If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work (in ft-lb) is needed to stretch it 3 in. Beyond its natural length?

Answer:

True

Step-by-step explanation:

Answer: (3/6) then (2/6)

Step-by-step explanation:

FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.

Answer:

x = -3 and y = 9

Step-by-step explanation:

          4y + 6x = 18 -----------------(I)

         3y - 2x = 33 -----------------(II)

Multiply equation (II) by 3.

(I)                 4y + 6x = 18

(II)*3            9y - 6x = 99  {Now add the equations}

                  13y        = 117

Divide both sides by 13,

                        y   = 117 ÷ 13

                          [tex]\boxed{\bf y = 9}[/tex]

Substitute y = 9 in equation (I) and obtain the value of 'x',

        4*9 + 6x = 18

           36 + 6x = 18

Subtract 36 from both sides,

                    6x = 18 - 36

                    6x = -18

Divide both sides by 6

                      x = -18 ÷ 6

                     [tex]\boxed{\bf x = -3}[/tex]

[tex] \\ 4y + 6x = 18 \\ \\ 6x= 18 - 4y \\ = x = 3 - \frac{2}{3 }y \\ x = - \frac{2}{3} y+ 3[/tex]

The perimeter of a rectangular outdoor patio is 106 ft. the length is 9 ft greater than the width.  Hence, the dimensions of the patio are 38 ft and 47 ft.

Given that the perimeter of a rectangular outdoor patio is 106 ft. The length is 9 ft greater than the width. Now we need to find the dimensions of the patio.

Step 1: Let's consider the width of the patio be x feet.

The length of the patio is given as 9 ft greater than the width.

So the length of the patio will be (x + 9) feet.

Step 2: The perimeter of a rectangle is given by P = 2(l + w).

So the perimeter of the patio is given as 106 ft.

Thus,2(l + w) = 1062(x + x + 9)

                    = 1062(2x + 9)

                    = 1062x + 1821

                     = 106x = 106 - 182x

                     = -76 (not possible)

Therefore, x = 38 ftSo the width of the patio is 38 ft The length of the patio is 38 + 9 = 47 ft

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The possible number of positive real zeros of the function is either 2 or 0.f(-x) = −2x5 − 3x2 − 2x − 1The number of sign changes in f(-x) is 1. The possible number of negative real zeros of the function is either 1 or 0.

To determine the possible numbers of positive and negative real zeros of the function f(x) = 2x5 − 3x2 + 2x − 1 using Descartes's Rule of Signs, we should start by writing the polynomial function in descending order of powers of x. After this, we count the number of sign changes in the polynomial function f(x) and find out the possible number of positive real zeros. Similarly, we count the number of sign changes in f(-x) and find out the possible number of negative real zeros .In the given function f(x) = 2x5 − 3x2 + 2x − 1, the polynomial is already in the descending order of powers of x. Therefore,

we count the sign changes in f(x) and f(-x) as follows: f(x) = 2x5 − 3x2 + 2x − 1The number of sign changes in f(x) is 2. Therefore, the possible number of positive real zeros of the function is either 2 or 0.f(-x) = −2x5 − 3x2 − 2x − 1The number of sign changes in f(-x) is 1. Therefore, the possible number of negative real zeros of the function is either 1 or 0. Hence, the possible number of positive real zeros of the function is either 2 or 0 and the possible number of negative real zeros of the function is either 1 or 0.

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Answer:

3

Step-by-step explanation:

You are subtracting 1 less each time, starting at 3:

9 - 3 = 6

6 - 2 = 4

Therefore, you will subtract 1 from 4:

4 - 1 = 3

3 is your answer.

~

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The probability that a random driver reports 0 injuries is 0.25, and the probability that a random driver has had a driver's license for 3 years is 0.25.

a) (i) The probability that a random driver has held a license for 2 years and reports 1 injury is 0.125.
(ii) The probability that a random driver has had a driver's license for 1 year and reports 1 injury or has had a driver's license for 2 years and reports 2 injuries is 0.3125.

b) The marginal probability distributions of ???? and ???? are given in the table below:

   ????
   ???? = 0
   ???? = 1
   ???? = 2
   ???? = 3
 
   ???? = 0
   0.25
   0.125
   0.0625
   0.03125
 
   ???? = 1
   0.25
   0.25
   0.125
   0.0625
 
 
   ???? = 2
   0.25
   0.25
   0.25
   0.125
 
   ???? = 3
   0.25
   0.25
   0.25
   0.25
 The probability that a random driver reports 0 injuries is 0.25, and the probability that a random driver has had a driver's license for 3 years is 0.25.

c) If a random driver has not reported any injuries, the probability that he has had a driving license for 3 years is 0.25.

d) ????(????) =  1, ????(????) = 1.5, ????????????(????) = 0.5, ????????????(????) = 0.9.

e) The covariance between ???? and ???? is 0.225, and the correlation coefficient is 0.45. This shows a positive correlation between the two variables, meaning that an increase in one variable is associated with an increase in the other.

