A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.

By adding fractions, we conclude that the correct option is the third one:

"one and two sevenths tubes"

We know that:

The total amount of paint will be given by the direct addition of these two fractions, notice that the denominator is the same in both cases, so we can just add the numerators.

5/7 + 4/7 = (5 + 4)/7 = 9/7

We can rewrite this as:

9/7 = 7/7 + 2/7 = 1 + 2/7

Thus, the correct option is the third one

"one and two sevenths tubes"

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Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km.  Point C's distance from A is 5.92 km east and 2.16 km south.

To find the distance from point B to point A, the Cos function should be used.

Point A's distance from B can be found as:

= Cos (143 - 90) x distance from point A

= Cos (53°) x 2.7

= 1.62 km

The distance of C from A eastward is:

= 1.62 + 4.3

= 5.92 km

As C is southward from point A, the function to be used is the Sin function.

The distance southward of c from A is:

= Sin(53°) x 2.7

= 2.16 km

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The complement of the interval [2, 3) is  ( -∞, 2) ∪ (3, ∞).

According to the given question.

We have an interval [2, 3).

Let A = [2, 3)

Which is defined as

[2, 3) = {x ∈ r : 2 ≤ x < 3}

This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.

And, here it is also given that the universal set is r ( set of real numbers).

As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.

[tex]A^{c} = U - A[/tex]

Where,

[tex]A^{c}[/tex] is the complement of interval A

Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.

So, we can say that

[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]

Where, [tex]A^{c}[/tex] is the complement of the interval A.

Hence, the complement of the interval [2, 3) is  ( -∞, 2) ∪ (3, ∞).

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Answer:

PQ = 20 cm

QR = 15 cm

Step-by-step explanation:

The probability that a class of 50 has an average midterm mark that is less than 75 is value=0

Average is the mathematics mean, and is calculated by means of adding a group of numbers and then dividing with the aid of the count of these numbers. for instance, the average of 2, three, three, five, 7, and 10 is 30 divided with the aid of 6, that is five.

The common is described as the implied value that is identical to the ratio of the sum of the number of a given set of values to the whole wide variety of values gift within the set.

There are three primary sorts of common: imply, median, and mode. each of those techniques works slightly differently and frequency effects in barely specific regular values. The suggestion is the maximum normally used average. To get the suggested fee, you add up all of the values and divide this total by using the number of values.

The probability that a class of 50 has an average midterm mark that is less than 75

n = 50

P(<75)=P(Z<75)

P(Z<75−786√50)

P(Z<−3.5355)

We will look for the value in the StandardNormal able. We will get the value=0

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The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.

The given expression according to the task content is; a³b⁵/a⁴b.

It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;

a^(3-4)b^(5-1)

Consequently we have;

b⁴/a.

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Answer:

16.66666667

Step-by-step explanation:

=12+10.66666667-6

=22.66666667-6

=16.66666667

8 Guidelines for Critically Evaluating a Statistical Study

1. Identify the Goal, Population, and Type of Study

2. Consider the Source

3. Examine the Sampling Method

4. Look for Problems in Defining or Measuring the Variables of

Interest

5. Watch Out for Confounding Variables

6. Consider the Setting and Wording of Any Survey

7. Check That Results Are Fairly Represented in Graphics or

Concluding Statements

8. Stand Back and Consider the Conclusions

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The maximum possible area would have a length of 24 feet and width of 12 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the length and y represent the width, hence:

Since beth has 48 ft fencing and cover 3 sides, hence:

x + 2y = 48  

x = 48 - 2y     (1)

Also:

Area (A) = xy

A = (48 - 2y)y

A = 48y - 2y²

The maximum area is at A' = 0, hence:

A' = 48 - 4y

48 - 4y = 0

y = 12 feet

x = 48 - 2(12) = 24

The maximum possible area would have a length of 24 feet and width of 12 feet.

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Answer:

Step-by-step explanation:

[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]

[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]

The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].

A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..

A monomial is expressed as a product of two or more other monomials when it is factored.

Here,

a = 125

[tex]$b=27 p^{12}$[/tex]

To find: a - b

a - b = 125 - [tex]27 p^{12}$[/tex]

a - b =  [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]

We know that,

[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]

Finding the factored form of a - b using this method:

[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]

[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]

So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].

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Answer:

Step-by-step explanation:

Comment

The first thing you should notice once you have read it, is there is a plus sign required. That means you are likely to get a binomial (two different things that won't reduce or combined).

So what you get is

18*g + 5

Notice where the place sign is. It is between 18g and 5. The result cannot be simplified any further.

Answer

18g + 5

Answer:

Step-by-step explanation:

X-INTERCEPT

Plug y=0 into the equation and solve the resulting equation −6x=−7 for x.

The x-intercept:

[tex]\left(\frac{7}{6},0\right)\approx \left(1.16666666666667,0\right)[/tex]

Y-INTERCEPT

Plug x=0 into the equation and solve the resulting equation 3y=−7 for y.

The y-intercept:

[tex]\left(0, - \frac{7}{3}\right)\approx \left(0,-2.33333333333333\right)[/tex]

Answer:

[tex]x[/tex]-intercept = ([tex]-\frac{7}{6}[/tex]  , 0)

[tex]y[/tex]-intercept = (0 , [tex]-\frac{7}{3}[/tex])

Step-by-step explanation:

[tex]6x + 3y = -7[/tex]

• The x-intercept is the point at which the line crosses the x-axis, that is, where y = 0.

∴ [tex]6x + 3(0) = -7[/tex]

⇒ [tex]6x = -7[/tex]

⇒ [tex]x = \bf -\frac{7}{6}[/tex]

∴ The x-intercept is at the point ([tex]-\frac{7}{6}[/tex] , 0).

• Similarly, the y-intercept is the point at which the line crosses the y-axis, that is, where x = 0.

∴ [tex]6(0) + 3y = -7[/tex]

⇒ [tex]3y = -7[/tex]

⇒ [tex]y = \bf - \frac{7}{3}[/tex]

∴ The y-intercept is at the point (0 , [tex]-\frac{7}{3}[/tex]).

The volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.

To find the volume of the cube that perfectly fits an 18 ft³ pyramid:

We have been provided that:

Therefore, the volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.

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The correct question is given below:

The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube?

(A) 6 cubic feet

(B) 18 cubic feet

(C) 54 cubic feet

(D) 72 cubic feet

Answer:

She used 9 tiles which are 3 cm long

Step-by-step explanation:

cuz 3x9=27 and yea

The perimeter of the triangle is 56.4 units.

The perimeter of the triangle can be found as follows:

The perimeter of a figure is the sum of the whole sides. Therefore, the perimeter of a triangle is the sum of the three sides.

perimeter of a triangle = x + y + z

where

Therefore,

perimeter of the triangle = 19.8 + (9.8 + 8.4) + (8.4 + (19.8 - 9.8))

perimeter of the triangle = 19.8 + 18.2 + 18.4

perimeter of the triangle = 56.4

perimeter of the triangle = 56.4 units

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Answer:

Yup Yup

Step-by-step explanation:

yessah

Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.

The given inequality x<8 can be written in the interval notation as,

x = (-∞,8)

Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).

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The algebraic solution to the situation is as follows:

x + y = 750

10x + 6y = 6860

The number of adult and student are 590 and 160 respectively.

One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.

One evening,750 people attended the play and the total receipts were 6860.

Therefore,

let

x = number of adult ticket

y = number of student tickets

Therefore,

x + y = 750

10x + 6y = 6860

10x + 10y = 7500

10x + 6y = 6860

4y = 640

y = 640 / 4

y = 160

Hence,

x  = 750 - y

x = 750 - 160

x = 590

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Answer:

20 percent

40 percent

20 percent

20(.008) percent

Step-by-step explanation:

6) 54 - 45 = 9

45 / 9 = 5

100 / 5 = 20

20 percent

7) 60 - 36 = 24

60 / 24 = 2.5

100 / 2.5 = 40

40 percent

8) 30 - 24 = 6

30 / 6 = 5

100 / 5 = 20

20 percent

9) 24.99 - 19.99 = 5

24.99 / 5 = 4.998

100 / 4.998 approx. = 20.008

20.008 percent (or rounded 20 percent)

The distance of the boat from its starting point is 156.226 .

According to the question

A boat sails on a bearing of 63 degree for 124 miles

i.e

By making 63 degree covers 124 miles

therefore ,

In figure below

AC = 124 miles

Then turns and sails 201 miles on a bearing of 192 degree

therefore ,

In figure below

CD = 201 miles  

Now,

According to the sum of triangle

∠ACB + ∠ABC + ∠BAC = 180°

∠ACB + 90° + 63° = 180°

∠ACB = 27°

CE = 180°  (Straight line )

therefore,

∠DCE = 192°  -  180°

          = 12°

As ∠C = 90°

therefore

∠ACD = ∠C - ∠DCE - ∠ACB

          = 90° - 12°- 27 °

          = 51°

Now,

The distance of the boat from its starting point = AD

By using Law of Cosines

As

The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.

The Law of Cosines (also called the Cosine Rule) says:

c² = a² + b² − 2ab cos(C)

As we have 2 sides and one angle available we can use   Law of Cosines

Therefore,

by substituting the value

(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)

(AD)² = (124)² + (201)² − 2*124*201 cos(51)

AD = 156.226

Hence, the distance of the boat from its starting point is 156.226 .

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-5x - 5 = 3x + 19

---Move the x's to one side

-5x - 3x - 5 = 3x - 3x + 19

-8x - 5 = 19

---Isolate the -8x by removing the -5 from the left side

-8x - 5 + 5 = 19 + 5

-8x = 24

---Divide both sides by -8 to get x by itself

x = -3

Hope this helps!

-5x-5= 3x+19

= > -5x-3x= 19+5

= > -8x= 24

= >-x=24/8

= >x= -3

Answer:

negative

Step-by-step explanation:

[tex]s^{67}<0 \\ \\ t^9>0 \\ \\ \implies \frac{s^{67}}{t^9}<0

[/tex]

Answer:

Step-by-step explanation:

The sign of a product or quotient cannot be determined by the positive number (t), so we can ignore it. The sign of the expression will be negative if and only if there are an odd number of negative factors.

Here, there are 67 (an odd number) negative factors, so the expression will be negative.

Answer:

g(1) = 1

Step-by-step explanation:

Since 1 ≠ -2  and  1 ≠ -1

Then we must use the expression:

g(x) = x³ - x² + 1  ,to calculate g(1).

Therefore

g(1) = (1)³ - (1)² + 1

     = 1 - 1 + 1

     = 0 + 1

     = 1

The equations exist [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex] then the value of

x = -6, x = -2 and y = -15, y = 1.

[tex]y =4x+9[/tex] ?

The given equations are [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex]

[tex]$-\left(x\:+\:2\right)^2\:+\:1\:=\:4x\:+\:9[/tex]

[tex]$-x^{2}-4 x-3=4 x+9[/tex]

Subtract 9 from both sides, we get

[tex]$-x^{2}-4 x-3-9=4 x+9-9[/tex]

Simplifying the equation, we get

[tex]$-x^{2}-4 x-12=4 x[/tex]

Subtract 4x from both sides

[tex]$-x^{2}-4 x-12-4 x=4 x-4 x[/tex]

[tex]$-x^{2}-8 x-12=0[/tex]

Solve with the quadratic formula

[tex]$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(-1)(-12)}}{2(-1)}[/tex]

[tex]$\sqrt{(-8)^{2}-4(-1)(-12)}=4[/tex]

[tex]$x_{1,2}=\frac{-(-8) \pm 4}{2(-1)}[/tex]

Separate the solutions

[tex]$x_{1}=\frac{-(-8)+4}{2(-1)}, x_{2}=\frac{-(-8)-4}{2(-1)}[/tex]

[tex]$x=\frac{-(-8)+4}{2(-1)}=-6[/tex]

[tex]$x=\frac{-(-8)-4}{2(-1)}= \quad-2[/tex]

The solutions to the quadratic equation are x = -6, x = -2

From the above equation [tex]y =4x+9[/tex],

substitute the value of x, then we get

Put, x = -6 then y = 4(-6) + 9 = -15

Put, x = -2 then y = 4(-2) + 9 = 1

The system of equations exists (–2, 1) and (–6, –15).

Therefore, the correct answer is (–2, 1) and (–6, –15).

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Answer:

(–2, 1) and (–6, –15)

Step-by-step explanation:

flvs testing (i am not completely sure btw)

just substitute that into a last equations (seperatly if you understand=== -2 and 1 as x and y; -6 and -15 as x and y)

Answer:

1/2

Step-by-step explanation:

Assume the coin is a fair coin.

Since we already know that the first 9 tosses were heads, the probability of 9 straight heads in the first 9 tosses is 1.

It all depends on the last toss. There is an equal probability of heads and tails in a single toss of a fair coin.

p(heads) = 1/2

p(10 heads) = 1/2

Ok so the answer is 1/2

a. log₈8 = 1

b. log₇6/5

c. log₉3¹

1. log₈ 2 * 4 would produce an integer

= log₈8 = 1

The output is an integer

2. log₇6/5 would give us an irrational number

= log₇1.2

This would give us an irrational number

3. log₉3¹ would give us a rational number

= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9

= 1/2

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Answer:subtraction

Step-by-step explanation: to find out how many fewer tickets were sold on Sunday you would need to subtract 34012 by 29879. The solution would be how many fewer tickets were sold on Sunday compared to Saturday.