A force of 80 pounds on a rope is used to pull a box up a ramp inclined at 10 degrees from the horizontal. The rope forms an angle of 33 degrees with the horizontal. How much work is done pulling the box 26 feet along the ramp?

Answer:

Required equation of line in point-slope form is:

\(y-5 = -\frac{3}{5}(x+5)\)

Step-by-step explanation:

Given equation of line is:

\(y = \frac{5}{3}x+2\)

The slope-intercept form of line is:

\(y = mx+b\)

Comparing both we get

m = 5/3

We have to find the equation of a line that is perpendicular to given line and passes though (-5,5)

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line then

\(m.m_1 = -1\\\frac{5}{3} . m_1 = -1\\m_1 =-\frac{3}{5}\)

Point-slope form is given by:

\(y-y_1 =m_1(x-x_1)\\\)

Putting m = -3/5 and (x1,y1) = (-5,5)

\(y-5 =-\frac{3}{5}(x-(-5))\\y-5 = -\frac{3}{5}(x+5)\)

Hence,

Required equation of line in point-slope form is:

\(y-5 = -\frac{3}{5}(x+5)\)

Answer:

30

Step-by-step explanation:

60% of what number = 18  is equivalent to:

60% × ? = 18  

18 ÷ 60%  

18 ÷ (60 ÷ 100)  

(100 × 18) ÷ 60  

1,800 ÷ 60  

30

Answer:

x = 10

Step-by-step explanation:

5x - 18 = 3x +2 ( subtract 3x from both sides )

2x - 18 = 2 ( add 18 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

Answer:

FtD

Step-by-step explanation:

Electric potential is given by option is (ii) Vout(z) = 4πε₀ zq and Vin(r) = 4πε₀Rq.

The electric potential is the amount of electrical potential energy that a single charged particle has due to its location in an electric field. The change in electric potential energy in an electric field is given by the formula W = q ΔV, where W is the work done on the particle, q is the charge, and ΔV is the potential difference. Electric Potential Inside and Outside a Spherical Shell. According to Gauss' law, the electric field inside a conductor is zero. As a result, the electric potential is the same throughout the conductor. Consider a uniformly charged spherical shell with a total charge Q and radius R. Since the electric field inside the spherical shell is zero, the electric potential inside the spherical shell is the same throughout as outside. Inside the shell, we have Vin(r) = 4πε₀Rq and outside the shell, we have

Vout(z) = 4πε₀zq.

The electric potential inside and outside a uniformly charged spherical shell of radius R is therefore given by (ii) Vout(z) = 4πε₀ zq and Vin(r) = 4πε₀Rq.

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Answer:

A

Step-by-step explanation:

75% of the air pressure at sea level is simply

0.75 × Po

this is what we need to set as the expected result of the function, and it becomes the left side of the equation.

we don't change anything on the right side for this, as the full, unchanged function has to be used to find the h for the desired result.

Answer:

no solutions exist

Step-by-step explanation:

You can rewrite the denominator as:

-2(2x-6) so the equation becomes:

\(-\frac12 \cdot \frac{2x-6}{2x-6} > 0\)

from which you can see that not only should x ≠ 3, but for all values of x≠3 the equation is false.

Answer:

a) $340

b) $20

Step-by-step explanation:

a) in the summer (July and August) he earned 160 + 180 = $340

b) in July he earned 160 ÷ 8 = $ 20

Javonie earned $340 over the summer and he charged $20 per dog in July.

The amount of money he earned over the summer is the sum of the money he earned in July and the sum of the money he earned in August

Total amount earned in the summer = amount earned in July + amount earned in August

$160 + $180 = $340

The amount he charged per dog in July can be determined by dividing the total amount earned in July by the total number of dogs he walked.

Amount charged per dog = amount earned in July / total dogs worked

$160 / 8 = $20

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the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Step-by-step explanation:

\({ \frac{10}{100} \times 3150 = 315\)

Answer: 36 square units

Step-by-step explanation:

Divide the figure into 2 shapes: a rectangle and a triangle. Count the squares to find the dimensions of each figure. The rectangle has a width of 4 units and a length of 6 units. The triangle has a base of 6 units and a height of 4 units.

The formula for the area of a rectangle is length * width. The area of the rectangle is 4*6 = 24 square units.

The formula for the area of a triangle is (base * height)/2. The area of the triangle is (4*6)/2 = 24/2 = 12 square units.

Add the areas of both the rectangle and triangle. 24+12 = 36 square units.

Mario has 3,628,800 different ways to arrange the 10 science fiction novels on his shelf.

When we want to arrange a set of n distinct objects in a row, the number of possible arrangements is given by n factorial, or n!, which is the product of all positive integers from 1 to n. In other words, n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1.

In this case, Mario has 10 science fiction novels that he wants to arrange on a shelf, and each of these novels is distinct. Therefore, there are 10 possible choices for the first book he places on the shelf. Once he has placed the first book, there are only 9 remaining books to choose from for the second position. For the third position, there are 8 remaining books to choose from, and so on. Therefore, the total number of possible arrangements of the 10 books is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.

Therefore, Mario has 3,628,800 different ways to arrange the 10 science fiction novels on his shelf.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Answer:

0

Step-by-step explanation:

the equation on finding slope is y2 - y1/x2 - x1

so it is...

