A family drives 509 miles to their vacation destination. It takes them 8.6 hours to get there. What was their average velocity in miles per hour?

Answer:

x = -3 ; y = 5

Step-by-step explanation:

Hey there!

This question has given us information about both of the given variables, x, and y

It tells us the y is equal to x plus 8 and that x plus y is equal to 2

If y is equal to x plus 8, we can

substitute the y value into the second equation

This will give us the following equation:

x + (x + 8) = 2

Now we simplify to solve for x

2x + 8 = 2

2x = -6

x = -3

Now that we know the x value, we can substitute that value into any one of the two equations given to solve for y

I'm going to use the first equation

Since we know that x is -3, we can now input it into the first equation and then simplify;
y = -3 + 8

y = 5

Answer:

Step-by-step explanation:

[tex]\tt y=x+8\\x+y=2[/tex]

Substitute y= x+8, into x + y=2:-

[tex]\tt x+y=2[/tex]

Let y = x+8

[tex]\tt x+x+8=2[/tex]

[tex]\tt 2x+8=2[/tex]

Solve for x :-

[tex]\tt 2x+8=2[/tex]

Subtract both sides by 8:-

[tex]\tt 2x+8-8=2-8[/tex]

[tex]\tt 2x=-6[/tex]

Divide both sides by 2:-

[tex]\tt \cfrac{2x}{2} =\cfrac{-6}{2}[/tex]

[tex]\boxed{\bf x=-3}[/tex]

Now, to solve for y, Substitute x = -3 into y=x+8:-

[tex]\tt y=x+8[/tex]

Let x = -3

[tex]\tt y=-3+8[/tex]

Simplify:-

*-3 + 8 = 5*

[tex]\boxed{ \bf y=5}[/tex]

Therefore, the solutions to the given system are x= -3 & y =5.

______________________

Hope this helps!

Answer:

[tex]\measuredangle \textsf{ BCA is Actue.}[/tex]

[tex]\measuredangle \textsf{ CAB is Actue.}[/tex]

[tex]\measuredangle \textsf{ ABC is Right}.[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked what type of angles are provided.}[/tex]

[tex]\textsf{First, the question is asking for the \underline{measure}, which \underline{affects} the types of angles.}[/tex]

[tex]\textsf{This Triangle is a \underline{Right Triangle}, according to the \underline{Angle Markings}.}[/tex]

[tex]\textsf{One angle must be \underline{Right}, and that angle is} \ \boxed{ \measuredangle \textsf{ABC.}}[/tex]

[tex]\textsf{Becuase a Triangle adds up to \underline{180}}^{\circ}\textsf{, the other \underline{2} angles are \underline{less than 90}}^{\circ}.[/tex]

[tex]\textsf{Meaning, that} \ \boxed{\measuredangle \textsf{BCA}} \ \textsf{and} \ \boxed{\measuredangle \ \textsf{CAB}} \ \textsf{are \underline{Acute}.}[/tex]

[tex]\fbox{\textsf{Notes:}}[/tex]

[tex]\textsf{An Acute Angle is \underline{less} than 90}^{\circ}.[/tex]

[tex]\textsf{A Right Angle is \underline{equal} to 90}^{\circ}.[/tex]

[tex]\textsf{An Obtuse Angle is \underline{greater} than 90}^{\circ} \textsf{, but \underline{less} than 180}^{\circ}.[/tex]

[tex]\textsf{A Straight Angle is \underline{equal} to 180}^{\circ}.[/tex]

[tex]\textsf{A Reflex Angle is \underline{greater} to 180}^{\circ} \textsf{, but \underline{less} than 360}^{\circ}.[/tex]

2

you divide 8 with 4 and the answer is 2

Answer:

720

Explanation:

[tex]2:125[/tex]

[tex]x:45000[/tex]

to go from 125 to 45000 we need to multiply by 360

that's why we will multiply 2 with 360 to balance both ratios

when we do that we get 720

2:125

[tex]\bold{720:45000}[/tex]

Answer:

720

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is not 855.3^2cm

Answer:

2, 3

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, if you reflect the point (-2, 3) over the y-axis, it will become (2, 3).

(Sorry, I tried to provide a picture but I could not.)

Answer:

Step-by-step explanation:

The answer to your question is a.

