What is the value of s in the equation 3 r equals 10 plus 5 s, when r equals 10? 4 8 100 200

Answer:

f( x ) = - x² - x + 42

Step-by-step explanation:

The polynomial function will have to include the zeroes with opposing signs, considering that when you isolate the value x say, you will take that value to the opposite side, changing the signs,

f(x) = (x + 7)(x - 6)

Now as you can see, x extends to negative infinity, such that,

f(x) = - (x + 7)(x - 6) - that negative makes no difference whatsoever on the zeroes of the function. All we want to do now is to expand this, and we receive out simplified solution.

Goal : [tex]expand\:-\:\left(x\:+\:7\right)\left(x\:-\:6\right)[/tex],

[tex]- xx+x\left(-6\right)+7x+7\left(-6\right)[/tex] = [tex]- xx-6x+7x-7\cdot \:6[/tex] = [tex]-\left(x^2+x-42\right)[/tex],

Expanded Solution : [tex]-x^2-x+42[/tex],

Polynomial Function : f( x ) = [tex]-x^2-x+42[/tex]

Answer:

A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Step-by-step explanation:

We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.

For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.

Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                     P.Q.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15

[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06

[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11

[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09

[tex]n_1[/tex] = sample of 25-mil film = 8

[tex]n_2[/tex] = sample of 20-mil film = 8

[tex]\mu_1[/tex] = population mean speed for the 25-mil film

[tex]\mu_2[/tex] = population mean speed for the 20-mil film

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005

Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.

So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;

P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98  {As the critical value of t at 14 degrees of

                                             freedom are -2.624 & 2.624 with P = 1%}  

P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98

P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] <  ) = 0.98

P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98

98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]

= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]

 = [-0.042, 0.222]

Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.

Answer:

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]

Step-by-step explanation:

Hey there!

Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.

Look at the image below ↓

By looking at the image we can conclude that the equation for the perpendicular line is,

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].

Hope this helps :)

Answer:

[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]

Step-by-step explanation:

Part 1: Finding the new slope of the line

Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.

Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].

Part 2: Using point-slope formula and solving in slope-intercept form

Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].

Then, use the point-slope equation to get b, or the y-intercept of the equation.

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]

Answer:

The volume of sphere is 267.95 units³.

Step-by-step explanation:

Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :

[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]

[tex]let \: r = 4[/tex]

[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times 64[/tex]

[tex]v = \frac{256}{3} \times 3.14[/tex]

[tex]v = 267.95 \: {units}^{ 3} [/tex]

Answer:

  7

Step-by-step explanation:

The signed sum of sequential odd numbers must be zero, as must the signed sum of sequential even numbers.

The minimum number of sequential even numbers that have a sum of 0 is 3: 2+4-6 = 0.

The minimum number of sequential odd numbers with a sum of zero is 4: 1-3-5+7=0.

Since we start with an odd number, we can get these sets of numbers in 7 days. The attached diagram shows one possible route.

Answer:

a) The five ordered pairs are:-

(1,60) , (2,120) , (3,180) , (4,240) , (5,300)

b)When You divide the y value by x value for each ordered pair u find the slope.

c)The graph shows a proportional relationship.Because as x-value increases so does y-value.

d)Y=mx+b-->  Y=60x (No y-intercept because it starts from 0)

e)If a person hiked for 9 hours then the distance would be 540. Because If u plug in the number of hours in the x value of the equatione then u will get 540. Here's the work:-

Y=60(9)

Y=540

Step-by-step explanation:

Hope it helps u. And if u get it right pls give me brainliest.

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

[tex]f'(x)=3x^2 +6x-72[/tex]

Now, we are going to make the derivative equal zero and find the answers of the equation.

[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]

So we have that the critical points are the answers to this equation:

[tex]x+6= 0 \\x= - 6[/tex]

and

[tex]x-4=0\\x=4[/tex]

Thus, the critical points are x=-6 and x=4

Using it's concept, it is found that the critical numbers of the function are:

x = -6 and x = 4.

The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = x^3 + 3x^2 - 72x[/tex]

The derivative is:

[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]

[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]

Then:

[tex]f^{\prime}(x) = 0[/tex]

[tex]3(x^2 + 2x - 24) = 0[/tex]

[tex]x^2 + 2x - 24 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.

[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]

[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]

[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]

The critical numbers of the function are x = 4 and x = -6.

A similar problem is given at https://brainly.com/question/16944025

Answer:

The probability is  [tex]P(X > x) = 0.0013499[/tex]

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 25[/tex]

      The standard deviation is [tex]\sigma = 5 \ minutes[/tex]

      The random number  [tex]x = 40[/tex]

Given that the time taken is  normally distributed  the probability is mathematically represented as

     [tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]

Generally the z-score for the normally distributed data set is mathematically represented as

        [tex]z = \frac{X - \mu}{\sigma }[/tex]

So  

     [tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]

    [tex]P(X > x) = 0.0013499[/tex]

This value is obtained from the z-table

Answer:

The highest number on a die is 6. when we roll out two die the total sum cannot be more that 12. and each sum having the same probability of showing up.

The outcome of our experiment can be 2,3,4,5,6,7,9,10,11 or 12.

Step-by-step explanation:

Statistical experiment can be simply stated as the likelihood of an an event to occur or not.

Answer:

B

Step-by-step explanation:

To solve this you do 80/100=.8

You than do .8×60= 48

Answer:

[tex]-5<x<26[/tex].

Step-by-step explanation:

We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.

Angle opposite to larger side is larger.

Since, 14 < 15, therefore

[tex]2x+10<62[/tex]

[tex]2x<62-10[/tex]

[tex]2x<52[/tex]

[tex]x<26[/tex]          ...(1)

We know that, angle can not not negative.

[tex]2x+10>0[/tex]

[tex]2x>-10[/tex]

[tex]x>-5[/tex]        ...(2)

From (1) and (2), we get

[tex]-5<x<26[/tex]

Therefore, the range of values of x is [tex]-5<x<26[/tex].

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57

Answer:

792

Step-by-step explanation:

The first three composite numbers are 4,  6 ,8

so 4^3+6^3+8^3=64+216+512=792

Answer:

The amount of thermal energy that is generated is 1000 joules.

Step-by-step explanation:

Let consider the person diving into a pool as a closed system, that is, a system with only energy interaction with the surroundings. According to the First Law of Thermodynamics, which is a generalization of the Principle of Energy Conservation, the total energy of the system is neither destroyed, nor created, only transformed. The initial gravitational potential energy is transformed into translational kinetic and thermal energy. That is to say:

[tex]U_{g} - K - Q = 0[/tex]

Where:

[tex]U_{g}[/tex] - Gravitational potential energy, measured in joules.

[tex]K_{tr}[/tex] - Translational kinetic energy, measured in joules.

[tex]Q[/tex] - Thermal energy, measured in joules.

The thermal energy is now cleared:

[tex]Q = U_{g}-K[/tex]

Given that [tex]U_{g} = 8000\,J[/tex] and [tex]K = 7000\,J[/tex], the amount of thermal energy that is generated is:

[tex]Q = 8000\,J - 7000\,J[/tex]

[tex]Q = 1000\,J[/tex]

The amount of thermal energy that is generated is 1000 joules.

Answer:

1000J

Step-by-step explanation:

EDGE2020

Answer:

0.40517 is the probability

Step-by-step explanation:

The first thing to do here is to calculate the corresponding z-score

Mathematically;

z-score = x-mean/SD

from the question,

x = 78, mean = 75 and SD = 12.5

Plugging these values in the z-score equation, we have;

z-score = (78-75)/12.5 = 3/12.5 = 0.24

So the probability we want to calculate is that;

P(z < 0.24)

we can get this by using the standard normal distribution table,

The value according to the table is;

0.40517

Answer:

We conclude that the true average stopping distance exceeds this maximum value.

Step-by-step explanation:

We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;

X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.

Let [tex]\mu[/tex] = true average stopping distance

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30      {means that the true average stopping distance exceeds this maximum value}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30      {means that the true average stopping distance exceeds this maximum value}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                              T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft

            n = sample size = 6

So, the test statistics =  [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex]  ~  [tex]t_5[/tex]

                                    =  4.898

The value of t-test statistics is 4.898.

Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average stopping distance exceeds this maximum value.

Answer:

[tex]\large \boxed{\sf \ \ \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }=4 \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to find the following limit.

[tex]\displaystyle \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }[/tex]

First of all, for any x real number different from 4 and positive, we can write

[tex]\dfrac{x-4}{\sqrt{x}-\sqrt{4}} = \dfrac{(x-4)(\sqrt{x}+\sqrt{4})} {(\sqrt{x}-\sqrt{4})(\sqrt{x}+\sqrt{4})}} ==\dfrac{(x-4)(\sqrt{x}+\sqrt{4})}{x-4}=\sqrt{x}+\sqrt{4}[/tex]

so the limit is

[tex]\sqrt{4}+\sqrt{4}=2+2=4[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

¡Hola! ¡Ojalá esto ayude!

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La fórmula para calcular el área de cualquier triángulo es:

base multiplicada por la altura y dividida por dos.

||

||

||

\/

Bh / 2.

Answer:

[0, infinity)

Step-by-step explanation:

clarence, I believe you meant y = |3x + 1|.  The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).

Answer:

If [tex]r >> h[/tex], the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

[tex]A = \pi \cdot r^{2} + 2\pi\cdot s[/tex]

Where:

[tex]r[/tex] - Base radius of the cone, measured in inches.

[tex]s[/tex] - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

[tex]s = \sqrt{r^{2}+h^{2}}[/tex]

Where [tex]h[/tex] is the altitude of the cone, measured in inches. If [tex]r >> h[/tex], then:

[tex]s \approx r[/tex]

And:

[tex]A = \pi\cdot r^{2} +2\pi\cdot r[/tex]

Given that [tex]A = 1885.7143\,in^{2}[/tex], the following second-order polynomial is obtained:

[tex]\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0[/tex]

Roots can be found by the Quadratic Formula:

[tex]r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}[/tex]

[tex]r_{1,2} \approx -1\,in \pm 24.521\,in[/tex]

[tex]r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in[/tex]

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

Answer:

Step-by-step explanation:

3(2)^2 + 4(1)^2

3(4) + 4

12+4= 16

Answer:

[tex]\huge\boxed{16}[/tex]

Step-by-step explanation:

[tex]3x^2+4y^2\ \text{for}\ x=2;\ y=1.\\\\\text{Substitute:}\\\\3(2)^2+4(1)^2=3(4)+4(1)=12+4=16\\\\\text{Used PEMDAS}[/tex]

Answer:

Step-by-step explanation:

m= the amount of money the mechanic makes.

h= the amount of money the helper makes.

m=h+5

m+h=114

h+5+h=114

2h+5=114

h=54.50

m=59.5

Helper makes $9 an hour.

Mechanic makes $9.92 an hour.

The earning of helper each earn per hour is 7$ /hr.

To find earning of helper per hour.

science that deals with the addition, subtraction, multiplication, and division of numbers and also the properties and manipulation of numbers.

Given that:

let the cost /per hour of helper be x

and that of the mechanic is x+5

now for 6 hour job total earning is

6(x+x+5) = 114

=> 2x+5 = 19

so, 2x = 14 or x = 7

the earning of helper is = 7$ /hr

and earning of mechanic is = 12$/hr

So, the earning of helper each earn per hour is 7$ /hr.

Learn more about arithmetic here:

https://brainly.com/question/17120168

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Answer:

Number:3.75

Equation:7 x-9=3(x+2)

Step-by-step explanation:

Let the number be x.

According to the question,

7 x-9=3(x+2)

7 x-9= 3 x+ 6

7 x- 3 x= 9+6

4 x= 15

x=15/4

x=3.75

If you verify the answer you will get,

11.25=11.25

Thank you!

Answer:

[tex]\boxed{1.5}[/tex]

Step-by-step explanation:

First point is given (8, -2)

                               (x₁, y₁)

Second point is given (12, 4)

                                     (x₂, y₂)

Apply the slope formula.

[tex]slope=\frac{rise}{run}[/tex]

[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope=\frac{4-(-2)}{12-8}[/tex]

[tex]slope=\frac{6}{4}=1.5[/tex]

A slope is also known as the gradient of a line. The slope of the line through these two data points is 1.5°F per hour.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

Given that the temperature recorded at 8 am is –2°F, while the temperature recorded at 12 pm is 4°F. The number of hours between 8:00 am to 12 pm is 4 hours. Therefore, the slope of the line through these two data points is,

Slope, m = [4°F – (–2°F)] / 4 hours = 6°F / 4 hours = 1.5°F per hour

Hence, the slope of the line through these two data points is 1.5°F per hour.

Learn more about Slope of Line here:

https://brainly.com/question/14511992

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Answer:

6.3 ft

Step-by-step explanation:

The ladder lying on the wall with an elevation of 39° forms a right angled triangle.

Hypotenuse = length of ladder = 10 ft

Opposite = x = ?

θ = 39°

Use trigonometric ratio formula to find, x, which is how far the ladder goes up the wall.

The trigonometric ratio formula to use is:

sin(θ) = opposite/hypotenuse

Sin(39) = x/10

Multiply both sides by 10

10*sin(39) = x

x = 10*sin(39)

x = 6.29 ≈ 6.3 ft (to nearest tenth)

Answer:

6.3 ft

Step-by-step explanation:

did the quiz got it right

Answer:

answer 1 /9x^3

Step-by-step explanation:

9ײ/81×⁵​

change the expression to indices form

3^2 x^2 /3^4 x^5

1 /3^2 x^3

1 /9x^3

Answer:

A horizontal cross-section is obtained when the plane that passes through the solid object is parallel to its base. On the other hand, a vertical cross section is found when the intersecting plane is perpendicular to the base of the solid. These are known as a parallel cross-section and perpendicular cross section.

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

[tex] \frac{4x + 1}{6x} \div \frac{x}{3x - 1} [/tex]

[tex] = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} [/tex]

[tex] = \frac{(4x + 1)(3x - 1)}{x(6x)} [/tex]

[tex] = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } [/tex]

[tex] = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } [/tex]

Answer:

Step-by-step explanation:

Let the length of first piece be L .

Length of second piece = 56 - L

radius of circle made from first piece

R = L / 2π

Area of circle = π R²

= L² / 4π

side of square made fro second piece

= (56 - L) / 4

area of square = ( 56-L)² / 16

Total area

A = L² / 4π + ( 56-L)² / 16

For smallest possible combined area

dA / dL = 0

dA / dL = 2L /  4π - 2( 56-L)/16 =0

2L /  4π = 2( 56-L)/16

.159 L = 7 - .125 L

.284 L = 7

L = 24.65 inch

other part = 56 - 24.65

= 31.35 inch .