6 - 6 = 0

6 - -5 = 11

0/11 but that doesnt work so I believe the slope is zero because the denominator is not the one being a 0

hope I helped ;)

Answer: its a zero slope

Step-by-step explanation: i just put them on a graph - uh i think there is another way to do it but i forgot

The pearson correlation coefficient is equal to 4.6/1.25, or 3.68. This is approximately equal The closest answer is e. 0.98.

Coefficient is a numerical or statistical value used to measure the strength or magnitude of a relationship between two or more variables. It is commonly used in mathematics, physics, engineering, and economics to quantify the strength of a linear relationship between two variables. In mathematics, coefficients are used to measure the degree of influence of a certain variable on the relationship between two variables.

The correlation between x and y can be found by calculating the Pearson correlation coefficient. This can be done by first calculating the covariance of x and y, which is equal to 4.6, and then dividing it by the standard deviation of x multiplied by the standard deviation of y, which is equal to 1.25.

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A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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Answer:

3x+2

Step-by-step explanation:

2x-2+X+4

= 2x+X+4-2

= 3x+2

There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.

The following are the steps to find the number of positive factors of a number:

Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:

24 = 2 × 2 × 2 × 3

Step 2: Same bases should be added in powers. So, the factors we can write as

24 = 2³ × 3¹

Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.

I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.

So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.

It is given that, m, p, and t are distinct positive prime numbers.

Then, the number of positive divisors greater than 1 for the number m³pt are

m³× p × t

Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,

N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16

So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.

Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.

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The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.


In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.

Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978

Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.

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Answer:

The second option is correct.

Step-by-step explanation:

\(Solution,\\Breadth(b)=5cm\\Length (l)=4cm+6cm=10cm\\Now ,\\Area=l*b=5cm*10cm=50cm^{2}\)

The equation to solve the height of the trapezoid is 45h = 1,575

Given data ,

Let the area of the trapezoid be A

Now , the value of A = 1,575 cm²

And , the Top(base2) = 63cm and  Bottom(base1) = 27 cm

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

On simplifying , we get

1,575 = (63 + 27) / 2 x h

1575 = 45h

Hence , the equation is 1575 = 45h

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The complete question is attached below :

The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?

A 850.5h = 1,575

B 1,701h = 1,575

C 90h = 1,575

D 45h = 1,575

Top(base2) = 63 cm

Bottom(base1) = 27 cm

Answer:

8 1/4(Decimal:-8:25)

Step-by-step explanation:

simplify:

-51/4 - 3

=8 1/4 (decimal:-8.25)

Answer:

The answer would be 8 1/4

Step-by-step explanation:

-5 1/4 + (-3)

let's start with the whole numbers:

-5 + (-3) = -8 because it's just like adding positives but add a negative sign

so then we just add the -1/4 and you get -8 1/4

*you have to put the second number in parentheses because its how you properly write the equation Ex: -2+8+(-3)+(-1 5/6)=...

* also note that when you add two negatives it becomes a positive!!!

In sampling distribution, it is not necessarily true that the expected value of j will be equal to the expected value of k, and the variability of j will be equal to the variability of k.

The properties of the sampling distribution of an estimator depend on the sample size, the population distribution, and the estimator itself. While it is possible that the expected value and variability of j and k may be equal under certain conditions, this cannot be assumed without further information.

More information about the specific estimator and the population distribution is needed to determine the properties of the sampling distributions for different sample sizes.

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The history graph for this wave at x=6 m, for t=0s to 6s is the snapshot graph of a wave at t=0s but opposite direction. The graph is attached below.

A history graph is a graph that displays the displacement of the wave as a function of time at a certain location in space. It provides a history of that specific period in the medium.

What is a wave?

A wave is a dynamic disturbance propagating and causing one or more quantities to depart from equilibrium. Quantities may oscillate regularly around an equilibrium (resting) value at certain frequency if a wave is periodic.

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From the triangle, the values of a and b are 5.1 units and 4.4 units respectively

You should know that a triangle is a polygon with three sides, three vertices, three angles  whose sum of angles is 180⁰

Using the trig ratio of Cosine

CosY=Adjacent/Hypothenuse

cos31=w/6

Cross multiplying we have

6*cos31=w

w=5.1 units

Then to find b, note that /VW/=/VY/=5.1

<VYX=<VWX............... base angles of isosceles triangle  WVY

Using cosine again from trig.

Cos31=b/5.1

5.1*cos31=b

simplify to get b=4.4 units

Therefore b= 4.4 units  

a=90-31       (remaining 2 angles of a right angled triangle)

a=59⁰

In conclusion, the value of a=59⁰ and the value of b=4.4 units

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Answer:

5x-2

Step-by-step explanation:

distribute the negative to get

7x+3-2x-1

simplify by combining like terms

5x-2

Answer:

76

Step-by-step explanation:

Answer:

9.09

Step-by-step explanation:

\(\frac{0.81}{0.09} + \frac{0.81}{9}\)

= 9 + \(\frac{0.81}{9}\)

= 9+ 0.09

= 9.09

I hope this helped!! If so please rate and mark brainliest <3!!

Answer: slope =1/2  y intercept (0,6)

Step-by-step explanation: use the slope and y intercept form y=mx + b

Answer:

17 miles

Step-by-step explanation: