A wheelchair ramp for a business cannot be steeper than 5∘. A similar ramp for a home can be 10∘.
What is the difference in degrees of these two ramps? Explain.

Answer:

'x' only has one solution

Step-by-step explanation:

First multiply both sides by 'x^2'

40x = -5x^2

(bring both values to one side and factorize to solve for 'x')

5x^2 +40x=0

5x(x+8)=0

5x= 0 ; x+8 = 0

x=0 ; x=-8

x cannot equal to '0' as zero cannot be a denominator.

Hence, x=-8 is the only correct solution.

So, 'x' only has one solution.

A Histogram would be the best for the data representation of the girls by dietitian.

Histogram, it is an approximate representation of the distribution of numerical data. The most popular graph for showing frequency distributions is a histogram. Though it also closely resembles a bar chart, there are significant differences. One of the seven basic quality tools is this useful gathering and analyzing information tool.

Variable = the height of 13-year-olds in the state of Texas.

Where the height of each bar represents the frequency of observations.

[tex]\sf (2-2.5) \ feet[/tex]

[tex]\sf (2.6-3) \ feet[/tex]

[tex]\sf (3.1-3.5) \ feet[/tex]

[tex]\sf (4.1-4.5) \ feet[/tex]

So, The best graphical representation of the dietitian's data would be a histogram.

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Shelly ordered the 16 candy bags.

The operation or process of finding the difference between two numbers or quantities, denoted by a minus sign (−).

We have the information from the question:

Shelly paid a total of $15 for bags of candy she ordered on-line.

The cost of each bag was $0.75

Shipping charge was a flat rate $3.00

We have to find the how many bags of candy did shelly order.

Now, According to the question:

We have to subtract shipping charge from total paid charges, we get:

Total paid - shipping charge

=> 15 - 3

= 12

Number of bags = 12/ 0.75

Number of bags = 16

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The answer is −63,868. To get this just put it into a calculator.

Answer:

P(less than 2) = P(1) = 1/6

A is correct.

Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.

The equation used to calculate the force the glove exerts on the ball during the collision is the impulse-momentum equation. This equation states that the force applied to an object is equal to the change in momentum of the object over time. Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.

To calculate the force the glove exerts on the ball during the collision, you can use Newton's second law of motion, which states:

Force (F) = Mass (m) × Acceleration (a)

In this scenario, the mass (m) refers to the mass of the baseball, and the acceleration (a) is the change in the baseball's velocity divided by the time it takes for the collision to occur. Keep in mind that the acceleration will have a negative value, as the ball is decelerating during the collision.

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The Laplace transform of f(t) = 12 cos t - 6 is ℒ{f(t)} = 12s / (s^2 + 1) - 6/s.

To find the Laplace transform ℒ{f(t)} of the function f(t) = 12 cos t - 6, we can apply the Laplace transform property involving the cosine function and a trigonometric identity. The property states:

ℒ{cos(at)} = s / (s^2 + a^2)

Using this property, we can split the Laplace transform into two parts:

ℒ{f(t)} = ℒ{12 cos t} - ℒ{6}

Applying the Laplace transform property to each term:

ℒ{12 cos t} = 12 * ℒ{cos t} = 12 * (s / (s^2 + 1^2)) = 12s / (s^2 + 1)

ℒ{6} = 6 * ℒ{1} = 6 * (1 / s) = 6/s

Combining the two terms, we have:

ℒ{f(t)} = 12s / (s^2 + 1) - 6/s

Therefore, the Laplace transform of f(t) = 12 cos t - 6 is ℒ{f(t)} = 12s / (s^2 + 1) - 6/s.

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Thus, the velocity of money in would be 3.5 .

The velocity of money is a measure of the rate at which money changes hands in an economy. It is calculated by dividing the nominal GDP by the money supply.

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Answer:

280 degrees.

Step-by-step explanation:

The way you work this out is by:

1) Work out 240-360

2) Subtract the answer from 360

3) Divide the answer of step 2 into however many angles you have (in this instance 4).

4) Then use one of these angles and subtract it from 360. This will give you a reflex angle.

5) That's it.

Answer:

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

We know that the sum of interior angles of a quadrilateral is 360°.

Show this as a sum using angle measures in the diagram:

You can check that the sum of these integers is indeed five times the second integer, which is -3.

Let x be the second integer in the sequence. Then the six consecutive integers are x-2, x-1, x, x+1, x+2, and x+3. The sum of these integers is:
(x-2) + (x-1) + x + (x+1) + (x+2) + (x+3) = 6x + 3
We know that this sum is equal to five times the second integer, which is x. Therefore, we can write the equation:
6x + 3 = 5x
Simplifying this equation, we get:
x = -3
So the second integer in the sequence is -3, and the six consecutive integers are:
-5, -4, -3, -2, -1, 0
You can check that the sum of these integers is indeed five times the second integer, which is -3.

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The area of the triangular parcel of land is approximately 305,682.4 square feet.

