What is lim x->-1 sin(pie/6))



this is a timed

Answer:

Option B is the correct answer

Step-by-step explanation:

h(x) = 5x + 2, h(8)

h(8) = 5(8) + 2

h(8) = 40 + 2

h(8) = 42

Thus, The answer is 42

The perimeter of the given rectangle is, 19.2112

Given that, the vertices of the rectangle are A(-3,-2), B(-5,-5), C(1,-5), D(3,-2) .

to find the perimeter through the given vertices, we need to calculate the distance from the vertices AB,BC,CD,DA.

we already know that the sum of all sides of the rectangle is known as the perimeter of the rectangle.

Using distance formula between 2 vertices , √[(x2-x1)²+(y2-y1)²]

AB = √[(-5+3)²+(-5+2)²]

     = √[(-2)²+(-3)²]

     =  √[4+9]

     =  √[13]

     =  √13

AB = 3.6056

BC = √[(1+5)²+(-5+5)²]

     = √[(6)²+(0)²]

     =  √[36+0]

     =  √[36]

     =  √36

BC = 6

CD = √[(3-1)²+(-2+5)²]

     = √[(2)²+(3)²]

     =  √[4+9]

     =  √[13]

     =  √13

CD = 3.6056

DA = √[(-3-3)²+(-2+2)²]

     = √[(-6)²+(0)²]

     =  √[36+0]

     =  √[36]

     =  √36

DA = 6

Therefore perimeter of the rectangle with given vertices is ,

  = AB+BC+CD+DA

  = 3.6056+6+3.6056+6

  = 19.2112

  = 19 (rounded to nearest tenth).

Therefore the perimeter of the rectangle with given vertices is 19.2112

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Answer:

D.  45/8

Step-by-step explanation:

The value of function g (7) is,

⇒ g(7) = 45/8

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Function is,

⇒ g(x) = 7/8x - 1/2

Now, Plug x = 7 in above equation,

⇒ g(x) = 7/8x - 1/2

⇒ g(7) = 7/8 (7) - 1/2

⇒ g(7) = 49/8 - 1/2

⇒ g(7) = 49/8 - 4/8

⇒ g(7) = 45/8

Thus, The value of function g (7) is,

⇒ g(7) = 45/8

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Answer:

3

HCF of 12, 45 and 75 by Prime Factorization

As visible, 12, 45 and 75 have only one common prime factor i.e. 3. Hence, the HCF of 12, 45 and 75 is 3.

Step-by-step explanation:

Given,

The initial balance in the checkbook is $463.18.

The deposite money is $265.

The amount of check is $198.73.

The charge paid for bank is $2.50.

The ending balance at the month end is,

Hence, option b ($526.95) is correct.

Marcia bought 15 pizzas for her birthday party to accommodate the 30 people, with each person eating 3 slices of pizza that was cut into sixths.

To determine the number of pizzas Marcia bought for her birthday party, let's break down the given information.

We know that there were 30 people at the party, and each person ate 3 slices of pizza.

The pizza was cut into sixths, and there were 12 slices in total.

Since each person ate 3 slices, and each slice is 1/6 of a pizza, we can calculate the total number of pizzas consumed by multiplying the number of people by the number of slices each person ate: 30 people \(\times\) 3 slices/person = 90 slices.

Now, we need to determine how many pizzas Marcia bought. Since there were 12 slices in total, and each slice is 1/6 of a pizza, we can calculate the total number of pizzas using the following formula:

Total pizzas = Total slices / Slices per pizza.

In this case, the total slices are 90, and each pizza has 6 slices.

Thus, the number of pizzas Marcia bought can be calculated as follows: Total pizzas = 90 slices / 6 slices per pizza = 15 pizzas.

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the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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Answer:

4 miles per hour

Step-by-step explanation:

We can divide 45 minutes by 3 to get 15 minutes:

So that is 1 mile in 15 mins

Then we multiply both sides by 4 to get 60 mins:

4 miles in 60 mins

So his rate was 4 miles per hour

Answer:

4 miles per hour

Step-by-step explanation:

Convert to a decimal by dividing the numerator by the denominator.

4 miles per hour

Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

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Answer:

Answer is D

Step-by-step explanation:

Day 1 = 60

Day 2 = 120

Day 3 = 180

Day 4 = 240

Day 5 = 300

Day 6 = 360

Day 7 = 420

Day 8 = 480

The graph D will show the best relationship between  the number of days and the number of frozen treats sold.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

It is given that he sells 60 frozen treats per day so everyday the frozen treats are multiplied by 60.

We can see the linear relationship between frozen treats and number of days.

Day 1 -  60

Day 2 - 120

Day 3-  180

Day 4-   240

Day 5-  300

Day 6-  360

Day 7-  420

Day 8-  480

Hence the graph D will show the best relationship between  the number of days and the number of frozen treats sold.

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Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

Answer:

Probability = 1 / 5

Step-by-step explanation:

Assuming that rates are from 1 to 5 ; with equal probability of being 1, 2 , 3 , 4, 5 each.

So, probability of 3 stars = Outcomes with 3 stars / Total outcomes

= 1 / 5

Therefore, there are 72 different orders in which the eight targets can be broken according to the given rules.

To find the number of different orders in which the eight targets can be broken, we can consider the arrangement of the columns and the targets within each column. Since there are three targets in each of the first two columns and two targets in the third column, we can focus on the relative order of breaking the targets within each column. Let's represent the columns as follows:

Column 1: T T T

Column 2: T T T

Column 3: T T

To calculate the number of different orders, we can count the permutations of breaking the targets within each column and then multiply them together.

For Column 1, there are 3 targets, so there are 3! = 3 × 2 × 1 = 6 possible orders.

For Column 2, there are also 3 targets, so there are 3! = 6 possible orders.

For Column 3, there are 2 targets, so there are 2! = 2 possible orders.

To find the total number of different orders, we multiply the number of orders for each column:

Total number of orders = 6 × 6 × 2

= 72

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Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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Answer:

106°

Step-by-step explanation:

they are parallel to each other

Answer: 106

Step-by-step explanation:

Answer:

First option -34.5 > x

Step-by-step explanation:

Because the blue line is behind the point -34.5, x has to be less than -34.5

Answer:

L=65m

W=23m

Step-by-step explanation:

\(3W-4=L\\2L+2W=176\\\\2L+2W=176\\-2L+6W=8\\8W=184\\W=23m\\L=23*3-4=65m\)

The length and width of the rectangle are 63m and 25m.

A rectangle is a quadrilateral, a 2d shape that has four sides and four vertices.

We have,

The perimeter of a rectangle = 176 m

Length of the rectangle = L = 3 x (W- 4 )

Width of the rectangle = W

The perimeter of a rectangle is given by:

176 = 2 ( L + W )

176 = 2 ( 3 ( W - 4 ) + W )

176 = 2 ( 3W - 12 + W )

176 = 2 ( 4W - 12 )

176 = 8W - 24

176 + 24 = 8W

200 = 8W

W = 200 / 8

W = 25 m

Now,

Put W = 25 in L = 3 x ( W - 4 )

L = 3 x ( 25 - 4 )

L = 3 x 21

L = 63 m

We can cross-check:

Perimeter = 2 ( 63 + 25 ) = 2 ( 88 ) = 176 m

Thus the length and width of the rectangle are 63m and 25m.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

32 gallons

Step-by-step explanation:

A standard showerhead in Marty's house dispenses 7 gallons of water per minute. If he showers for 8 minutes, he uses:

1 minute = 7 gallons

8 minutes = x

x = 7 × 8 minutes = 56 gallons of water

We are told that:

Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x

The equation for the energy saving shower:

y = 3x

Where x is the number of minutes spent in the shower

For 8 minutes

y = 3 × 8

y = 24 gallons

The gallons of water Marty saved each day with the change in showerheads if he uses the shower for 8 minutes each day is calculated as:

56 gallons - 24 gallons

= 32 gallons

The iterated integral is 128 when it is converted to the polar coordinates integral( upper= a, lower= 0) integral.

Polar coordinate systems are those in which each point on a two-dimensional coordinate system's plane is determined by its distance from the reference point and an angle is taken from that reference direction. The point of reference is Pole. The line segment ray from the pole in the direction of the reference is known as the polar axis.

here ,

given integrated integral is

x\(x\sqrt{x^{2} + y^{2} } dydx\)

where r is a half circle in the xy plane

the circe is  y = \(\sqrt{4 - x^{2} }\)

\(y^{2}\) = 4 - \(x^{2}\)

\(x^{2} + y^{2}\) = 4

= 16 [ -4 ] [ -2]

= 16 ( 8 )

= 128

As a result, the iterated integral is 128 when it is converted to the polar coordinates integral( upper= a, lower= 0) integral.

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Answer:

2:5

Step-by-step explanation:

WHichever one they ask you for first is the first number in the ratio. Meaning 2 solid figures are 2:1 plain figures.

A-1 = (ATA)-1AT, and therefore ATA is also invertible.

If A is invertible, it means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. This means that A has an inverse, denoted by A-1.

Now, let's consider the matrix ATA. To show that it is also invertible, we need to find a matrix C such that (ATA)C = C(ATA) = I. We can do this by substituting B = A-1 into the equation and multiplying both sides by A:ATAA-1 = AIA-1 = AA-1 = I

This means that C = A-1 is the inverse of ATA, so (ATA)-1 = A-1. Now, let's substitute this back into the equation to find A-1:A-1 = (ATA)-1AT = A-1ATA-1AT = A-1IT = A-1

Thus, we have shown that A-1 = (ATA)-1AT, and therefore ATA is also invertible.

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Answer:

17.5

Step-by-step explanation:

35℅ of 100 is 35 so 200 would be half that

Answer:

Hey!

Your answer is 17.5%!

Step-by-step explanation:

Can be written as...35/200

Now...

MULTIPLY THE NUMERATOR AND DENOMINATOR BY 100...

35/200 × 100/100

35×100/200 × 1/100

SOLVED!!!

▶ HOPE IT HELPED ◀

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

180

Step-by-step explanation:

Answer:

The second choice

Step-by-step explanation:

i dunno how to explain it