The height (h) of an object thrown from the top of a ski lift 2308 feet high after (t) seconds is h= - 16t² +32t+2308.
For what times is the height of the object at least 1300 feet?

The height of the object is at least 1300 feet from _______ seconds to _______ seconds.

Slope of relationship between length of icicle and time = −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches .The correct option is D.

What is slope?

The slope of a line is defined as the change in vertical coordinate with respect to the change in horizontal coordinate of that line.

Given,

A student is measuring the length of an icicle, y, every hour, x

At present icicle is 9 inches long

melting at rate of 0.6 per hour

y = 9 - 0.6 x

Where y is the length of the icicle after x hours

comparing with slope intercept form of line: y = m x + c

slope m = -0.6

Hence, - 0.6 is the slope, represents that the length of the icicle decreases by 0.6 inches every hour.

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A pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions. Option D is the correct answer.

The dimension of an item in mathematics is, approximately speaking, the quantity of degrees of freedom of a moving point on the object. To put it another way, a dimension is indeed the amount of distinct factors or coordinates required to define the location of a point that must be on an object. For instance, a point has a dimension of zero; a line has a size of one since a point can only move along a line in one direction (or its opposite); a plane has a dimension of two; etc.

The volume of the wooden board is given by the formula:

V = (l)(b)(h)

V = (2)(6)(14)

V = 168 cubic inches.

The volume of pile of 3 boards has dimensions:

l = 14

b = 6

h = 3(2)

V = 3(168) = 504 cubic inches.

Similarly, piling the boards and changing the height.

The volume of pile of four boards = 4(168).

The volume of pile of 5 boards = 5(168)

The volume of pile of 6 boards = 6(168) = 2(3(168))  = 2(Volume of pile of 3 boards)

Hence, a pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions.

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Answer:

3 times greater

Step-by-step explanation:

To find out how many times greater the population of Chicago is than Austin, we can divide the population of Chicago by the population of Austin:

Population of Chicago / Population of Austin = 2,720,546 / 900,000

Simplifying the expression by dividing both the numerator and denominator by 100,000, we get:

Population of Chicago / Population of Austin = 27.20546 / 9

Dividing these numbers, we get:

Population of Chicago / Population of Austin = 3.022838

Therefore, the population of Chicago is about 3 times greater than the population of Austin.

52 cm is equivalent to nearly 20.47 inches, rounded to two decimal places.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimeters,

Used in the International System of Units,

This is the metric system's present configuration.

52 centimetres equal 20.47 inches (centimeters).

To convert centimeters to inches,

We can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 52 cm to inches,

You can divide 52 by 2.54:

52 cm / 2.54 = 20.47 inches

So, 52 cm is equivalent to nearly 20.47 inches,

rounded to two decimal places.

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I am to believe the answer is Yes because you add the exponents

Answer:

The answer is 50, the median. The median is the value where 50% of the data lie above and below.

Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

A list's values are added together to get the average values, also known as the group's mean, which is then multiplied by the maximum population of list items. Similar progression trends can be seen in math. The average of the actual numbers 5, 8, and Nine is 3, while a mean of the actual numbers 5, 7, & 9 is 4, and indeed the number 21 times three (there now multiple 3 numbers) equals seven. This is demonstrated by the following equation.

Here,

Given :

First sequence :

=> 7,21,63 ....

We can see it is a type of geometric progression:

As,

=> 21/7 = 3

=> 63/21 = 3

So, it's nth formula is :  aⁿ = a(3)ⁿ

And

Second sequence :

=> 3, 8, 13,....

it is a type of arithmetic progression:

As,

=> 8 -3 =5

=> 13 -8 = 5

So, it's nth formula is :  aⁿ = a + (n-1)5

Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

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Answer: 18x+24

Step-by-step explanation:

Found that a short stanza contains 8 lines and a long stanza contains 9 lines.

What is linear equation ?

A linear equation is an equation that describes a straight line in a two-dimensional coordinate system. The general form of a linear equation is:

y = mx + b

Explanation:
Let's use "s" to represent the number of lines in a short stanza and "l" to represent the number of lines in a long stanza.

From the problem, we know that Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. This can be written as the equation:

10s + 2l = 98

We also know that Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. This can be written as the equation:

3s + 7l = 87

We want to find the values of s and l that satisfy both of these equations. We can use algebra to solve for s and l.

Multiplying the first equation by 3, we get:

30s + 6l = 294

Multiplying the second equation by 2, we get:

6s + 14l = 174

Now we can add the two equations together to eliminate the variable s:

30s + 6l + 6s + 14l = 468

Simplifying and rearranging, we get:

36s + 20l = 468

Dividing both sides by 4, we get:

9s + 5l = 117

Now we have a new equation that relates the values of s and l that satisfy both sets of stanzas. We can use this equation along with one of the original equations to solve for either s or l.