We can use Heron's formula to find the area of a triangular parcel of land. This formula states that the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c)/2
Using the lengths of the sides given in the problem, we can calculate the semi-perimeter:
s = (860 + 820 + 1038)/2 = 1759
Then we can plug this value into Heron's formula to find the area:
Area = √(1759(1759-860)(1759-820)(1759-1038))
Area = √(1759×899×939×721)
Area = √(93587715844)
Area = 305682.4 square feet (rounded to the nearest tenth)
Therefore, the area of the triangular parcel of land is approximately 305,682.4 square feet.

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The angle that the ramp makes with the ground is approximately 19 degrees.

the   angle    that the ramp makes with the ground can be found using trigonometry. the tangent of the angle is equal to the height of the ramp divided by the horizontal distance it covers:

tan(θ) = height / distance

where θ is the angle, height is 3.5 ft, and distance is 10 ft.

tan(θ) = 3.5 / 10θ = arctan(3.5 / 10)

θ = 19.1 degrees (rounded to the nearest degree)

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The experimental probability is 29/100 and the number of workers that walk is 1102

The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space.

The formula for this is given as;

P(E) = Number of occurrence of an event / Total number of times experiment is carried out.

a. Experimental probability = 29/100

b. To predict the total number of workers that walk, we can go as;

(29/100) * 3800 = 1102

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The approximate demand when the price is decreased to $2.25 is 4,800 boxes.

We know that demand is inversely proportional to price, so we can set up the following equation:

x ∝ 1/p

If x denotes demand and p denotes price. We can introduce a proportionality constant k to this equation:

x = k/p

Using the information in the problem, we can calculate the value of k. The demand is 1,800 boxes when the price is $6:

1,800 = k/6

Solving for k, we get:

k = 6 x 1800

k = 10,800

Now we can use this value of k to find the demand when the price is $2.25:

x = 10,800/2.25

x ≈ 4,800

Therefore, the approximate demand when the price is $2.25 is 4,800 boxes.

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the volume of the sphere is 4186. 6 ft³

The formula for calculating the volume of a sphere shape is expressed with the equation;

V = 4/3 πr³

Such that the parameters of the formula are expressed thus;

Now, substitute the values as shown in the diagram, we have that;

Volume = 4/3 × 3.14 × 10³

Find the cube value

Volume = 4/3 × 3.14 × 1000

Multiply the value

Volume = 12560/3

Divide the values

Volume = 4186. 6 ft³

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The input value (x) at which the two functions have equal values is x = 5.

From the given information, we have f(x) = 3 and g(x) = x - 2.

We want to find the input value (x) for which f(x) = g(x) is true.

Setting the two functions equal, we have:

3 = x - 2

To find the value of x, we can solve this equation:

x - 2 = 3

Adding 2 to both sides:

x = 5

Therefore, the input value (x) at which the two functions have equal values is x = 5.

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Answer:

G(9, -5)

Step-by-step explanation:

Point G is not shown in the figure, but I assume point G is on the bottom side of the square, directly below point F.

We are told each side of the square is 8 units long.

Starting at point E, to get to point G, go 8 units right and 8 units down.

Start at E(1, 3).

Then go 8 units right to point F(9, 3).

Now go 8 units down to point G(9, -5).

Therefore, the distribution of B(s) + B(t) is a normal distribution with mean 0 and variance 2(t - s).

The distribution of the sum of two independent Brownian motions, B(s) and B(t), where s ≤ t, is itself a normal distribution.

If we consider B(s) and B(t) as two random variables, each following a normal distribution with mean 0 and variance t - s, then their sum B(s) + B(t) will also follow a normal distribution. The mean of the sum will be 0 + 0 = 0, and the variance of the sum will be (t - s) + (t - s) = 2(t - s).

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Answer:

[tex]5 + 2\sqrt{3}[/tex]

    &          

[tex]5-2\sqrt{3}[/tex]

Step-by-step explanation:

Okay! The equation is : 2x²+26=20x

Right off the bat we notice that this can be simplified. We divide all numbers by a common multiple: 2.

Our resulting equation is [tex]x^2 + 13= 10x[/tex]

Now, in order to plug this equation into our quadratic formula, we need to rearrange this equation into the [tex]ax^2 + bx +c = 0[/tex] format.

In order to do that, we simply move the 10x to the left side of the equation, resulting in this: [tex]x^2 - 10x + 13[/tex]

Here is the quadratic formula:

(-b±√(b²-4ac))/ 2a

I will include a picture of the quadratic equation at the bottom (because the typed equation is strange).

So looking at our previously found formula, x^2 - 10x + 13, we know that a: 1

b: -10

c: 13

Now, we plug in our values!

(-(-10) ± √((-10)²-(4(1)(13))) / 2(1)

Simplify! (10 ± √(100-52)) / 2

Simplify again! (10 ± √48) / 2

Now we must simplify the square root. If we try to find the square root of 48, it comes out to 6.92820323, which is a very messy number. We will NOT be using this number. We will instead find the factors of 48.

