t - 6 1/3 = - 9 3/4
solve this !

A. The equation d = s * t shows relationship between the quantities.

B. They would cover a distance of 10 miles in 20 minutes.

C. Rounded to the nearest tenth, the biker would bike for 96.0 minutes.

What is distance?

Distance is the measure of the physical space between two objects or points. It is a scalar quantity that is usually measured in units such as meters, kilometers, miles, etc. In physics, distance is considered to be a fundamental concept and is often used in conjunction with time to calculate other physical quantities, such as speed and acceleration.

a. We can define the following variables:

t: time in minutes

d: distance traveled by the biker in miles

s: speed of the biker in miles per minute

Using these variables, we can write the equation d = s * t to represent the relationship between them.

b. If the biker rides for 20 minutes, we can use the equation d = s * t to find the distance traveled. Assuming the biker's speed is 0.5 miles per minute, we get:

d = 0.5 * 20 = 10 miles

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can use the equation t = d / s to find the time taken, where s is again assumed to be 0.5 miles per minute:

t = 48 / 0.5 = 96 minutes

Rounded to the nearest tenth, the biker would have ridden for 96.0 minutes to cover 48 miles.

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The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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The amount of sales tax would be 1.75%

Answer:

A coordinate grid with 2 lines. The first line passes through (negative 4, negative 3), (0, negative 3), and (4, negative 3). The second line passes through (0, negative 5) and (2, 4). The lines appear to intersect at about one-half, negative 3.

Solve the system of equations algebraically. Verify your answer using the graph.

y = 4x – 5

y = –3

What is the solution to the system of equations?

((StartFraction one-fourth EndFraction, negative 3), –3)

((StartFraction one-half EndFraction, negative 3), –3)

(–3, (negative 3, StartFraction 2 over 3 EndFraction))

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

i just did it

Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

a. The probability of less than 3 tonnes/yr being discharged is 0.031.

b. The probability of discharge between 1 and 3 tonnes/yr is 0.094.

In part (a), we calculate the probability that the discharge from a facility is less than 3 tonnes/yr by integrating the probability density function from 0 to 3. This represents the area under the probability density curve for the given range. The result is the probability that the discharge is within that range.

In part (b), we calculate the probability that the discharge is between 1 and 3 tonnes/yr by integrating the probability density function from 1 to 3. Again, this represents the area under the probability density curve for the specified range. The result gives us the probability of the discharge falling within that range.

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The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

2/18 or 1/9

Step-by-step explanation:

just directly multiply it 2×1=2

6×3=18 so 2/18 simplify 1/9

Answer:

x = 6

Step-by-step explanation:

Equation

(1 + 5 + 10 + x)/4 = 5.5                    Multiply both sides by 4

Solution

4* (1 + 5 + 10 + x ) /4 = 5.5 * 4

16 + x = 22                                     Subtract 16 from both sides

16-16+x = 22- 16

x = 6

Answer:

Yes

Step-by-step explanation:

A triangle is a "right" triangle if its lengths fullfil the Pythagorean theorem:

\(a^2+b^2=c^2\)

Here, a and b are the shorter "legs" of the triangle, adjacent to its right angle, while c is the "hypotenuse," the longest side and the one opposite the right angle.

If we call the 1.9 cm and 2.7 cm our legs, the sum of their squares is:

\(2.7^2+1.9^2=10.9\) cm

While squaring our hypotenuse gives us

\(3.3^2=10.89\) cm

The fact that we measured the triangle's side lengths to 1 decimal point of accuracy means that there's a little margin of error baked into the measurement. The two previous calculations are within 0.01 cm of each other, which is more than close enough, so we can say that yes, this could be a right triangle.

This can help ensure that the responses are accurate and reliable.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is the measure of the likelihood that an event will occur or not occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

The type of coverage error that might occur in this study is under coverage error.

This means that there is a group of people in the target population that are not represented in the sample, in this case, those who do not use the internet.

Two ways to avoid bias in this study are:

Using probability sampling methods:

Probability sampling methods such as simple random sampling, stratified sampling, or cluster sampling can help ensure that each member of the target population has an equal chance of being included in the sample. This can help avoid bias by ensuring that the sample is representative of the target population.

Using proper survey design:

The survey should be designed in a way that avoids leading questions, loaded questions, or questions that are ambiguous or unclear.

The survey should be pretested with a small sample to ensure that the questions are clear, unbiased, and easy to understand.

Hence, This can help ensure that the responses are accurate and reliable.

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Answer:

https://brainly.com/question/14526835?referrer=searchResults#

some one already answered the question you have  

Step-by-step explanation:

The ratio test can be used to determine whether the series ∑(n=1 to ∞) (2^n)! converges or diverges.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. On the other hand, if the limit is greater than 1 or does not exist, the series diverges.

To apply the ratio test to the series ∑(n=1 to ∞) (2^n)!, we need to find the ratio of successive terms. Let's consider the n-th term and the (n+1)-th term: a_n = (2^n)!, and a_(n+1) = (2^(n+1))!.

The ratio of successive terms is given by a_(n+1)/a_n = (2^(n+1))!/(2^n)!.

Simplifying the expression, we have (2^(n+1))!/(2^n)! = (2^(n+1))(2^n)(2^n-1)...(2)(1)/(2^n)(2^n-1)...(2)(1).

Most of the terms in the numerator and denominator cancel out, leaving (2^(n+1))/(2^n) = 2.

Taking the absolute value of this ratio, we have |2| = 2.

Since the absolute value of the ratio is a constant (2), which is greater than 1, the limit of the ratio as n approaches infinity does not exist. Therefore, by the ratio test, the series ∑(n=1 to ∞) (2^n)! diverges.

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Answer:

\( {16a}^{2} - 4 {a}^{2} - 4a - 1 \\ = 12 {a}^{2} - 4a - 1 \\ = (2a - 1)(6a + 1)\)

Answerp explanation:\(12\alpha x^{2} -4\alpha -1\)

Answer:

Step-by-step explanation:

Answer:

If each side of tangle is increased by 25 %, then find the percentage increase or decrease in area

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Let the number be x.

x^2 - 21 = 4x

x^2 - 4x - 21 = 0

(x - 7)(x + 3) = 0

x - 7 = 0 or x + 3 = 0

x = 7 or x = -3

Answer: -3

Answer:

-3

Step-by-step explanation:

I got it right

Yes, the line 1 and line 2 are parallel lines as the sum of both given angles is 180°.

Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same face of the transversal.

The majority of the time, it comes from the latin word "com-," which often means "along with." Co-interior angles are located on the same face of a transversal as well as between two lines. The significant correlations angles in each diagram are referred to as co-interior angles. Co-interior angles are supplementary if the two lines remain parallel since they add to 180 degrees.

In the given diagram:

= 75 + 105 (co-interior angles)

= 180° (supplementary angles)

So,

line 1 || line 2

Thus, the line 1 and line 2 are parallel lines as the sum of both given angles is 180°.

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The speed of the curve at t=4 is approximately 40.63.

We have a given curve as follows:

¯ r ( t ) = ⟨ 5 t 2 − 6 , 7 t − 6 , t 3 8 t ⟩ at t = 4

To find the speed of the curve at t=4, we need to evaluate the magnitude of its velocity vector at t=4.

Velocity vector is the derivative of the curve with respect to time.

Hence, we start by finding the derivative of the curve. The derivative of the curve can be obtained as follows:¯ r'(t) = ⟨10t, 7, (3/8)t² - (3/8)⟩We can now evaluate the velocity vector at t=4:

¯ r'(4) = ⟨10*4, 7, (3/8)(4²) - (3/8)⟩= ⟨40, 7, 1.5⟩

To find the speed of the curve at t=4, we need to evaluate the magnitude of the velocity vector at t=4. The magnitude of a vector can be obtained using the formula:

|v| = √(v₁² + v₂² + v₃² +...)

Therefore, the speed of the curve ¯ r ( t ) = ⟨ 5 t 2 − 6 , 7 t − 6 , t 3 8 t ⟩ at t = 4 is:

|¯ r'(4)| = √(40² + 7² + 1.5²)= √(1600 + 49 + 2.25)= √1651.25≈ 40.63

The speed of the curve at t=4 is approximately 40.63.

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According to the given statement

The area of Colorado is 67.43 times greater than the area of Rhode Island

Area is typically thought of as a specific instance of volume for two-dimensional regions. By applying axioms, one can define area as the relationship between a set of real numbers and a collection of particular plane figures.

Area is a mathematical concept that describes the size of a region on a planar or curved surface. The area of an open surface or the border of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

According to the given values;

The area of Rhode Island = 43.07 billion square feet.

The area of Colorado = 2.9045 trillion square feet.

43.07 billion =43,070,000,000

2.945 trillion =2,9045,000,000,00

Now we have to find how many times as great is the area of Colorado than the area of Rhode Island.

For this ,we divide area of Colorado by area of Rhode Island.

=2,9045,000,000,00/43,070,000,000

=67.43

So, the area of Colorado is 67.43 times greater than the area of Rhode Island.

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Given

Procedure

Now for y

The answer would be x = 2.75 and y = 1.25

Answer:

anything :P

Step-by-step explanation:

The dimensions of the poster to be taken so that the least amount of poster is used are 17 by 34.

What is area of rectangle?

Area of rectangle = length x breadth

The dimensions of any rectangular figure can be found using this formula.

According to the given question:

Let x and y be the dimensions of the poster

The area of the poster, A= x*y

Margin at both up and bottom is 2 inches, at the right and left is 1 inch

(x-4)(y-2)= 450

Let us make y subject of the formula

(y-2) = 450/(x-4)

y = [450/(x-4)] + 2

If we substitute into the area A equation we have

A= x { [ 450/(x-4)] + 2}

A= 2x + (450x)/(x - 4)

If we differentiate we have

A'(x)= [2 + 450(x-4) + 450x ]/ (x-4)²

=[ 2(x-4)² + 450(x -4) + 450x ] / (x-4)²

=[ 2(x² - 8x +16) + 450(x-4) + 450x ] /(x-4)²

If we simplify this we have

=[ 2x² -16x +32 + 450x - 450x - 1800]/ (x-4)²

=( 2x² -16x - 1800) / (x-4)²

At A'(x)= 0

= ( x² - 8x - 1800) / (x-4)² =0

If we divide through by 2 we have

x² - 8x - 900= 0

X= 34 or -26 then we choose the positive one, then x= 34

Then from area of the poster

A= (x-4)(y-2)= 450

Substitute 34 as value of x

(34-4)(y-2)= 450

30(y-2)= 450

30y - 60 = 450

30y = 510

y = 17

Hence dimensions of the poster is 17 by 34.

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Answer:

Step-by-step explanation:

75

Answer:

no they are different numbers, however their signs are inverted

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

-2x+3 is not the same as 2x-3 because, let's say we set each equation equal to something...

-2x+3 = 10                   2x-3 = 10

     -3     -3                      +3    +3

------------------              -----------------

-2x = 7                        2x = 13

x = \(\frac{7}{2}\)                               x = \(\frac{13}{2}\)

x = 3.5                           x = 6.5

As we can see, these equations are not the same, because, when we set them equal to the same value, the answers are different.

Hope this helps! :D

Answer:

$0.42 per apple

Step-by-step explanation:

There are \(7\frac{1}2}\) grams on the scale in all once she added 2 5/6 grams to the scale.

The International System of Units (SI) is the modern form of the metric system and is the most widely used measurement system in the world. It consists of seven basic units of seven basic quantities.

Length is the meter, mass is the kilogram, time is the second, electric current is the ampere, temperature is the kelvin, amount of matter is the mole, and luminosity is the cand. SI also includes derived units such as Newton (force) and Pascal (pressure), which are combinations of base units. SI is the standard measurement system in most countries around the world and is used in scientific, engineering, and commercial applications.

Given,

initial weight = \(4\frac{2}{3} = \frac{14}{3}\)

Final weight = \(2\frac{5}{6} = \frac{17}{6}\)

Final weight = \(\frac{14}{3} + \frac{17}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}\)

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To calculate the slope between 2 points we use the following equation:

Replacing the points:

In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.

For the perpendicular case, the slope is equal to:

For the perpendicular case, the slope is zero and would equal one parallel to the X axis.

Answer:

Step-by-step explanation:

The question is asking us to find the slope.

First, we will find the slope of the line that passes through (4,8) and (4,6).

We'll use the slope formula:

\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data :

\(\bf{m=\dfrac{6-8}{4-4}}\)

\(\bf{m=\dfrac{-2}{0}}\)

\(\bf{m=not\:de fined}\)

If a line's slope is not defined, then it's a vertical line:

                                       \(\rule{1}{350}\)

------

Now, what is the slope of a line that's parallel to the one above? Well, since parallel lines have equal slopes, that one will have an undefined slope too.

As for perpendicular lines, they have slopes that are negative reciprocals of each other. We got that the slope is -2/0. The negative reciprocal of that is 0/2, which simplifies to 0.

Alternatively, you could look at it this way: a horizontal line (a line with zero slope) is perpendicular to a vertical line. So the slope of that line is m = 0.

\(\rule{350}{1}\)

Total number of outcomes for randomly choosing a vehicle = 25

What is outcome of an event?

Suppose an event is happening. The results which are possible in that event is known as outcome of that event.

Number of sportscar a car dealership has = 12

Number of sports utility vehicle a car dealership has = 6

Number of luxury car a car dealership has = 7

Total number of outcomes for randomly choosing a vehicle

                                                                                  = 12 + 6 + 7 =              

                                                                                  =  25

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3