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Answer:

Let's start by assigning a variable to the original side length of the square photograph. We'll use g to represent this length.

According to the problem, each side of the new photograph will be 1 inch more than twice the original side length g. This means that the new side length will be:

2g + 1

Since this is a square photograph, all four sides are equal in length. Therefore, the area of the new photograph can be represented by the square of the new side length:

(2g + 1)^2

To simplify this expression, we can use FOIL (First, Outer, Inner, Last) to expand the squared binomial:

(2g + 1)^2 = (2g + 1)(2g + 1)

= 4g^2 + 2g + 2g + 1

= 4g^2 + 4g + 1

So the trinomial that represents the area of the enlarged photograph is:

4g^2 + 4g + 1

To check our work, we can plug in a value for g and compare the areas of the original and enlarged photographs. For example, if g = 2 (meaning the original side length is 2 inches), then the area of the original photograph is:

2^2 = 4 square inches

And the area of the enlarged photograph is:

4(2)^2 + 4(2) + 1 = 25 square inches

This makes sense, since the new photograph has sides of length 2(2) + 1 = 5 inches, and therefore an area of 5^2 = 25 square inches, which is indeed 1 inch more than twice the original area of 4 square inches.

what are the answer choices?

Answer:

3/4

Step-by-step explanation:

The graph fοr the sοlutiοns οf the inequalities have been plοtted and attached belοw.

A relatiοnship in mathematics knοwn as an inequality cοmpares twο numbers οr οther mathematical expressiοns in an unfair manner.

Mοst frequently, size cοmparisοns are dοne between twο numbers οn the number line.

We are given twο inequalities as x - 3 ≤ 8 and 6x < 72.

Nοw, οn sοlving the first inequality, we get⇒ x - 3 ≤ 8⇒ x ≤ 11Similarly, οn sοlving the secοnd inequality, we get⇒ 6x < 72⇒ x < 12

Nοw, οn the graph the sοlutiοns are plοtted and attached belοw. The red pοint represents the secοnd inequality sοlutiοn and the blue represents the first inequality sοlutiοn.

Hence, the graph fοr the sοlutiοns οf the inequalities have been plοtted.

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Answer:

(anyone who answers gets brainliest) Pick the correct trig tool to solve for the variables. There’s a solve for x problem I was struggling with. You don’t have to do them all, thank you

Step-by-step explanation:

Answer:31.58% i think

Step-by-step explanation:

600 of 1900 can be written as:

600/1900

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

600/1900 x 100/100 = 600x100/1900) x1/100= 31.58/100

Therefore, the answer is 31.58%

Answer:

see below

Step-by-step explanation:

[tex]SA = 2\pi r \ \ (h+r)[/tex]

[tex]130=2(3.14)(7\div2)(h+(7\div2))[/tex]

[tex]130\div(2(3.14)(7\div2)) = h+(7\div2)[/tex]

[tex]5.91=h+(7\div2)[/tex]

[tex]h = 5.91-3.5[/tex]

Answer Below:

Answer:

The statement "The function is decreasing on the interval (0, ∞)" is true about h(x).

To see why, let's take the derivative of h(x) and examine its sign:

h(x) = -2√x

h'(x) = -2/(2√x) = -1/√x

Since √x is always positive, h'(x) is negative for all x > 0. This means that h(x) is decreasing on the interval (0, ∞).

Therefore, the correct answer is: The function is decreasing on the interval (0, ∞).

Answer:

y = (-1/3)x + 3.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.

The slope of the given line Y=3x-5 is 3. Therefore, the slope of a line perpendicular to this line would be -1/3.

Now, using the point-slope form of a line, we can write the equation of the line passing through (-9,6) and having a slope of -1/3:

y - 6 = (-1/3)(x - (-9))

Simplifying:

y - 6 = (-1/3)x - 3

y = (-1/3)x + 3

Therefore, the equation of the line that passes through (-9,6) and is perpendicular to the line Y=3x-5 is y = (-1/3)x + 3.

Answer:

[tex]\boxed{\mathtt{Area \approx 104.7m^{2}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the area of 1/3 of a circle.}[/tex]

[tex]\textsf{Let's review the formula needed to find the area of a \underline{whole} circle.}[/tex]

[tex]\large\underline{\textsf{Formula:}}[/tex]

[tex]\mathtt{Area = \pi (radius)^{2}.}[/tex]

[tex]\textsf{We should know that a circle is 360}^{\circ}. \ \textsf{We are given 120}^{\circ} \textsf{of a circle.}[/tex]

[tex]\textsf{The area of \underline{1/3} of a Circle is the area of a whole circle \underline{divided by 3.}}[/tex]

[tex]\textsf{Let's begin solving for the area.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{Area = \pi (10)^{2}}[/tex]

[tex]\large\underline{\textsf{Evaluate:}}[/tex]

[tex]\mathtt{Area = 100\pi }[/tex]

[tex]\large\underline{\textsf{Divide by 3:}}[/tex]

[tex]\mathtt{\frac{Area}{3} = \frac{100\pi }{3}} [/tex]

[tex]\boxed{\mathtt{Area \approx 104.7m^{2}}}[/tex]

Therefore , the solution of the given problem of probability comes out to be 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672,

Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .

Here,

=> P(X = k)  = (n choose k) * p * k * (1-p) (n-k)

where p is the chance of success and (1-p) is the probability of failure, (n choose k) is the binomial coefficient, and P(X = k) is the probability of k successes in n trials.

The likelihood that precisely 3 planes will depart on time is:

P(X = 3)

=> (6 choose 3) * 0.60 * 0.40 * 0.311

The likelihood that up to 4 planes depart on time is:

=> P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

         = > (6 choose 0) * 0.60^0 * 0.40^6 + (6 choose 1) * 0.60^1 * 0.40^5 + (6 choose 2) * 0.60^2 * 0.40^4 + (6 choose 3) * 0.60^3 * 0.40^3 + (6 choose 4) * 0.60^4 * 0.40^2

         ≈> 0.672

The likelihood that at least three planes will depart on time is:

P(X >= 3) = 1 - P(X < 3)

         = 1 - P(X = 0) - P(X = 1) - P(X = 2)

         = 1 - (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) * 0.60^1 * 0.40^5 - (6 choose 2) * 0.60^2 * 0.40^4

         ≈ 0.695

=> P(X>=3) = 1 - P(X3) = 1 - P(X0) - P(X = 1) - P(X = 2)

=>  1 - (6 choose 0) (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) (6 choose 1) * 0.60 * 0.40 * 6 (select 2) * 0.60 * 0.40 * 4

≈> 0.695

Therefore, the likelihood that precisely 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672, and the likelihood that at least 3 flights will depart on time is roughly 0.695.

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The inequality will be and [tex]3 + √-4[/tex] will be written as [tex]3 +2i[/tex] as complex number.

What are complex numbers?

In mathematics, a complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). Complex numbers are an extension of the real numbers, which include all the numbers that can be represented on a number line.

The real part of a complex number a + bi is the real number a, and the imaginary part is the real number bi.

A. Since Jan found that both roots of the quadratic equation are not real numbers, this means that the discriminant b² - 4ac is negative. Therefore, the inequality that must always be true for Jan's quadratic equation is:

[tex]b² - 4ac < 0[/tex]

B. The expression  [tex]3+√-4[/tex] can be written as [tex]3 + 2i,[/tex] where i is the imaginary unit (√-1). This is because √-4 is equal to 2i, so [tex]3+√-4[/tex] can be written as [tex]3 + 2i.[/tex] Therefore, [tex]3+√-4[/tex] written as a complex number is 3 + 2i.

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The required angle of the incline of the hill, to the nearest degree, is 37 degrees.

We can use trigonometry to find the angle of the incline of the hill.

we can see that Nick has hiked 10 miles up the hill, and is now at point A. His starting point is at point O, which is 8 miles east of A. Let's call the angle at A, between the incline of the hill and the horizontal ground, theta.

We can use the tangent function to find theta:

[tex]$$\tan(\theta) = \frac{h}{8}$$[/tex]

where h is the height of the hill (the distance from A to the horizontal ground at O).