Answer:

a)3,6,9,12,15

b)9,18,27,36,45

c)14,28,42,56,70

Step-by-step explanation:

multiply each of it with 1,2,3,4 and 5 :)

Answer:

3-3,6,9,12,15

9-9,18,27,36.45

14-14,28,42,56.70

The length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

we shall represent the length of the diagonal with the letter x so by Pythagoras rule we can write:

x² = 34² + 45²

x² = 1156 + 2025

x² = 3181

x = √3181 {take square root of both sides}

x = 56.4004

Therefore, the length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.

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Two consecutive number between [tex]2 \frac{3}{10}[/tex] and [tex]4 \frac{1}{2}$[/tex] are 3 and 4.

Composite number are those number which follow a particular sequence whether it is normal, even, odd or any other sequence.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         AP) is the best method to identify whether the number are consecutive or not.

So here, we can write as [tex]\frac{23}{10}=2.3[/t[/tex]                                                                                                                                                                                                                                                                                         ex] and we can write [tex]\frac{1}{2}[/tex] as [tex]frac| {9}{2}=4.5[/tex]

So, two composite number are 3 and 4.

Arithmetic Progression, (AP) A sequence can called in as AP when the difference between them are common which means the each previous is differ from its preceding one by a constant quantity.

[tex]a_n=a_1+(n-1) * d[/tex] where, [tex]a_1=[/tex] first termed= common difference [tex]a_n=[/tex] term in the sequence

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Answer:

To find how much yarn Tina used for the third doll, we can subtract the total amount of yarn used for the first two dolls from the total amount of yarn used.

Total amount of yarn used = 10 1/2 yards

Amount used for first doll = 3 1/2 yards

Amount used for second doll = 4 1/8 yards

To add 3 1/2 and 4 1/8, we need to find a common denominator:

3 1/2 = 7/2

4 1/8 = 33/8

Common denominator = 8

So, 3 1/2 = 28/8 and 4 1/8 = 33/8

Total amount used for first two dolls = 28/8 + 33/8 = 61/8

Subtracting the total amount used for the first two dolls from the total amount of yarn used:

10 1/2 - 61/8 = 84/8 - 61/8 = 23/8

Therefore, Tina used 23/8 yards of yarn for the third doll.

The given statement is false. The solution has been obtained by using the concept of triangulation.

What is triangulation?

Based on the principles of trigonometry, triangulation is a technique used to locate a fixed point. According to these principles, it is possible to compute the other two sides and angle of a triangle if just one side and two angles of the triangle are known.

We are given a statement that to use the method of triangulation you need measurement from at least three locations.

The statement is false because for this, we need only two points.

Hence, the given statement is false.

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Question: To use the method of triangulation, you need measurements from at least three other locations.

A.True

B.False

Answer:

21

Step-by-step explanation:

The equation to find the area of a space is length x width. Divide the total area by the width to find the length.

Answer:

El tanque tardará aproximadamente 48 minutos en llenarse.

Step-by-step explanation:

Podemos encontrar la tasa de llenado del depósito sumando las tasas de flujo de los tres grifos:

Tasa de llenado = 60 + 70 + 80 = 210 litros/minuto

Luego, podemos usar la fórmula:

Tiempo = Volumen / Tasa de llenado

Donde el volumen es 10.080 litros y la tasa de llenado es 210 litros/minuto. Sustituyendo estos valores, obtenemos:

Tiempo = 10.080 / 210 ≈ 48 minutos

Por lo tanto, tardará alrededor de 48 minutos en llenarse el depósito de capacidad 10.080 litros si recibe agua por tres grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto.

¡Espero que esto ayude! Lo siento si no es así. ¡Si necesitas más ayuda, pregúntame! :]

Hello !

Answer:

[tex] \large \boxed{ \sf y = - 3 + \frac{9}{2} x}[/tex]

Step-by-step explanation:

We want to isolate y in the following equality :

[tex] \sf9x - 2y = 6[/tex]

First, let's substract 9x from both sides of the equality :

[tex] \sf9x - 2y - 9x= 6 - 9x[/tex]

[tex] \sf - 2y = 6 - 9x[/tex]

Now let's divide both sides by -2 :

[tex] \sf \frac{ - 2y}{ - 2} = \frac{6 - 9x}{ - 2} [/tex]

[tex] \boxed{ \sf y = - 3 + \frac{9}{2} x}[/tex]

Have a nice day ;)

Answer:

Fifty eight and twenty-three hundredths

Step-by-step explanation:

According to the given information, your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $0.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Let's call the amount of money Sarah spent on groceries "S".

