How do you find the legs of a 45 45 90 triangle given the hypotenuse?

The distance of the ball thrown is 67 ft. approx.

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 θ=63 and length of the field as 60 and let d be the distance

∴ Cos (180-63-90)=60/d

                  d        = 60/cos(27)

                   d       = 67 (approx)

Hence, The distance of the ball thrown is 67 ft. approx.

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Answer:
y = 1/9 + 2/9x

Step-by-step explanation:

9y - 2x = 1

9y = 1 + 2x             (get rid of x)

y = 1/9 + 2/9x        (divide 9 on both sides)

The 95% confidence interval for the true mean number of reproductions per hour for the bacteria is given as follows:

(3.78, 4.22)

The bounds of the confidence interval are calculated according to the equation presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 4, \sigma = 1.9, n = 283[/tex]

Hence the lower bound of the confidence interval is of:

[tex]4 - 1.96\frac{1.9}{\sqrt{283}} = 3.78[/tex]

The upper bound of the confidence interval is of:

[tex]4 + 1.96\frac{1.9}{\sqrt{283}} = 4.22[/tex]

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The length of the rectangle is 3l/4, and the breadth of the rectangle is s = 3l/4

Let's call the original breadth of the rectangle "b" and the original length of the rectangle "l". From the information given, we know that:

4b = 3l

We also know that when the breadth is increased by 1m and the length is reduced by 1m, the rectangle becomes a square. Therefore, the new breadth and new length are equal. Let's call the new breadth and length "s".

s = b + 1 = l - 1

We can substitute the first equation into the second equation to get:

s = b + 1 = (3l/4) - 1

Now we can solve for s:

s = b + 1m = (3l/4) - 1m

s = (3l/4) - 1m + 1m = (3l/4) = l - 1m

Now we can substitute this back into the first equation:

4b = 3(l - 1m)

We can now solve for b:

4b = 3l - 3m

b = (3l/4) - (3m/4)

Therefore, the original breadth of the rectangle was (3l/4) - (3m/4) and the original length was 3l/4.

We can find the value of length and breadth by substituting the value of s in the first equation

4s = 3l

s = 3l/4

So, the length of the rectangle is 3l/4, and the breadth of the rectangle is s = 3l/4

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The value of x is 8.

Angles are formed whenever two or more straight lines intersect. These angles produced thus have individual and some common properties of which some can add up to form complementary angles, or supplementary angles.

Two angles are said to be supplementary if the value of their sum add up to 180^o.

From the given question, we can deduce that;

m<1 + m<2 = 180^o              (definition of complementary angles)

(17x - 30) + (7x + 18) = 180^o

17x - 30 + 7x + 18 = 180^o

24x - 12 = 180

24x = 180 + 12

24x = 192

x = 192/ 24

  = 8

x = 8

The value of x is 8.

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After solving the equation: the nearest cent, the interest earned is $467.

Interest is a mathematical concept used to describe the cost or gain associated with the use of money over a period of time. It is usually expressed as a percentage rate of the principal (the amount borrowed or invested). Interest can be earned or paid, depending on the situation.

Using the formula B=p(1+r)t, John's final balance after 1 year is B = 4069(1+0.12)1 = $4,536.28.
The interest earned in 1 year is the difference between the final balance and the starting amount, which is $4,536.28 - $4,069 = $467.28. To the nearest cent, the interest earned is $467.

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Answer:

10 mm

Step-by-step explanation:

Draw an equilateral triangle. Label each side 12 mm.

Draw one altitude from one vertex perpendicular to the opposite side. Label the length of the altitude h.

The altitude divided the opposite side into two congruent segments, each one measuring 6 mm.

Now use the Pythagorean Theorem.

a² + b² = c²

(6 mm)² + h² = (12 mm)²

36 mm² + h² = 144 mm²

h² = 144 mm² - 36 mm²

h² = 108 mm²

h = 6√3 mm

h ≈ 10 mm

Answer: 3.5 cm or 35 mm

Step-by-step explanation:

12/3 =4 for each side of triangle

cutting the triangle in half, bottom side(a) 4 becomes 2

2^2 + b^2 = 4^2

4 + b^2 = 16

subtract 4 from both sides

b^2 = 12

b = 3.464 cm or 3.5 cm

convert 3.5 cm to 35 mm

Answer:

Irrational

Step-by-step explanation:

it equals 6.7 which is not a perfect square

Answer:

Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.

Step-by-step explanation:

To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.

To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).

Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.

Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.

The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the greatest possible quotient as required is; 25.

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Yes, 10 is an even number because 10 is completely divisible by 2 that's why it is an even number.10 modulo 2 equals zero.

let's first try to understand what are numbers.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that use digits or symbols to represent them. the system of numbers

a helpful collection of numbers

that reflects the number's algebraic and mathematical structure.

offers a common depiction.

Even numbers An even number is any number that can be divided by 2 precisely. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14.

So 10 is an even number.

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Answer:

==================================

a1 = 85 = first term

d = -4 = common difference

an = a1 + d(n-1)

an = 85 - 4(n-1)

an = 85 - 4n + 4

an = -4n+89

a10 = -4*10+89

a10 = 49 is the tenth term

Jeremiah average velocity during the drive was 80 km/h while the instantaneous velocity at one point was 105 km/h

An equation is used to show the relationship between numbers and variables.

Average velocity is the ratio of total distance travelled to total time taken. Instantaneous velocity is the velocity at a particular point in time.

Jeremiah completed a straight, 120 km drive in 1.5 hours, hence:

Average velocity = total distance / total time

Average velocity = 120 km / 1.5 hours = 80 km/h

At one point during the drive, he saw that his speedometer read 105 km/h, hence:

Instantaneous velocity = 105 km/h

The average velocity is 80 km/h while the instantaneous velocity is 105 km/h

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In answering the question, we discovered that a sample size of 20 was required in order to reach this conclusion.

The sample size is the number of observations used to estimate a certain population. The population was used to determine the sample size.

The act of promoting a product to increase sales is known as advertising. Based on the scenario given, the advertisement is misleading for the following reasons:

For this finding to be reliable, a sample size of 20 samples is rather small. Although the company was aware that the fertilizer treatment might get rid of weeds in approximately 2 weeks, customers said it would take 4 weeks for all of the weeds to die.

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The expression for the perimeter of a square will be p = 4s.

The perimeter of a figure of shape can be gotten the total length of the boundary which the figure or the shape has. it's gotten by adding all the length that the shape has.

It should be noted that a square has four equals sides. The expressions for the perimeter of a square will be:

p = 4 × s.

p = 4s

where s = number of sides.

p = perimeter

For example if the side is 2cm. The perimeter will be calculated by multiplying 4 by the value of the sides. In this case, this will be calculated as:

= Value of sides × 4

= 2 × 4

= 8cm

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The equation given as -y = 3x is a direct variation. The constant of variation is - 1/3

It shows the relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

A straightforward correlation between two variables is referred to as direct variation. In this case, the constant of variation will be k.

This will be Illustrated as:

y = kx

-1 = 3k

Divide

k = -1/3

The constant is - 1/3.

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The age group that falls between two standard deviations is 20 to 28.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

Given, The average age of a university student was found to be 24 with a standard deviation of 2.

Therefore, age group is within 2 standard deviations of the mean is,

24 + 2×2 = 24 + 4 = 28,

And 24 - 2×2 = 24 - 4 = 20.

So, The age group between 20 to 28 falls within 2 standard deviations of the mean.

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No, 8,15 and 16 is not a Pythagorean triplet.

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a, b, and c which is a right triangle that exists with legs a,b, and hypotenuse c.

By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying  a²+b²=c²

One of the simplest Pythagorean triples is the set “3,4,5.”

Now, substitute the values in the above equation:

16²=8²+15²

256=64+225

256[tex]\neq[/tex]289

Therefore, (8,15,16) is not a Pythagorean triplet.

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Answer:

Hypothesis - She is a spoiled brat who has rich parents. But where did they                                                                            get their wealth?

Conclusion - Her parents are hard workers who have made it up the ladder of wealth.

2. If the measure of an angle is 58*, then the angle is acute

Hypothesis - acute angles are from 1* to 89* which makes it the smallest angle. But why when the word acute means severe?

Conclusion - We know that anything below 90* is an acute angle.

This should be a start. I will finish in a sec...

Answer:

1.  Hypothesis:  Lola wants.  

    Conclusion:  Lola gets.

2. Hypothesis:  The measure of an angle is 58°.

    Conclusion:  The angle is acute.

3.  Hypothesis:  The segments are diagonals of a rectangle

    Conclusion:  The segments are congruent.

4.  Hypothesis:  You are a Filipino.

    Conclusion:  You are a God-fearing person.

5.  Hypothesis:  You are a good citizen.

    Conclusion:  You will obey rules and regulations.

Step-by-step explanation:

In a statement, the Hypothesis is the part after the "if", and the Conclusion is the part after the "then".

1.  If Lola wants, then Lola gets.

2.  If the measure of an angle is 58°, then the angle is acute.

3.  If the segments are diagonals of a rectangle, then the segments are congruent.

4.  If you are a Filipino, then you are a God-fearing person.

5.  If you are a good citizen, then you will obey rules and regulations.

By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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The first row of the SHORT BINGO card contains 5 numbers, one from each of the sets $1-10$, $11-20$, $21-30$, $31-40$, and $41-50$. Since the WILD square is in the middle of the card, it does not affect the possibilities for the first row.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

For the first column, there are 10 possibilities, as it can contain any number from the set $1-10$.

For the second column, there are 10 possibilities, as it can contain any number from the set $11-20$.

For the third column, there are 9 possibilities, as it can contain any number from the set $21-30$ except the one already used.

For the fourth column, there are 10 possibilities, as it can contain any number from the set $31-40$.

For the fifth column, there are 10 possibilities, as it can contain any number from the set $41-50$.

The total number of distinct possibilities for the values in the first row of a SHORT BINGO card is the product of the possibilities for each column, which is:

10 * 10 * 9 * 10 * 10 = 90000.

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Probability that the Captain does NOT hit the pirate's ship × Probability that the pirate hits the Captain's ship = (2/5) × (1/5) = (2/25) = 0.08

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.

The probability that the pirate hits the Captain's ship, but the Captain misses

= 2/25) = 0.08

P(C) = (3/5) is the likelihood that the captain will strike the pirate ship.

P(C') = 1 - (3/5) = (2/5) is the probability that the captain will miss the pirate ship.

P(p) = (1/5) is the likelihood that the pirate will sink the captain's vessel.

P(p') = 1 - (1/5) = (4/5) is the probability that the pirate will miss the captain's ship.

The likelihood that the pirate will hit the captain's ship while the captain misses is increased if they both fire their cannons at the same moment.

P(C' n p) is he needed probability.

P(C' n p) = P(C') P since the two events are independent of one another (p) The likelihood that the pirate will sink the captain's vessel but that the capain will miss = (Chance that the Captain misses the pirate's ship) (Chance that the pirate hits the Captain's ship) = (2/5) × (1/5) = (2/25) = 0.08

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On solving the provided, we can say that - here in graphs by solving the equation - [tex]x^2 + y^2 = > 2^2 = > 4[/tex]

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here from graph,

x= 0

and y = 2

so, in equation

[tex]x^2 + y^2 \\2^2\\4\\[/tex]

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The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.

A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.

A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where

aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.

'x' is the variable.

p(x) means "polynomial in terms of variable x"

'n' is a non-negative integer, it is the degree of p(x).

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Answer: 1/2 is the slope.

Step-by-step explanation: (-2-6)/(2-6) = -8/-4

-8/-4 Simplified is 1/2

Therefore 1/2 is your slope

Hope this helps!

The solution to the equation is g = 4π² ( L / T² )

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

The formula to determine the time period of a simple pendulum is given by

T = 2π √ ( L / g )   be equation (1)

where L = length of string

g = acceleration due to gravity

On simplifying the equation , we get

Divide by 2π on both sides of the equation , we get

√ ( L / g ) = T / 2π

Squaring both sides of the equation , we get

( L / g ) = T² / ( 2π )²

( L / g ) = T² / 4π²

Now , taking reciprocals on both sides of the equation , we get

g / L = 4π² / T²

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

g = 4π² ( L ) / T²

On simplifying the equation , we get

g = 4π² ( L / T² )

Therefore , the value of A is 4π² ( L / T² )

Hence , the equation is g = 4π² ( L / T² )

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Equivalent function has the same domain and range. Equivalent and equal terms are not the same both have different meanings in mathematics.

A function is said to be equal if its Domain and Range are identical. Complete solution, step by step: A and B should be two sets. Now, by function, we mean a rule that guarantees that f(a)=b exists for all a. As a result, set A is referred to as the Domain of File and set B as the Range Off.

Despite being comparable to 1 + 1, 2 is believed to be equal to 2. When two items or amounts are exactly the same, as when 12 is equal to 12, yet 12 is equivalent to 2/4 since they reflect the same value, we can say that they are equal.

In mathematics, an equivalent can be defined in one of two ways. This is thus because there are various definitions for the concept of equivalent in mathematical theory. Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects.

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The rate of change for the graph, when x=0 and x=1 is 2 units.

What is average rate of change?

This expression represents the average rate of change of the function f(x) over the range a<=x<=b, is less than or equal to x, and is less than or equal to b -

[f(b)-f(a)]/b-a

​

The rate of change of graph is determined by the formula -

[f(b)-f(a)]/b-a

[f(1)-f(0)]/1-0

Here, in the graph it can be clearly seen that f(0)=-1 and f(1)=1.

Plugging in the values -

[1-(-1)]/1

(1+1)/1

2

Therefore, the rate of change is 2 units.

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