null hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Consider the given process:

      [tex]x_{t} = c+\alpha x_{t-1}+\beta _{t} \\E[\beta _{t}]=0\\[/tex]

Obtain mean,

     [tex]E[x _{t}]=\frac{c}{1-\alpha }[/tex]

This works only when |α|<1. If α=1 this doesn't work, it blows up, because , [tex]E[x _{t}]\neq E[x _{t-1}][/tex] i.e. the process is not stationary.

The constant refers to the term c.

The trend is easy too:

    [tex]x_{t} +c+\alpha t+\alpha x_{t-1} +\beta_{t}[/tex]

In this case,

  [tex]E[x _{t}]=\frac{c+\alpha t}{1-\alpha }[/tex]

So, if you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

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Answer:

Hope it helps

Step-by-step explanation:

f(3)-g(5) = 8(.5) - (2(5)+1) = 4 - 11 = -7

Answer:

2/10

Step-by-step explanation:
0.2 is 2 tenths. and 2/10 is also two out of ten. two out of ten is two tenths. therefor it is 2/10

Answer:

After rotating the ordered pairs 90° counterclockwise around the origin, they will become:

(3, -2)

(-7, -4)

(-4, 5)

(-6, 8)

To rotate a point 90° counterclockwise around the origin, you can use the following transformation matrix:

[[0, -1],

[1, 0]]

To rotate a point (x, y) by 90° counterclockwise, you can multiply the transformation matrix by the point, which will give you the new coordinates of the point after the rotation. For example, to rotate the point (2, 3) 90° counterclockwise, you can multiply the transformation matrix by the point:

[[0, -1],

[1, 0]] * [2, 3] = [3, -2]

Similarly, you can rotate the other points 90° counterclockwise using the same transformation matrix.

The original size of the bag is given by the equation A = 14 ounces

What is an Equation?

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 original size of the bag be = A

Now , the equation will be

The increased size of the bag = 16.8 ounces

The percentage increase in the size of the bag = 20 %

So , the equation for the percentage increase in the size of the bag is

Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag

Substituting the values in the equation , we get

A + ( 20/100 ) x A = 16.8

( 120 / 100 ) A = 16.8

On simplifying the equation , we get

Multiply by 100 on both sides of the equation , we get

120A = 1680

Divide by 120 on both sides of the equation , we get

A = 14 ounces

Therefore , the value of A is 14 ounces

Hence , The original size of the bag is 14 ounces

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Answer:

Step-by Graph the line using the slope and y-intercept, or two points

Slope=3

y-intercept=18-step explanation:

By Midsegment theorem we find the length of KL is 8.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We know by midsegment theorem, the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The length of midsegment KL =1/2 of the length of the third segment FH.

KL = 1/2(FH)

KL = 1/2(16)

KL is sixteen divided by 2.

KL = 8

Hence, the length of KL is 8.

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The 2x2 linear system can be solved by the method of substitution .

In the question ,

it is given that ,

a 2x2 linear system is the system in which there are 2 equations with two unknown ,

Step (1) : we take the value of 1 variable from 1 equation ,

Step(2) : we substitute the value of that variable in equation(2) and solve to get the solutions .

let us understand the method of substitution with the help of example .

Let the 2x2 linear system be 2x + 3y = 14   and x + y = 12

From , x+y=12 , we get

x = 12 - y ,

Substituting the value of x in 2x + 3y = 14 ,

we get ,

2(12 - y) + 3y = 14

So , y = -10  

putting in x = 12 - y ,

we get ,

x = 12-(-10) = 22 .

Therefore , the method to solve the 2x2 linear system is explained .

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Answer:

9/20

Step-by-step explanation:

hope it helps!

Could you please give me brainliest for this? Thank you!

Answer:

Step-by-step explanation:

cdcdfcdfvdsfdf

Step-by-step explanation:

Simulteanous Equations are multiple equations with corresponding number of unknown variables.

They can be solved by 2 methods: Substitution and Elimination Method.

x = 4

y = 8

We will use the Elimination Method since the question specify as so.

4x - 3y = -8 (Equation 1)

9x - 3y = 12 (Equation 2)

By using Equation 1 - Equation 2,

4x - 9x - 3y - (-3y) = - 8 - 12

-5x - 3y + 3y = - 20

-5x = - 20

x = - 20 ÷ - 5 = 4

Now we substitute x = 4 into Equation 1.

4(4) - 3y = - 8

16 - 3y = - 8

-3y = - 8 - 16

-3y = - 24

y = - 24 ÷ - 3

= 8

Therefore the varables are:

x = 4

y = 8

The correlation coefficient that represents a perfect linear relationship between x and y is 1 and -1. (Option C and D)

The correlation coefficient refers to a statistical measure of the strength of a linear relationship between two variables and lies with the range from -1 to 1. In other words, a correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another.

A linear relationship is a statistical term which is used to describe a straight-line relationship between two variables. A perfect linear relationship refers to a relationship in which one of the variables can be perfectly explained by a linear function of the other and can be achieved by the correlation coefficient of 1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

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The evergreen tree grew 2.4 feet taller the next year.

Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

It is given by:

Percentage = (given value / total value) * 100%

From the question, the tree has a base height of 20m, if it grew 20% taller then;

tree height = 12 x (20/100)

tree height = 12 x 0.2

tree height = 2.4

Therefore, the tree grew 2.4 feet taller the next year.

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To find rank of mark

From the given options 1st option is correct

both 1 and 2 need

Given statements are

1. there are 45 students in class.

2. 12 students scored less than mark.

we need both 1 and 2 statements to find the rank of mark

without knowing the class strength we cannot find the rank of marks

and we should also know that how many students have scored less than mark in 2nd statement it is given that 12 students scored less than mark.

from the given options 1st option is correct

both 1 and 2 need

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It is false, that the margin of error of a confidence interval is the error from biased sampling methods.

The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.

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The probability of surviving for 3 years will be 54.8.

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

one hundred eighty patients were treated for disease x from 2007 to 2009.

The probability of surviving for 3 years=P 2007*P 2009*P 2010.

According to given information,

The probability of surviving for 3 years will be 54.8.

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Answer: $18.50

Step-by-step explanation:

Take 277.50 divided by 15 = $18.50

The required price of each tube for rent is given as $18.6.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Renting 15 tubes for a float down the Ichetucknee River costs $277.50 for a group.
So,
Let the rent of each tube be x,
According to the question,
15x = 277.50
x = 277.50 / 15
x = 18.6

Thus, the required price of each tube for rent is given as $18.6.

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The length is 33.37 yards of the hypotenuse.

What is Congruence of triangles ?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In congruent triangle, corresponding sides are equal.

We know, Pythagorean theorem is

Hypotenuse ² = perpendicular² + base²

Let x = be the measure of length of two legs of a right triangle

H² = x² + x²

H² = 2x²

We know, x = 23.6 yards

H² = 2(23.6)²

H² = 1113.92

H = 33.37 yards

Hence, the length is 33.37 yards of the hypotenuse.

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The greatest number of servings that can be made from this package is 11.

This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Since the unopened package of cream cheese contains 8 1/4 ounces of cream cheese and a serving is 3/4 of an ounce.

The greatest number of servings that can be made from this package will be simply be gotten by dividing the fractions that are given in the question. In this case this implies that we have to divide 8 1/4 by 3/4. This will be illustrated as:

= 8 1/4 ÷ 3/4.

= 11

The above calculation simply shows that the greatest number of serving will be 11.

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Therefore width = 10cm

                 height = 20cm

                 length = 20cm

given that

volume = 4,000[tex]cm^{3}[/tex]

let height = h

    width = w

    length = l

width and length are equal

height = length = h

volume of box = height × width × height

             4000  = h × w × h

             4000 = [tex]h^{2}[/tex]w

                  w = 4000/[tex]h^{2}[/tex]

surface area(SA) = area of base + sum of area of each side

                           =  [tex]h^{2}[/tex] + hw + hw + hw + hw

                           =  [tex]h^{2}[/tex] + 4hw

substitute y = 4000/[tex]h^{2}[/tex]

SA =  [tex]h^{2}[/tex]  + 4x(4000/ [tex]h^{2}[/tex] )

SA =  [tex]h^{2}[/tex]  + 16000/h

Taking the derivative:

SA' = 2h - 16000/ [tex]h^{2}[/tex]

making SA' = 0:

0 = 2h - 16000/ [tex]h^{2}[/tex]

2h = 16000/ [tex]h^{2}[/tex]

2[tex]h^{3}[/tex] = 16000

[tex]h^{3}[/tex] = 8000

h = 20 cm

w = 4000 /  [tex]h^{2}[/tex]  = 4000 / 20² = 10 cm

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

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Answer:

The length of the side of the square should be 10ft

Step-by-step explanation:

Calculation of the length of the side:

Since A square has an area of 40 square feet.

As we know that the square does have 4 sides

So, the length of the side of the square should be

40 divided by 4

= 10ft

The length of the perimeter of the rectangle = 112 cm or 44 inches

Given in the question,

Area = [tex]105in^{2}[/tex]

= 677.4 [tex]cm^{2}[/tex]

Length of one side of the rectangle = 7 inches

= 17.7 cm

∴ Since the length of one side of the rectangle is given in the question we need to find the width of the rectangle to calculate the total perimeter of the rectangle

⇒ Area = length x width

⇒ 677.4 = 17.7 x width

⇒ Width = [tex]\frac{Area}{Length}[/tex]

⇒ Width = [tex]\frac{677.4}{17.7}[/tex]

⇒ Width = 38.2 cm

As we got both the length and the width of the rectangle, now we can calculate the perimeter,

⇒ Perimeter = [tex]2( length + width)[/tex]

⇒ Perimeter = [tex]2(17.7 + 38.3)[/tex]

⇒ Perimeter = 2 x 56 cm

⇒ Perimeter = 112 cm

⇒ In inches = 44 inches

Therefore, the length of the perimeter is = 112cm or 44 inches

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The periodic table is useful for understanding atomic properties that show periodic trends. Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element, including its size and its electronic properties.

Therefore, 6 minutes and 40 seconds are needed to test possibilities.

Combinations are sometimes known as selections. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. To denote the number of unique r-selections or combinations among a set of n items, we write n C r. Combinations are distinct from arrangements or permutations.

Here,

The first two numbers in this three-term series are 17 and 24, and the third one remains a mystery.

Given that there are 40 options for the third number and that each try takes 10 seconds, we have 40 x 10 seconds, or 400 seconds, to try every possible combination.

Thus,

=> 400 seconds  is equals to 6 minutes and 40 seconds

Therefore, 6 minutes and 40 seconds are needed to test every scenario.

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