find a formula for the general term a n an of the sequence assuming the pattern of the first few terms continues. { 3 , − 1 , − 5 , − 9 , − 13 , ... } {3,-1,-5,-9,-13,...}

Answer:

y = 7      x = 45

Step-by-step explanation:

\(x=45\) because the triangle is a right angle isocele triangle so 180-90 =90

90 / 2 =45 = x

\(\frac{7\sqrt{\:2}}{\sin \left(90\right)\:}=\frac{y}{\sin \left(45\right)}\) so  y = 7

Answer:

y =7

this is your answer

The slope of the any line parallel to the line y-5 = 25/2(x+4)  is equal and its value is 25 /2 .

We have given equation y-5 = 25/2(x+4) .

On simplifying , we get

      y - 5 = 25 x/2 +50

       y = 25 x /2 +55

On comparing the above equation with slope intercept form y = mx + b ,

we get m = 25 / 2

All the lines which are parallel to any other line have equal slope.

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Answer: The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.

The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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Answer:

2, 3, and 7 are not function

The rest are

Step-by-step explanation:

In a function every X has one and only one y

2 is not a function because X=5 has 2 different y's

3 is not a function because X=2 has 2 different Y's

7 is not a function because X=b has 2 different Y's

The absolute maximum value of the function f(x) = 5x cos(x) on the interval 0 ≤ x ≤ π, correct to six decimal places, is approximately 5.000000.

To find the absolute maximum value of the function f(x) = 5x cos(x) on the interval 0 ≤ x ≤ π, we can use Newton's method to locate the critical points and evaluate the function at those points.

First, we find the derivative of f(x) with respect to x:

f'(x) = 5 cos(x) - 5x sin(x)

Next, we set the derivative equal to zero to find the critical points:

5 cos(x) - 5x sin(x) = 0

Using Newton's method, we can iteratively approximate the critical points. Let's choose an initial guess x₀ = π/2 and iterate using the formula:

xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ)

Performing the iterations, we obtain:

x₁ ≈ 1.570796

x₂ ≈ 1.570796

Since both x₁ and x₂ converge to approximately 1.570796, we have a critical point at x = 1.570796.

Next, we evaluate f(x) at the critical point and the endpoints of the interval:

f(0) = 0

f(1.570796) ≈ 5.000000

f(π) ≈ 0.000000

From the above evaluations, we can see that the absolute maximum value of f(x) on the interval 0 ≤ x ≤ π is approximately 5.000000.

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Answer:

5.79

Step-by-step explanation:

I think I'm not very sure tho

It's 7.723, not 5.79.

If you get your bodmas correctly, you should get 7.723.

Solution:

Do "((-4.6) - 1.9) first, which is -6.5 basically.

After that it is (-2.78) x (-2.8), which is 7.784.

After that do (2.2 - 1.8) ÷ ((-4.6) - 1.9), which is -0.061

After that 7.784 + -0.061, which makes it 7.723.

Answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15

These problems are really brute force, there is no real clever way. I only just listed all possible combinations

HOWEVER, notice in answer.

5 1 9

5 2 8

5 3 7

5 4 6

Since ALL the sets contain a 5, we just subtract 5 from 15.

So we need TWO terms in a set and they add up to 10, and also are unique.

This is quite easy.

1 9

2 8

3 7

4 6

5 5 (does not work because cannot repeat digit)

thus , answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15

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Answer:

equal parts of this story is the order I am the first thing to say about this

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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El sistema de ecuaciones que permite obtener el precio por litro de los dos tipos de gasolina es 8x + 10y = 302.12 y 12x + 12y = 400.08​ (opción D)

Una ecuación es una expresión matemática que se caracteriza por representar una igualdad entre dos miembros separados por el signo igual. La ecuaciones incluyen elementos conocidos e incógnitas relacionados mediante operaciones matemáticas.

De acuerdo a lo anterior la respuesta correcta es 8x + 10y = 302.12 y 12x + 12y = 400.08​. Por que estas ecuaciones expresan matemáticamente los datos que se tienen y las incógnitas con las letras x y y.

Por ejemplo, la primera expresa que 8 (litros) por el precio del galón de gasolina Magnum (x), más 10 (litros) por el precio del galón de gasolina Premium (y) es igual a 302.12, que fue el precio total que pagó Carlos por la gasolina.

La segunda ecuación expresa que 12 (litros) por el precio del galón de gasolina Magnum (x) más 12 (litros) por el precio del galón de gasolina Premium (y) es igual a 400.08, que fue el precio total que Raquel pagó por la gasolina.

Esta pregunta está incompleta porque faltan las opciones e información sobre la gasolina. A continuación está la información completa y las opciones.

Carlos compró 8L de gasolina Magnum y 10 litros de gasolina premium por 302.12

Raquel compró 12L de gasolina Premium y 12L de gasolina magnum por 400.08

A) 8x + 12y = 302.12

10x + 12y = 400.08

B) 8x + 12y = 400.08

10x + 12y = 302.12

C) 8x + 10y = 400.08

12x + 12y = 302.12

D) 8x + 10y = 302.12

12x + 12y = 400.08​

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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The perimeter of the card is 32 centimeters. Perimeter of a square is given by 4x, where x is the length of each side of the square.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

In this case, x=4.

Therefore, the perimeter of the card is 4x = 4(4) = 32.

The perimeter of a square is determined by multiplying the length of each side by 4. In this case, the length of each side of the square tank you card is x=4. Therefore, the perimeter of the card can be calculated by multiplying 4 with 4 which is equal to 32 centimeters. This means that the perimeter of the tank you card when x=4 is 32 centimeters.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

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Answer:

x > -6

Step-by-step explanation:

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

\(\frac{7}{16}\)

Step-by-step explanation:

\(\frac{7}{8}\) x \(\frac{1}{2}\) = \(\frac{7}{16}\)

7 x 1 = 7

8 x 2 = 16

Let me know if this helps!

1) The statement of Lin is correct.

2) (a) When scale factor, k = 9, area of the new triangle = 8100 square inches

(b) When k = 3/4, area of the new triangle = 56.25 square inches.

Given that,

A triangle has area 100 square inches.

It's dilated by a factor of k = 0.25.

When the triangle is dilated by a scale factor of k, then, each of the base and height is dilated by the scale factor of k.

So new area of the triangle after the dilation with the original triangle having base = b and height = h is,

Area of new triangle = 1/2 (kb)(kh) = k² (1/2 bh) = k² × Area of original triangle

Here original area = 100 square inches.

k = 0.25

New area = (0.25)² 100 = 6.25 square inches

So the correct statement is that of Lin.

Mai may found the new area by just multiplying the scale factor with 100, instead of taking the square of the scale factor. That is why she got 25 square inches as the new area.

2) (a) When k = 9,

Area of the new triangle = 9² (100) = 8100 square inches

(b) When k = 3/4

Area of the new triangle = (3/4)² (100) = 56.25 square inches

Hence the areas are found.

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The function f has the property injective. (D)

An injective function is also known as a one-to-one function, which means that for every unique output, there is a unique input.

In this case, the function f maps the single element in the domain {1} to the single element in the codomain {1}, and there is only one possible output for the single input, so it is injective.

It does not have the properties of being increasing, decreasing, strictly increasing, strictly decreasing, or surjective because the function is a constant function mapping the single element in its domain to the single element in its codomain.

As a result, it does not change in value and cannot be classified as increasing or decreasing. Additionally, it is not surjective because the codomain contains one element that is not mapped to by the function.

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190 student tickets were sold.

Let's assume the number of adult tickets sold is "A" and the number of student tickets sold is "S." According to the given information:

The price of an adult ticket is $3.00, so the revenue from adult tickets is 3A dollars.

The price of a student ticket is $1.50, so the revenue from student tickets is 1.5S dollars.

The total number of tickets sold is 260, so A + S = 260.

The total revenue from all tickets sold is $495.00, so 3A + 1.5S = 495.

We can solve this system of equations to find the values of A and S. First, let's solve the A + S = 260 equation for A:

A = 260 - S

Now substitute this value of A in the second equation:

3(260 - S) + 1.5S = 495

780 - 3S + 1.5S = 495

-1.5S = 495 - 780

-1.5S = -285

S = -285 / -1.5

S = 190

Therefore, 190 student tickets were sold.

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Step-by-step explanation:

for any matrix multiplication number of columns of first matrix should be equal to number of rows of second matrix.

For AB

A has 3 columns and B has 3 rows so it matches . Hence can be multiplied.

For BA

B has 2 columns and A has 2 rows it also matches so can be multiplied

Answer:

Step-by-step explanation:

Zero exponent numbers = 1

When you try to multiply an exponent by zero, it equals one.

Negative exponents is just a 1/x

Negative just flips over the equation.

For example, 9^-1

1/9^1

1/9

Answer:

Step-by-step explanation:

Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.

Example:  x^0 = 1

Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.

An example of negative exponents is \(3^{-2}\).

(English) Are you referring to 125 = (5x + 30) or 125(5x + 30)? Just so I can help you properly solve the problem. Thanks!

(Spanish) ¿Te refieres a 125 = (5x + 30) o 125(5x + 30)? Solo para que pueda ayudarte a resolver correctamente el problema. ¡Gracias!

Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

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Answer:

11

Step-by-step explanation:

5x + 5 = 4x + 16 ( being alternate angles)

5x - 4x = 16 - 5

x = 11

Hope it will help :)

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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Answer:

f(- 2) = - 4

Step-by-step explanation:

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = (- 2)² + 3(- 2) - 2 = 4 - 6 - 2 = - 4

A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

x + 3y = 2 ------ (2)

x = 2 - 3y ------ (3)

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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We have three points that represent the vertices of the triangle

- A( -1, 5 )

- B( 4, 5 )

- C( -1, 1 )

We need to calculate the distances between the points to calculate the perimeter

To calculate the distances we must use the next equation

Distance for AB:

Distance for BC:

Distance for AC:

Finally, the perimeter is

So, the answer is

The amount of apple juice needed in a 64 fluid ounce bottle of cranapple juice is 40.8 fluid ounce.

The beverage company makes 100% cranapple juice which is made up of 3 1/4 cranberry juice to 5 3/4 apple juice. Converting to decimal, it is made up of 3.25 cranberry juice to 5.75 apple juice. The ratio of cranberry juice to apple juice in the cranapple juice would be

=3.25/5.75

=> Total ratio = 3.25 + 5.75 = 9

The amount of apple juice needed in a 64 fluid ounce cranapple juice would be

5.75/9 × 64 = 40.8  fluid ounce

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