Do the sides 7 cm 24 cm and 25 cm form a right-angled triangle give reason?

El número A = 52 es una solución del sistema de ecuaciones lineales.

En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:

A / 4 = B / 9

A + B = 169

Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:

B = 169 - A

Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:

A / 4 = (169 - A) / 9

9 · A = 4 · (169 - A)

9 · A = 676 - 4 · A

13 · A = 676

A = 52

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The answer in the correct number of significant figures is 30.5.

What is the significant figure?

Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

We have given,

6.221 × 7.11 − 13.7

first, we determine the product of 6.221 and 7.11 and round the value to a minimum number of significant figures which is "3"   since  7.11 has "3" significant figures and 6.221 has "4" significant figures

so Product = 6.221 × 7.11 = 44.2

now we do the subtraction and round the answer to a minimum decimal number

44.2 - 13.7

30.5  

Hence, the answer in the correct number of significant figures is 30.5.

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As per the ratio proportion, the length of 600 miles freeway is 6 inches on the map.

What is ratio proportion?

Ratio proportion is an equation where two sides of it are equal. A ratio or proportion maintains the equality between two fractions.

Given, 0.5 inches represent 50 miles.

Let, x inches represent 600 miles.

Therefore, as per the ratio proportion, we can write:

0.5 : 50 = x : 600

⇒ 0.5/50 = x/600

⇒ x = (600 × 0.5)/50 = 6.

Therefore, the length of 600 miles freeway is 6 inches on the map.

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The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.

To calculate the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts, we need to calculate the point estimate and margin of error. The point estimate is the proportion of first-year students who stated they intend on majoring in liberal arts

(62/100 = 0.62).

The margin of error is 1.96 times the standard error

(SE = √(p(1-p)/n) = √(0.62(1-0.62)/100) = 0.04).

The lower bound of the 95% confidence interval is the point estimate minus the margin of error

(0.62 - 0.04 = 0.58).

The upper bound of the 95% confidence interval is the point estimate plus the margin of error

(0.62 + 0.04 = 0.66).

Therefore, the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.

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The number of minutes per mile that Lin does ride will be 8 minutes per mile.

Lin rides at a speed of 6 miles / 48 minutes = 0.125 miles per minute. For us to convert this to minutes per mile, we have to take the reciprocal of this value, which is 1 / 0.125 = 8 minutes per mile.

To convert speed from miles per minute to minutes per mile, you can take the reciprocal of the value which means is the upside value and top. In this case, 0.125 miles per minute to minutes per mile is 8 minutes per mile.

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a. Since both a strong-positive and weak-positive correlation are formally considered to be "growing," this is ambiguous (positive slope). In the same way, negative correlation. Speaking strictly in terms of truth or untrue, I would classify this as false

b. This is once more a little tricky. When "r" is zero, there isn't any evidence of a linear link. It doesn't necessarily follow that the variables don't correlate with one another. The answer is probably True if this is a course on statistics for beginners. If not, False.

c. This is simple to understand. Inverse relationships are indicated by negative coefficients. One grows while the other shrinks (or vice versa). False.

d. The range of the coefficient r is [0, 1] (inclusive), not (0,1). In this case, True if the text suggests [0,1].

e. Simple and accurate

f. Plain and simple, FALSE. Quite a high correlation coefficient

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Answer:

10cm

Step-by-step explanation:

Pythagoras

(6×6) + (8×8) = □×□

36 + 64 = 100

square root of 100 = 10

Answer:

Step-by-step explanation:

The condition for a triangle whose two sides are 6cm and 8cm is the triangle should be right angled triangle.

so by this condition,

            =>    (hypotenuse)^2 = (base)^2 + (perpendicular)^2

           =>      (hypotenuse)^2 =  (6)^2 + (8)^2

          =>        hypotenuse = 10 cm

so the thisrd side of triangle is 10cm.

The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

Now, According to the question:

We are informed that a card is drawn at random from a standard 52-card deck.

We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.

We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.

The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4×4 = 16}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event A, P(A) = 16/52.

The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event B, P(B) = 13/52.

The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.

The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.

Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

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The largest possible quotient of a positive 3-digit number divided by the sum of its digits if the 3 digits must be different is 41

The largest possible quotient of a positive 3-digit number divided by the sum of its digits is obtained when the 3 digits are as large as possible, subject to the constraint that they must be different.