Let's call the amount of money you spent on groceries "Y".

Let's call the amount of money your other roommate spent on groceries "O".

We know that:

S + Y + O = 82 (the total bill was $82)

Y = (S/2) - 0.05 (your groceries were $0.05 cheaper than half of Sarah's groceries)

O = Y + 2.10 (your other roommate's groceries were $2.10 more than your groceries)

We can use the second equation to substitute Y in the third equation:

O = Y + 2.10

O = (S/2) - 0.05 + 2.10

O = (S/2) + 2.05

We can now substitute both equations into the first equation:

S + Y + O = 82

S + ((S/2) - 0.05) + ((S/2) + 2.05) = 82

2S + 4 = 164

2S = 160

S = 80

Now that we know S, we can substitute it into the other equations to find Y and O:

Y = (S/2) - 0.05 = (80/2) - 0.05 = 39.95

O = Y + 2.10 = 39.95 + 2.10 = 42.05

So your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $80 - ($39.95 + $42.05) = $82 - $82 = $0.

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By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.

A semigroup is a mathematical structure consisting of a set of elements along with an associative binary operation. The operation must be associative, meaning that the result of the operation is independent of the order of the operands.

We can prove this by induction. Let S be a semigroup and x1, x2, x3, ..., xn be the elements of S.
Base Case: When n = 2, then the product of x1 and x2 is x1x2.
Inductive Step: Assume that the product of x1, x2, ..., xn (in that order) is equal. Then we can prove that the product of x1, x2, ..., xn+1 (in that order) is also equal.
Let a be the product of x1, x2, ..., xn (in that order). Then a = x1x2x3....xn.
Now the product of x1, x2, ..., xn+1 (in that order) is a x xn+1. Since S is a semigroup, a x xn+1 = x1x2x3....xn x xn+1.
Since the product of x1, x2, ..., xn (in that order) is equal, a = x1x2x3....xn. Therefore, the product of x1, x2, ..., xn+1 (in that order) is also equal.
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.

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The polynomial which is as described in the task content is; P (x) = -0.2 (x - 1)² (x +4).

It follows from the task content that; P(x) has a root of multiplicity 2 at x = 1 and a root with multiplicity of 1 at (x - 4).

Therefore, the polynomial would take the form;

P(x) = a (x - 1)² (x + 4)

Therefore, since the y-intercept is; y = -0.8

Therefore, we have that!

-0.8 = a (0-1)² (0+4)

-0.8 = 4a

a = -0.8 / 4

a = -0.2

Ultimately, the formula for the polynomial P(x) as given in the task content is; P (x) = -0.2 (x - 1)² (x +4).

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Answer:

c) 113°

Step-by-step explanation:

Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.

So the answer, quickly:

exterior angle

= 65° + 48°

= 113°

This is why:

(skip if you don't care)

The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°

So

x + 65° + 48° = 180°

x + y = 180°

y = 65° + 48°

See image.

Based on the given statement, the range of values of x is the values that do not exceed 82

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

The output of the operation cannot exceed 82

The range is teh set of the output values

This means that the range is all set of real values less than or equal to 82

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Answer:

Step-by-step explanation

The equation 8(x-9)=6(2x-12)-4x (option C) has an infinite number of solutions.

Let's simplify the given equation and solve for x:

8(x-9) = 6(2x-12) - 4x

8x - 72 = 12x - 72 - 4x // Distributing 6

8x - 72 = 8x - 72 // Simplifying

We can see that both sides of the equation are equal, and there is no variable 'x' present. This means that the equation is an identity and it will hold true for any value of x.

Therefore, this equation has an infinite number of solutions, since any value of x will satisfy the equation.

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The probability that the alumni member is male and did not attend graduate school is (546-206)/1214, or 83.09%.

Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability is used to describe the likelihood of something happening and to make decisions when dealing with uncertain situations. Probability theory is the mathematics of predicting the outcomes of events when the exact outcome is unknown.

In conclusion, the probability that the alumni member is female is 8.55%, that the alumni member is male is 16.91%, that the alumni member is female and went on to graduate school is 8.55%, that the alumni member is male and went on to graduate school is 16.91%, that the alumni member is female and did not attend graduate school is 79.60%, and that the alumni member is male and did not attend graduate school is 83.09%.