Let's use the first equation, 10s + 2l = 98. We can solve for s in terms of l:

10s + 2l = 98

10s = 98 - 2l

s = (98 - 2l)/10

Now we can substitute this expression for s into the equation 9s + 5l = 117:

9[(98 - 2l)/10] + 5l = 117

Simplifying and solving for l, we get:

l = 9

Now we can substitute this value of l back into either of the original equations to solve for s. Using the first equation:

10s + 2l = 98

10s + 2(9) = 98

10s = 80

s = 8

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The TI-84 calculator can be used to find the p-value associated with a hypothesis test, given the test statistic and the degrees of freedom (df).

Here are the steps to find the p-value on a TI-84 calculator:

Press the "2nd" button and then the "VARS" button (which is above the "STAT" button). This will open the DISTR menu.

Select "3: tcdf" from the menu by scrolling down with the arrow keys and pressing "ENTER".

Enter the test statistic and degrees of freedom. For a two-tailed test, enter the test statistic with the appropriate sign (positive or negative) and enter a very large number (such as 100 or 999) for the second argument.

For a one-tailed test, enter the test statistic and select "1" or "2" for the third argument, depending on the direction of the test.

Press "ENTER" to calculate the p-value.

The result displayed on the calculator screen will be the p-value associated with the hypothesis test, based on the test statistic and degrees of freedom entered.

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The question is -

How to find the p-value from the TI-84 calculator?

Answer:

Step-by-step explanation:

points

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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The length of the arc that outlines the sector is 15π centimeters.

What is the area of sector?

The area of a sector is given by the formula:

[tex]A=\frac{\theta}{360^{\circ}} \times \pi r^2[/tex]

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

To find the area of the shaded sector, we need to use the formula -

[tex]Area=\frac{central \angle}{360^{\circ}} \times \pi r^2[/tex]

In this case, the central angle is 270° and the radius is 10 cm. Plugging these values into the formula, we get:

Area of sector = [tex]\frac{270^{\circ}}{360^{\circ}} \times \pi (10)^2[/tex]

Area of sector = (3/4) x π x 100

Area of sector = 75π

So the area of the shaded sector is 75π centimeters.

To find the length of the arc that outlines the sector, we need to use the formula:

Length of arc = (central angle / 360°) x 2πr

Plugging in the values of the central angle and radius, we get:

Length of arc = (270/360°) x 2π x 10

Length of arc = (3/4) x 20π

Length of arc = 15π

Hence, the length of the arc that outlines the sector is 15π centimeters.

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Answer:

0.80*c = 20

Step-by-step explanation:

"80% of c is 20" can be written as:

  0.80*c = 20

80% of c is 0.80*c

"is" can be written as "="

Put these two together to obtain:

  0.80*c = 20

The surface area of the given prism above would be = 606cm²

To calculate the surface area of the given prism is to add all the area of the faces.

The area of the two triangles = 2(1/2 base×height)

where base = 12 cm

height = 8cm

area = 1/2× 12×8

= 48 × 2 = 96cm²

Area of rectangle =3( l×w )= 3(17×10)

= 3×170 = 510cm²

Therefore the surface area of the prism = 96+510 = 606cm².

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The correct answer is option C. f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)

Explanation:

To determine the correct answer, we need to look at the zeros of the given functions and compare them to the zeros shown on the graph. The zeros of a function are the values of x that make the function equal to zero. These are also the points where the graph of the function crosses the x-axis.

Option A: f(t) = (x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 1, x = 2, x = -1, and x = -2.

Option B: f(x) = x(x - 1)(x + 1)
The zeros of this function are x = 0, x = 1, and x = -1.

Option C: f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 0, x = 1, x = 2, x = -1, and x = -2.

Option D: f(r) = x(x - 1)(x - 2)
The zeros of this function are x = 0, x = 1, and x = 2.

Comparing the zeros of these functions to the zeros shown on the graph, we can see that option C is the correct answer. The graph shows zeros at x = 0, x = 1, x = 2, x = -1, and x = -2, which are the same zeros as the function f(x) = x(x - 1)(x - 2)(x + 1)(x + 2).

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Answer:°

Based on the given information, we can see that the pair of parallel lines are intersected by a transversal, which creates corresponding angles on the two lines. Using this fact, we can set up the equation:

2x + 105 = 70^2

First, we simplify 70^2:

70^2 = 4900

Then, we solve for x:

2x + 105 = 4900

2x = 4900 - 105

2x = 4795

x = 2397.5

Therefore, x is equal to 2397.5.

The relationship between the angles is that they are corresponding angles, which means they are congruent. We can use this fact to find the measure of the other angle that is marked in the diagram.

From the diagram, we can see that the angle marked as (2x + 10^5)° is supplementary to the angle marked as 70^2°. This means that the sum of their measures is 180 degrees. We can use this fact to find the measure of the angle marked as (2x + 10^5)°:

(2x + 10^5) + 70^2 = 180

2x + 10^5 + 4900 = 180

2x + 10^5 = 175

2x = 175 - 10^5

2x = -99825

x = -49912.5

correct me if im wrong

Step-by-step explanation:

Answer:

6 US tablespoons

Step-by-step explanation:

The exact volume of a cylinder with a radius of 10 m and a height of 8 m is 800π m³. This can be calculated using the formula for the volume of a cylinder, which is V = πr²h. (option 4)

In that, r is the radius and h is the height of the cylinder. In this case, r = 10 m and h = 8 m, so the volume can be calculated as V = π(10 m)²(8 m) = 800π m³.

To calculate this volume, we first use the formula for the volume of a cylinder, which states that the volume is equal to πr²h, where r is the radius and h is the height of the cylinder. In this case, the radius of the cylinder is 10 m and the height is 8 m, so the volume can be calculated as

This is the exact volume of the cylinder.

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Complete Question:

A cylinder has a radius of 10 m and a height of 8 m. what is the exact volume of the cylinder? responses

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

Step-by-step explanation:

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

15.585 is the radius of the cone

The y-intercept of the graph of this line is equal to 1.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this context, we can logically deduce that the y-intercept as shown in the image attached below is at point (0, 1).

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Answer:

Step-by-step explanation:

You want the graphical solution to the set of inequalities that describes the numbers of games (x) and songs (y) that Staci can buy with $20, if a game costs $2 and a song costs $1, and Staci wants to buy at least 12 items.

The inequalities that describe the numbers are ...

  2x +y ≤ 20 . . . . . Staci has at most $20 to spend

  x + y ≥ 12 . . . . . . Staci wants to buy at least 12 items

Each of these inequalities has a solid boundary line on its solution space graph. The shading is below the line for the first inequality, and above the line for the second one. The vertices of the triangular solution space are ...

  (0, 12), (0, 20), (8, 4)

Possible numbers are the coordinates of any grid point within the triangle or on its boundaries.

Mr. Davis' granola snacks will last for 20 days.

What is division ?

Division is a basic arithmetic operation used to find the quotient or the number of times one quantity is contained within another. In division, a dividend is divided by a divisor, and the result is the quotient. For example, 12 divided by 3 is 4, where 12 is the dividend, 3 is the divisor, and 4 is the quotient.

Division is the inverse operation of multiplication. If you know the multiplication facts, you can use them to help you divide numbers. For instance, if you know that 5 times 6 equals 30, then you also know that 30 divided by 5 equals 6, and that 30 divided by 6 equals 5.

According to given conditions:

To find out how many days Mr. Davis' granola snacks will last, we need to divide the total amount of granola by the amount he eats each day.

Let's say Mr. Davis made 10 lbs of granola snacks.

He eats 0.5 lb each day.

So we can use the formula:

Number of days = Total amount of granola / Amount eaten each day

Number of days = 10 lbs / 0.5 lb per day

Number of days = 20 days

Therefore, Mr. Davis' granola snacks will last for 20 days.

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Answer:

Step-by-step explanation:  15 feet of the ladder will be under the water because at first the ladder was 10 feet long then it  rises from under water

Answer:

410 is the outlier.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.

Step-by-step explanation:

Hope it helps! =D

The cone’s radius r in terms of x is x + 7

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

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Evaluate

r = x + 7

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As per multiplication, the value of 64 times π is 200.96

Multiplication is a fundamental arithmetic operation that involves repeated addition. In this case, we are tasked with finding the result of multiplying 64 and pi. Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is commonly denoted by the Greek letter "π".

To find the product of 64 and pi, we simply need to multiply these two numbers. Multiplication is typically represented using the "×" symbol or the "dot" symbol ( · ). In this case, we can write:

64 × π

Since pi is a mathematical constant, we typically use an approximation of its value in calculations. The commonly used approximation is 3.14, which is accurate to two decimal places. Thus, we can substitute 3.14 for pi and obtain:

64 × 3.14

Using the distributive property of multiplication, we can break down 64 into smaller factors that are easier to multiply with 3.14. For example, we can write:

64 = 60 + 4

Then, we can use the associative property of multiplication to group the factors in a way that makes the calculation easier. For instance, we can write:

64 × 3.14 = (60 × 3.14) + (4 × 3.14)

Now, we can use our knowledge of multiplication tables to calculate the products on the right-hand side. We get:

60 × 3.14 = 188.4

4 × 3.14 = 12.56

Therefore, the final result is:

64 × π = 188.4 + 12.56 = 200.96

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