The largest possible 3-digit number is 987, which has digits 9, 8, and 7.

The sum of its digits is 9 + 8 + 7 = 24.

The quotient of 987 divided by 24 is:

987/24 = 41.125

otherwise when expressed as a mixed number is read as 41 whole number 3/24

In conclusion, the largest possible quotient of a positive 3-digit number divided by the sum of its digits, when the 3 digits must be different, is 41.

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A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

The process of evaluating a function is typically straightforward when we have the function in the form of a formula. For instance, it is possible to evaluate the function f(x)=53x2 by first squaring the input number, multiplying by 3, and then subtracting the result from 5.

The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x.

To determine the outcome, simplify the values. The abscissa is the x value of the point (x, y). It shows how far a point is from the origin or from the x-axis' horizontal axis. 

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The value of the equation is y = 0.75x , where y is the total cost of the ticket and x is the original cost of the ticket

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

Let the original cost of the ticket be represented as x

Let the discounted price of the ticket be y

Now , the percentage of discount = 35 %

So , the discounted price of the ticket y = original cost of the ticket - ( 35/100 ) x original cost of the ticket

Substituting the values in the equation , we get

The discounted price of the ticket y = x - 0.35x

On simplifying the equation , we get

The discounted price of the ticket y = 0.75x

y = 0.75x   be equation (1)

Now , the cost of the ticket cannot be a negative value so it should lie in the first quadrant

Hence , the equation is y = 0.75x

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Answer: -1 2/5 i think im not sure (check explaination)

Step-by-step explanation:

slope formula= y2-y1/x2-x1
-3-4/8-3=-7/5,-1 2/5

Answer:

2.00 m in front of the concave mirror with a focal length of 30.0 m

Step-by-step explanation:

To find the distance from a concave mirror with a focal length of 30.0 m at which a 7.00-m-long baby blue whale must be placed to get a real image the size of a mature blue whale, we can use the mirror equation:

1/u + 1/v = 1/f

Where u is the distance between the object and the mirror, v is the distance between the image and the mirror, and f is the focal length of the mirror.

We know that v is negative because the image is real, and the same size of the mature blue whale that is 28m.

So, we can substitute the values we know into the equation:

1/u - 1/28 = 1/30

We can solve for u by multiplying both sides by 30u and getting:

30 - 28u = u

So u = 2m

Therefore, the 7.00-m-long baby blue whale must be placed 2.00 m in front of the concave mirror with a focal length of 30.0 m to get a real image the size of a mature blue whale.

The probability of rolling doubles with three rolls of two fair six-sided dice is 0.512.

How do you calculate probability?

Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.

The probability of rolling doubles with one roll of two fair six-sided dice is 16/36, or 1/6. This means that the probability of not rolling doubles with a single roll is 5/6.

The probability of not rolling doubles with two rolls is (5/6)^2, or 25/36.

The probability of not rolling doubles with three rolls is (5/6)^3, or 125/216.

Therefore, the probability of rolling doubles with three rolls of two fair six-sided dice is (216-125)/216, or 91/216, or 0.512.

P(doubles on 1 roll) = 1/6

P(not doubles on 2 rolls) = (5/6)^2 = 25/36

P(not doubles on 3 rolls) = (5/6)^3 = 125/216

P(doubles on 3 rolls) = 1 - (125/216) = 91/216 = 0.512

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The distance between Orlando and Jacksonville is approximately 230 miles.

What is the distance?

Distance refers to the measurement of the separation between two points in space. It can be thought of as the length of the path between two points, and it can be measured in various units such as meters, feet, miles, kilometers, etc.

The distance between Orlando and Jacksonville is approximately 230 miles (370 km) if you take the most direct route by car. The driving distance between Orlando and Jacksonville is around 4 hours and 30 minutes. It could vary depending on the route taken and traffic conditions.

Hence, the distance between Orlando and Jacksonville is approximately 230 miles.

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A reference tool that is used to determine how the fiber is to be orientated for a particular ply of fabric is called a lay plan or lay direction.

A lay plan is a detailed diagram that shows the orientation of fibers in each layer of a fabric, and it is used as a guide for the manufacturing process. The lay plan indicates the direction in which the fibers should be oriented in each layer of the fabric, which is essential for achieving the desired strength, stretch, and durability of the final product.

The lay plan is also used to ensure that the fibers are aligned in the same direction in each layer, which helps to prevent warping or other issues that can occur during manufacturing.

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A single song may be downloaded for $0.35. Adjusting the solution c = 0.35s yields the answer because c/s = 0.35.

An equation is an mathematical statement that uses an equal sign to express the relationship across two or more objects, such as variables or integers. Equations can be used to represent relationships between physical, chemical, and other sorts of events as well as to solve mathematical problems. An equation in mathematics is a claim made regarding the equivalence of two expressions. A assertion claiming two expressions equal equal is what an equation is, in other words.

This indicates that each music download costs $0.35. Consequently, it costs $0.35 to buy a single song.

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The word "correlation" is made by join forces the words "co" and "relation". The word "co" means jointly, thus, correlation means the relationship between any set of data when examine together.

In Statistics, the correlation coefficient is a compute defined between the numbers -1 and +1 and act for the linear interdependence of the set of data.

This data is then divided by the product of standard deviations for these variables.

The equation given below recap the above concept:

ρxy=Cov(x, y)/σxσy

Cov(x,y)=covariance of variables x and y

σx=standard deviation of x.

σy=standard deviation of y.

1. For a positive correlation: the values increase together.

2. For a negative correlation: one value decreases as the other increases.

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Answer:

"going from the point 0 comma negative 120 through the point 2 comma negative 100"

Step-by-step explanation:

Let y be the total income from the homecoming dance, and x the number of students who purchase tickets (at $10 each).  We are told that it costs $120 for the decorations.

The income from ticket sales would be:

1)  the number of tickets sold times $10/ticket, or $10

2) Less the expenses of decorating  (-$120)

We can write the total income as:

    y = $10x - $120

The graph of this function would be a straight line that has a y-intercept of -$120.  Before any ticket is sold, the cost of decorations must be considered.  If no tickets are sold (x=0), the total income is -$120.

Using the equation, we can calculate the income when 2 tickets are sold (x=2):

    y = $10x - $120

    y = $10*(2) - $120  [two tickets sold]

    y = -$100

Summary

 y = $10x - $120

 (0,-$120)

 (2,-$100)

This matches the statement "going from the point 0 comma negative 120 through the point 2 comma negative 100" provided in the answer options.

See the attached graph.

The curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞)

We have to consider the curve

                                               [tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]

Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.

The parametrization of the curve represented by the vector valued function

                                       [tex]r(t) = f(t)i + g(t)j + h(t)k[/tex]

This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on [tex]l[/tex] and r'(t) [tex]\neq[/tex] 0 for any value of t in the interval.

Now, we know the vector equation:

[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]

Differentiating r(t) with respect to r,

[tex]r'(t) = 16t i + 21t^{2} j[/tex]

At t = 0, equate r'(t) = 0.

[tex]r'(0) = 16(0) + 21(0)^{2}[/tex]

Therefore, the curve is smooth for all values except 0, as we can see above.

Hence, the curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞).

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The general solution of the given higher-order differential equation is y(x) = e2x + x2 + c4e3x + c5e-3x.

A general solution is an answer that can be applied to a wide range of problems. It is a broad-based approach that can be used to solve any problem, regardless of its complexity or specific details. General solutions take into account the overall goal of a problem, rather than its individual elements, and look for a way to achieve the desired result. Additionally, they are often easy to implement and can be applied to a variety of scenarios.

The general solution of the given higher-order differential equation, y(4) + y''' + y'' = 0, is given by

y(x) = c1e2x + c2e-2x + c3x2 + c4e3x + c5e-3x + c6x3.

Here, c1, c2, c3, c4, c5 and c6 are constants of integration.

To determine the values of these constants, we must use initial conditions. Suppose we are given y(0)=1 and y'(0)=2, then we can solve for the constants using this information.

Substituting y(0)=1 and y'(0)=2 into the equation, we get

1 = c1 + c2 + c3(0)2 + c4 + c5 + c6(0)3
2 = 2c3 + 3c6(0)2

Solving these equations, we get c1 = 1, c2 = 0, c3 = 1 and c6 = 0.

Therefore, the general solution of the given higher-order differential equation is

y(x) = e2x + x2 + c4e3x + c5e-3x.

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The price of one slice of pizza is $3.5, and the price of one drink is $3.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x be the price of one slice of pizza and y be the price of one drink.

The system of equations can be written as:

3x + 2y = 16.50

4x + 4y = 26

To find the price of one slice of pizza and the price of one drink, we can use the substitution or elimination method.

After solving the equation for x and y we get the values as:

x = 3.5 and y = 3

So, the price of one slice of pizza is $3.5, and the price of one drink is $3.

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Answer:

-4

Step-by-step explanation-

y2-y1

-------- = m = slope

x2-x1

8-12        -4

--------- =  ---- = -4

-2-(-3)      1

Voting rights for various segments in the United States was extended in stages from the time the United States gained independence, to the late 1900s.

In the late 1700s and early 1800s, voting rights were expanded to include more people, such as white men who owned property. The 15th Amendment was ratified in 1870, and prohibits the federal and state governments from denying a citizen the right to vote based on that citizen's "race, color, or previous condition of servitude."

The 19th Amendment was then ratified in 1920, and prohibits the federal and state governments from denying the right to vote to citizens of the United States on the basis of sex. Then the Voting Rights Act of 1965 was passed to overcome legal barriers at the state and local levels that denied African Americans the right to vote under the 15th Amendment. It was one of the most effective pieces of legislation passed during the Civil Rights Movement.

The 26th Amendment lowered the national voting age from 21 to 18 for all federal, state, and local elections.

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Full question is:

Extending Voting Rights; how have voting rights been extended in the United States since independence ?

The polyhedron with 10 vertices and 7 faces has 15 edges.

What is polyhedron?

A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.

Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:

10 (vertices) + 7 (faces) - E (edges) = 2

Simplifying the equation:

10 + 7 - E = 2

17 - E = 2

E = 17 - 2

E = 15

Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.

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The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The dramatization club is offering passes to their play to fund-raise for the show's costs. Every understudy ticket sells for $6.50 and every grown-up ticket sells for $11.50. The dramatization club should make at least $1300 from ticket deals to take care of the show's expenses.

Let 's' and 'a' be the number of tickets sold to students and adults, respectively. Then the inequality is given as,

6.5s + 11.5a ≥ 1300

The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

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a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)

x1=2, x2=4, x1+x2=6

An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.

b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=8

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=24

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.

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Therefore , the solution of the given problem of probability comes out to be  1/ ( 1+ y)x².

Evaluating the chance that a claim is true or that a particular event will happen is the focus of the mathematical field known as probability theory. A chance can be represented by any number between 0 and 1, with 1 denoting certainty and 0 typically expressing the possibility of occurrence. The possibility or possibility that a happening will occur is represented diagrammatically as probability. Figures 0 and 1, percentage ranging 0% - 100%, and some other characters can be used to represent probabilities. the percentage of times, out of all possible possibilities, that an incidence occurred within a good set with equally likely options.

Here,

Probability for X (for x≥0)

=> [tex]\int\limits^{ \infty}_{ 0}[/tex]x e⁻ˣ⁽¹⁺ⁿ⁾ dy

=> -e⁻ˣ   [tex]\int\limits^{ \infty}_{ 0}[/tex]de⁻ˣⁿ

=>e⁻ˣ

Probability for X exceed 3

=>   [tex]\int\limits^{ \infty}_{ 3}[/tex]f(x)dx

=>    [tex]\int\limits^{ \infty}_{ 3}[/tex]e⁻³dx

=> e⁻³

Probability for y ≥ 0

=>   [tex]\int\limits^{ \infty}_{ 3}[/tex]xe⁻ˣ⁽¹⁺ⁿ⁾ dy

=>  [tex]\int\limits^{ \infty}_{ 3}[/tex]x/1 + y d e⁻ˣ⁽¹⁺ⁿ⁾ = 1/ ( 1+ y)x²

Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².

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The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.

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.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.

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Using the table your total monthly fixed expenses is 977.43.

Rent payment $953. 20/month

Auto payment $165. 87/month

Telephone $56. 98/month

Auto insurance $714. 36/six months

Once-a-week outing $35. 00/week

= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)

= 1435.11

= 2412.54 - 1435.11

=977.43.

An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.

A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.

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