The probability that the alumni member is female is 104/1214, or 8.55%. The probability that the alumni member is male is 206/1214, or 16.91%. The probability that the alumni member is female and went on to graduate school is 104/1214, or 8.55%. The probability that the alumni member is male and went on to graduate school is 206/1214, or 16.91%. Finally, the probability that the alumni member is female and did not attend graduate school is (668-104)/1214, or 79.60%.

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Enquire οf each pupil in yοur math class. --> b. Cοnvenience

chοοsing every 5th persοn οn a list  --> d. Systematic

pulling 50 names frοm a hat --> a. Simple Randοm

Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified

selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster

Samples can be categοrized intο:

Cοnvenient: Sample taken frοm a pοοl that is easily accessible.

Put all the pοssibilities intο a hat, and draw sοme οf them at randοm.

Every kth cοmpοnent is taken in a systematic manner. If yοu wanted tο survey anything οn the street, fοr instance, yοu may interview every fifth persοn.

Cluster: This pοpulatiοn is brοken dοwn intο grοups, οr clusters, and each cluster's cοnstituents are surveyed.

Further divides the peοple intο several grοups. After that, thοugh, just a small percentage οf the grοup gets quizzed.

Thus, cοrrect match οf the sampling methοd are:

enquire οf each pupil in yοur math class. --> b. Cοnvenience

chοοsing every 5th persοn οn a list  --> d. Systematic

pulling 50 names frοm a hat --> a. Simple Randοm

Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified

selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster

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The equation of the given line is expressed as:

y = x - 3

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line between two coordinates is:

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

The pair of coordinate points marked are:

(4, 1) and (5, 2)

Thus, the equation of the line is:

(y - 1)/(x - 4) = (2 - 1)/(5 - 4)

y - 1 = x - 4

y = x - 3

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The statement "The Poisson distribution is always skewed right" is incorrect. Option A

The Poisson distribution is a discrete probability distribution that is used to model the probability of a given number of events occurring in a fixed interval of time or space, assuming that the events occur independently and at a constant rate.

The key features of the Poisson distribution include:

The statement "The Poisson distribution is always skewed right" is incorrect.

The Poisson distribution can be skewed left, right, or approximately symmetric depending on the value of its parameter lambda. If lambda is small, the distribution will be skewed right. If lambda is large, the distribution will be approximately symmetric.

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Answer: To calculate the standard deviation of a discrete random variable, we need to know the expected value and the variance. The variance of a discrete random variable X is given by:

Var(X) = Σ [ (x - E(X))^2 * P(X = x) ]

where the summation is taken over all possible values of X, and E(X) is the expected value of X.

We are given that the expected value of X is 1.95. Using the formula for the variance and the probabilities given in the table, we can calculate the variance as follows:

Var(X) = (0 - 1.95)^2 * 0.03 + (1 - 1.95)^2 * 0.31 + (2 - 1.95)^2 * 0.43 + (3 - 1.95)^2 * 0.14 + (4 - 1.95)^2 * 0.09

Var(X) = 1.1429

To find the standard deviation, we take the square root of the variance:

SD(X) = sqrt(Var(X))

SD(X) = sqrt(1.1429)

SD(X) ≈ 1.07

Therefore, the standard deviation of the number of cars owned by families in New York is approximately 1.07. None of the options given match this value exactly, but 0.99 is the closest.

Step-by-step explanation:

1. B.

2. C.

3. A.

4. C.

The area of the shaded portion in the image of right triangle attached is solved to be 401.85 square millimeters

The area of the shaded portion is solved by subtracting the area of the smaller triangle from the area of the bigger triangle

The area of a triangle is solved using the formula

= 0.5 base * height

Information given in the problem  

base1 = 24.8

base2 = 15.9

height1 =  34.2 mm

height2 = 21.9

where

base1 and height1 are for the bigger triangle while

base2 and height2 is for smaller triangle

area of shaded portion = 0.5(24.8 * 34.2) - 0.5(15.9 * 21.9)

area of shaded portion = 418.95 - 174.105

area of shaded portion =401.845

area of shaded portion = 401.85 square millimeters

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Answer:

x < 16

Step-by-step explanation: