Hi!! <3 Please help me with this question!! TYSM! :)

Step-by-step explanation:

when defined like this, we remember that when the right-angled triangular is inscribed into a circle, sine of an angle is the length of the opposite side of the angle divided by the radius. while cosine of the same angle is the adjacent side divided by the radius.

so, sin(angle) = 12/13 makes us imagine a circle of radius 13, and the side (or leg) opposite of the angle is 12.

now, Pythagoras tells us

c² = a² + b²

c being the Hypotenuse (which is the radius in our scenario), a and b are the legs.

13² = 12² + second leg²

169 = 144 + second leg²

second leg² = 25

second leg = 5

so,

cos(theta) = 5/13

tan(theta) = sin(theta) / cos(theta) =

= 12/13 / 5/13 = (12×13)/(5×13) = 12/5

sin²(theta) + cos²(theta) = (12/13)² + (5/13)² =

= 144/169 + 25/169 =

= 169/169 = 1

sec²(theta) - tan²(theta) =

= (1/cos(theta))² - (12/5)² =

= (1 / 5/13)² - 144/25 = (13/5)² - 144/25 =

= 169/25 - 144/25 = 25/25 = 1

A list of assertions and the justifications for each assertion are included in a two-column geometric proof.

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Answer:

  16 units

Step-by-step explanation:

You want the side length of a square pyramid with height 15 units and slant height 17 units.

The Pythagorean theorem can be used to find the distance from the midpoint of one side to the center of the square base.

  (b/2)² +15² = 17²

  (b/2)² = 289 -225 = 64

  b/2 = √64 = 8

Then the length of one side of the base is ...

  b = 2·8 = 16 . . . . units

Answer:

  48 m

Step-by-step explanation:

You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.

As shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.

  a² +b² = c²

  14² +b² = 50²

  b² = 50² -14² = 2304

  b = √2304 = 48

The length of XY is 48 meters.

__

Additional comment

In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.

We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).

Given f(x)=-5x2 + 2x + 9

      f(1)=-5(1)2+2(1)+9

      ∴f(1)=6

      f(2)=-5(2)2+2(2)+9

     ∴f(2)=-7

We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.

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The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] -  [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

Level A:

S.D. = 7

Level B: Mean = 20

S.D. = 6

So, [tex]\nu_1[/tex] = 22

[tex]\nu_2[/tex] = 20

Then,  [tex]\nu_1[/tex] - [tex]\nu_2[/tex]   = 22-20=2

and, [tex]\sigma_1[/tex] -  [tex]\sigma_2[/tex]

= (7)² ÷100+ 6² /150

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The number of new members that are women will be 25 women.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A games group has 65 men and 35 ladies as individuals. Another movement has quite recently started and a few new individuals have joined. Considering that the quantity of men is currently 60% of the absolute number of individuals.

The number of new members is 50.

Let the number of new men be 'x'. Then the equation is given below.

(65 + x) / (100 + 50) = 60%

(65 + x) / 150 = 0.60

65 + x = 90

x = 25

The number of new members were women will be given as,

⇒ 50 - 25

⇒ 25

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Yes, there is a transformation that maps shape I onto shape IV. If the figure I is reflected over the x-axis, we get figure IV.

In mathematics, a transformation is a function or a mapping that takes a set of inputs and produces a new set of outputs.

Transformations can be applied to geometric shapes, functions, and other mathematical objects to change their properties or positions.

There are various types of transformations that can be performed in mathematics, including translation, rotation, reflection, dilation, and more. Each type of transformation has its own specific rules and properties that dictate how it affects the original object.

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Full Question:

See the attached Image

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

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Answer:

d) 30

Step-by-step explanation:

1% of 10 inch is 0.1 inch

10 inch + 0.1 inch = 10.1 inch

10 inch - 0.1 inch = 9.9 inch

V = s³

For s = 9.9 in., V = (9.9 in.)³ = 970.299 in.³

For s = 10.1 in., V = (10.1 in.)³ = 1030.301 in.³

For 10 in., V = (10 in.)³ = 1000 in.³

|1000 in.³ - 970.299 in.³| = 29.701 in.³

|1000 in.³ - 1030.301 in.³| = 30.301 in.³

The error is 30 in.³.

The number of miles was each of Jerry’s flights travel is 240 miles.

A mile is characterized as the unit of length, which is precisely equivalent to 5280 feet, or 1760 yards, and normalized as precisely 1609.344 meters by the Peaceful accord in 1959. The biggest unit is generally used to quantify the distance between places that are not even close to one another.

Jerry flew 6 flights each month.

Total flights in 3 months = 3(6) = 18 flights

Let distance traveled in each flight be x

Then,

18x = 4320 miles

x = 4320/18

x = 240 miles

Thus, each flight flow 240 miles.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to find the number of tickets required per game, given that the relationship is proportional and 9 tickets are required for 3 games.

The equation of a proportional relationship can be written as ...

  y = kx

where k is the constant of proportionality.

Solving for k, we have ...

  k = y/x

Using a given ordered pair, we find ...

  k = 9/3 = 3

The constant of proportionality is 3 (tickets per game).

__

Additional comment

Since the relationship is given as being proportional, we only need one (x, y) pair to find the constant of proportionality.

Let y be the number of people that will attend the conference as a function of x. The given information tells us that when x = 0 (the admission price is $400), y = 1000. Additionally, for each $5 reduction in price, an additional 20 people will attend.

We can express this relationship as a function as follows:

This function tells us that the number of people that will attend the conference is equal to 1000, plus an additional 20 people for each $5 reduction in price (represented by the variable x).

For example, if the admission price is reduced by $10 (x = 2), the number of people that will attend the conference is given by:

y = 1000 + 20(2)

y = 1000 + 40

y = 1040

So, if the admission price is reduced by $10, 1040 people will attend the conference.

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a) The set notation is shown below.

b) 27 pupil have pencils only​.

A Venn diagram depicts the logical relationships between two or more sets of items by using overlapping circles or other shapes. They frequently serve to graphically organise things, demonstrating how similar and dissimilar the pieces are.

Given:

In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers.

25 have both pencils and pens,

30 have both pencils and rulers while 47 have both pens and rulers.

a) The set notation is

n(p)= 75

n(Pens)= 87

n(R)= 93.

n (p∩ pens) = 25

n (p∩ R) = 30

n (pens ∩ R) = 47

n (p∩ R ∩ pens) = x

c) Number of Pupil that have only pencils

= 75- [(30-7) + 25-7 +7]

=75-(23+18+7)

= 75-48

=27

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The  shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week

A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.

The complete question is : A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the shape of the sampling distribution of p hat and why?

A. approximately Normal, because all sampling distributions are approximately Normal

B. approximately Normal, because we would expect at least 10 success and 10 failures

C. skewed to the right, because 0.31 is lower than 0.5

D. skewed to the left, because 0.31 is lower than 0.5

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Answer:

not true:

3. AD = DC      

4. YZ = XW

explanation:

lower base is only congruent to upper base.

Step-by-step explanation:

The expression to represent the total yards of material needed for the requested quilts is 5(1.2x) or 6x.

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.

In this situation, Maribelle uses x yards of material to make a quilt and a customer requests 5 quilts that are 20% larger than the normal pattern.

The expression for this will be:

= 5[x + (20% × x)]

= 5[x + 0.2x]

= 5(1.2x]

= 6x

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A number type which is more appropriate for the domain of H include the following: A. Integers.

The appropriate domain include the following: C. 2000 ≤ y ≤ 2010.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1) such as 1, 10, 20, 2000, 2010, etc.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

Since the variable H(y) represents the leading number of home runs for season y of the National League between the years 2000-2010, an appropriate domain is given by;

Domain = 2000 ≤ y ≤ 2010 or [2000, 2010].

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Complete Question:

Which number type is more appropriate for the domain of H?

A. Integers

B. Real numbers

What's the appropriate domain?

0 ≤ y < 2010

0 < y < 73

2000 ≤ y ≤ 2010

42 ≤ y < 73

The quadratic equation whose roots are -6 and 3/4 is 14x²+21x-18=0

We should know that a quadratic equation is that whose highest power of the variable is 2

The given roots are

x=-6 and x=3/4

Let (x+6)(x-3/4)=0

Multiplying the brackets we have

[tex]X^{2}-\frac{3x}{4} +6x-\frac{18}{4}[/tex] =0

Find the LCM of the denominators

[tex]\frac{4X^{2}+21x-18 }{4} =0[/tex]

Cross and multiplying we have

[tex]4x^{2} +21x-18=0[/tex]

Therefore, the equation  is expressed in the form ax²+bx+v=0 Where a=4, b=21 and c=-18

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Answer:

y - 1/3x - 10 + 4 = 0

Step-by-step explanation:

What we know:

x = 12

y = 10

slope (m) = 1/3

y - y1 = m(x - x1) Point-slope form

Substitute in the values we have

y - 10 = 1/3(x - 12)

Bring all the values to one side

y - 10 - 1/3(x - 12) = 0

y - 1/3x - 10 + 4 = 0

Answer:

3/8

Step-by-step explanation:

75% of 1/2

3/4 of 1/2

3/4x1/2

3/8

Answer:

A. ∠1 = ∠7

B. ∠2 = ∠6

D. ∠6 + ∠7 = 180°

Step-by-step explanation:

⭐ Why A is correct

⭐ Why B is correct

❌ Why C is incorrect

⭐ Why D is correct

Answer:

The expression is B. 30m

The volume of the cylinder is 180π cm³.

What is volume ?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.

As diameter = 6cm

We know that radius is half of diameter

∴ radius = 3 cm

height = 20 cm

Volume = π r² h

             = π (3)²×20  

             = π × 9 × 20

             = 180 π cm³

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Answer:

D

Step-by-step explanation:

Because whee your finding the Grange of a fundtlon you Look at the Y value from the smallest Number to the largest Number.

Answer:

(D) 52

Step-by-step explanation:

sum up correct answers from questions 1, 2 and both 1 and 2 incorrect this time therefore we have --> 18+23+11=52 students

You could also do a Venn diagram to understand this better with 8 being the intersection of students who goth both 1 and 2 correct and 11 being left out as the number of students who got both questions incorrectly.

The way that the Three-Fifths Compromise affected the 1790 census results was B. Enslaved persons in each state were counted as three-fifths of a person.

A settlement known as the "three-fifths compromise" was reached at the 1787 Constitutional Convention and permitted Southern states to count some of their enslaved population as three-fifths of a person for taxes and representational purposes. This first happened in the 1790 census results.

Many of the Founding Fathers recognized that slavery went against the ideal of liberty that was at the heart of the American Revolution, but they were unable to act decisively to end it because they were dedicated to the sanctity of private property rights, the ideas of limited government, and the pursuit of intersectional harmony.

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The correct answer is Option A: Proposition I is true and Proposition II is true.

A researcher can use Pearson's chi square test of independence to determine if two nominal variables are independent or not. In this case, the researcher observed a chi-square value of 10.00430.

To determine whether the null hypothesis should be accepted or rejected, the researcher must compare the chi-square value to a critical value associated with the desired level of significance.

At the 5% significance level, the critical value is usually around 7.815, and at the 1% significance level, the critical value is usually around 10.827. Since the observed chi-square value (10.00430) is higher than the critical values for both the 5% and 1% significance levels, the appropriate decision could be a Type II Error for both levels of significance.

In other words, Proposition I (At the 5% significance level the appropriate decision could be a Type II Error) and Proposition II (At the 1% significance level the appropriate decision could be a Type II Error) are both true.

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k= 5.

[tex]ksin^{2} (x)+kcos^{2} (x)=5[/tex]

[tex]k(sin^{2} (x)+cos^{2} (x))=5[/tex]

Check attached image 1.

[tex]k(1)=5\\ \\k=5[/tex]

Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.

Check attached image 2.

As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.