We know that Nick hiked 10 miles up the hill, so we can use the Pythagorean theorem to find h:

[tex]$$h^2 = 10^2 - 8^2 = 36$$[/tex]

Therefore,

[tex]$$h = \sqrt{36} = 6$$[/tex]

Substituting into the equation for tangent, we get:

[tex]$\tan(\theta) = \frac{6}{8} = 0.75$$[/tex]

To find the angle whose tangent is 0.75, we can use the arctangent function:

[tex]$$\theta = \arctan(0.75)$$[/tex]

Using a calculator, we find that

[tex]$$\theta \approx 36.87^{\circ}$$[/tex]

Therefore, the angle of the incline of the hill, to the nearest degree, is 37 degrees.

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If the ratio of dogs to cats is 2:3 and there are 520 dogs, the number of cats is 780.

The ratio refers to the relative size of one quantity or value compared to another quantity or value.

Ratios are proportionate values stated in ratio form using (:), in percentages or fractions.

The ratio of dogs to cats = 2:3

The sum of ratios = 5

The number of dogs based on this ratio = 520 dogs

The total number of dogs and cats based on the above ratio and the number of dogs = 1,300 (520/2 x 5)

The ratio of cats to dogs = 3:2 or 3/5

The number of cats = 780 (1,300 x 3/5)

Thus, using the ratio of dogs to cat, with the number of dogs as 520, there are 780 cats.

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Answer:

21. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

In total, there are 8! (8 factorial) ways that the 8 finalists can stand on the stage. 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320. This means that there are 40,320 possible combinations in which the 8 finalists can stand on the stage.

To calculate this, we can use the formula n!, which stands for n factorial. n! is the product of all the numbers from n down to 1, so 8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This formula can be used to find the total number of combinations that 8 people can stand in on the stage.
It's important to remember that the order matters in this case, so a configuration where the finalists are standing in a line is different from a configuration where they are standing in a circle.
In conclusion, there are 40,320 ways in which the 8 finalists can stand on the stage. This can be determined by using the formula n!, which stands for n factorial.

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The submarine will take 14 seconds to safely reach the surface.

Speed is a measure of how quickly an object is moving, calculated as the distance traveled per unit time.

The submarine rises 183 feet, which means its depth decreases by 183 feet. Therefore, its depth is now 375 - 183 = 192 feet below sea level.

The submarine then dives 228 feet, which means its depth increases by 228 feet. Therefore, its depth is now 192 + 228 = 420 feet below sea level.

To reach the surface, the submarine needs to ascend a distance of 420 feet.

The speed of the submarine is given as 30 feet per second. Therefore, the time it will take for the submarine to reach the surface can be calculated as:

[tex]Time = \frac{Distance}{Speed} = \frac{420}{30}[/tex]

= 14 seconds

Therefore, it will take the submarine 14 seconds to safely reach the surface.

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Answer:

y=2(x+4)-3

Step-by-step explanation:

To make it parallel to y=2x+4, the slope needs to be the same

Point-slope form is: y=m(x-x1)+y1

In this case,

m = 2

x1 = -4

y1 = -3

So when put into point-slope form, it is y=2(x+4)-3

In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets. So far, 312440 copies have been sold.

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means.
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets.
We are given that the copies sold on first release date= 42800 copies.

And this is the 7.3 of the number of copies sold on date.

So, let the number of copies sold out on date is x.

Therefore, x= 7.3*42800 OR [tex]x= \frac{73}{10} * 42800= 73*4280= 312440[/tex]

Hence, the number of copies sold out on the date are 312440.

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The correct statement regarding the quadratic equation is given as follows:

C. There are two complex solutions.

A quadratic equation is modeled by the general equation presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given by the equation as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

The coefficients of the function for this problem are given as follows:

a = -2, b = 9, c = -12.

Hence the discriminant is given as follows:

Δ = 9² - 4(-2)(-12)

Δ = -15.

Negative discriminant, hence there are two complex solutions.

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The quadratic equation has two real solutions

Here we have the quadratic equation:

y = -2x^2 + 9x - 12

We want to study the solutions of the equations, so we need to look at the discriminant:

Generally for a*x^2 + b*x + c = 0 the discriminant is b^2 - 4ac

Here it is:

D = 9^2 - 4*-12*-2 = 33

A positive determinant means that there are 2 real solutions so the correct option is A.

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