2·2·2·2·3 = 48

So it looks like this: √2·2·2·2·3

We can pair up the similar numbers, so it looks like: √(2·2)(2·2)·3

Now, we move the pairs of twos to the front of the equation (but only one two from each pair is represented because they've been square-rooted) , and out of the square root, to get us: 2·2 √3, which equals 4√3

Now that we have the square root figured out, we re-enter the square root into the equation we had before (replacing the un-simplified version with the simplified version), which was (10 ± √48) / 2.

Here is the equation with the simplified root:  (10 ± 4√3) / 2

Now we notice that 10 and 4 are divisible by 2, so the equation becomes: (5 ± 2√3), which is 5+2√3, AND 5-2√3

Hope that helped!!!!

Probability that a student chosen at random from class is not a psychology major = 0.82

Probability is a branch of mathematics which tells about the occurrence of any event.

The sum of the probability of an event to occur and the probability of the same event not to occur is always equal to 1.

Mathematically, we can represent it as mentioned below:

P(E) + P(E') = 1

where P(E) = Probability of an event to occur.

And P(E') = Probability of an event not to occur.

According to the question,

The probability that a student chosen at random from class is a psychology major = P(E) = 0.18

As we know,

P(E) + P(E') = 1

Hence, Probability that a student chosen at random from class is not a psychology major = P(E') = 1 - P(E) = 1 - 0.18 = 0.82

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The given question is incomplete, complete question is:

The probability that a student chosen at random from your class is a psychology major is 0.18.

What is the probability that a student chosen at random from your class is not a psychology major?

The advantages of an open question include:

An open question is designed to elicit a broad and unrestricted response from the respondent. It encourages them to think creatively and explore various possibilities, which can lead to the introduction of new solutions. Unlike closed-ended questions that limit respondents to predefined options, an open question provides the freedom to express ideas, perspectives, and insights that may not have been considered before.

Furthermore, an open question allows the respondent to go in-depth with their answer. It prompts them to provide detailed explanations, examples, and personal experiences, allowing for a richer and more nuanced understanding of their thoughts and perspectives. This depth of response can unveil valuable insights, uncover underlying motivations, and provide context that may not have been captured with closed-ended questions. It also encourages active engagement and reflection from the respondent, as they are encouraged to express their thoughts and feelings in a more comprehensive manner.

Overall, open questions promote creativity, critical thinking, and a deeper exploration of ideas, making them advantageous in various contexts such as research, interviews, surveys, and problem-solving discussions.

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A good point estimate for the population proportion is 0.01714. Option D is correct.

A good point estimate to use for the population proportion to test the effectiveness of the flu vaccine can be calculated by dividing the number of people who got the flu (12) by the total number of participants in the study (700).

Point Estimate = Number of people who got the flu / Total number of participants

Point Estimate = 12 / 700

Using a calculator, the approximate value of the point estimate is 0.01714 (rounded to five decimal places).

Therefore, the good point estimate to use for the population proportion to test the effectiveness of the flu vaccine is 0.01714. Option D is correct.

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The table shows neither an arithmetic sequence nor a geometric sequence because it doesn't have a common difference and common ratio.

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 308,936,000 - 282,125,000 = 363,584,000 - 335,805,000

Common difference, d = 26,811,000 ≠ 27,779,000

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 308,936,000/282,125,000 ≠ 335,805,000/363,584,000

Common ratio, r = 1.095 ≠ 0.924

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3,9,10 >>> not a right triangle. because 3^2 + 9^2 is not equal to 10^2

27, 36, 45 >>> yes, a right triangle bc 27^2 + 36^2 = 45^2

11,13,17 >>>

11^2 + 13^2 = 290

The sqrt of 290 = 17.0293863659.

If you are in the lower grades, probably your teacher expects you to round this to 17. I honestly don't know how to answer bc I don't know what your teacher's expectations are for rounding.

I am a precise person, but I could see a teacher accepting YES RIGHT TRIANGLE bc it's basically 17.

4, 8, 9 >>> NOT a right triangle.

4^2 + 8^2 = 80

The sqrt of 80 = 8.94427191

I would say NO because this does not equal 9!

Answer:

Step-by-step explanation:

ajns

The value of angle x is 107°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

There is a theorem in circle geometry that states that : The angle subtended at the centre of a circle is twice the angle at the circumference.

This means if the angle at the circumference is 50, the angle at the center is 100.

The angle at the center = 360 - 146( angle at a point)

= 214°

2x = 214

x = 214/2

x = 107°

therefore the value of x is 107°

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The limit of the ratio is infinity, the series diverges for all values of x except x = 0 and the radius of convergence is r = 0.

To find the radius of convergence of the series, we can use the ratio test.

The ratio of the (n+1)th and the nth term of the series is:

|(x(n+1)) / (x(n))| = ((n+1)^3) / (5(n+1))

We take the limit of this ratio as n approaches infinity:

lim |(x(n+1)) / (x(n))| = lim (((n+1)^3) / (5(n+1))) = lim ((n^3 + 3n^2 + 3n + 1) / (5n)) = ∞

Since the limit of the ratio is infinity, the series diverges for all values of x except x = 0. Hence, the radius of convergence is r = 0.

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Answer:

-18

Step-by-step explanation: