Brainliest to correct answer!! What is the least common denominator of the rational expressions below?

Answer:

Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.

y= -3x+b

Now, we can substitute in the point given to find the intercept.

2= -3(4)+b

2= -12+b

b=14

Finally, put in everything we've found to finish the equation.

y= -3x+14

Answer:

y = -3x + 14

Step-by-step explanation:

First find the reciprocal slope since it is perpendicular.  Slope of the other line is 1/3 so the slope for our new equation is -3.  

Plug information into point-slope equation

(y - y1) = m (x-x1)

y - 2 = -3 (x-4)

Simplify if needed

y - 2 = -3x + 12

y = -3x + 14

Answer:

1. x/5

2. cubed root of 2x

3.x-10

4.(2x/3)-17

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Lets find the inverse function for function f(x)=2*x/3-17

To do that first express x through f(x):

2*x/3= f(x)+17

2*x=(f(x)+17)*3

x=(f(x)+17)*3/2   done !!!                        (1)

Next : to get the inverse function from (1) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=(x+17)*3/2 or f'(x)=3*(x+17)/2

This is function is No4 in our list. So f(x)=2*x/3-17 should be moved to the box No4  ( on the bottom) of the list.

2.  Lets find the inverse function for function f(x)=x-10

To do that first express x through f(x):

x= f(x)+10

x=f(x)+10   done !!!                        (2)

Next : to get the inverse function from (2) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x+10

This is function is No3 in our list. So f(x)=x-10 should be moved to the box No3  ( from the top) of the list.

3.Lets find the inverse function for function f(x)=sqrt 3 (2x)

To do that first express x through f(x):

2*x= f(x)^3

x=f(x)^3/2   done !!!                        (3)

Next : to get the inverse function from (3) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x^3/2

This is function No2 in our list. So f(x)=sqrt 3 (2x) should be moved to the box No2  ( from the top) of the list.

4.Lets find the inverse function for function f(x)=x/5

To do that first express x through f(x):

x=f(x)*5   done !!!                        (4)

Next : to get the inverse function from (4) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x*5 or f'(x)=5*x

This is function No1 in our list. So f(x)=x/5 should be moved to the box No1  ( on the top) of the list.

Answer:

answer C

Step-by-step explanation:

because the plan view of a solid 3-D figure is the view from the top which would be 3 squares in a row which is exactly what is shown in answer C.

Answer:

D

Step-by-step explanation:

D is the answer because every part of the cube is formed from 2 horizontal cubes

Answer:

87

Step-by-step explanation:

Answer:

-5i and 5i cannot be roots of the equation, since they are complex.

Step-by-step explanation:

A 3-degree polynomial equation must have 3 roots, if one of its roots is a complex number, then its conjugate must also be a root of the function. The problem already stated two roots, which are reals, therefore the last root must also be real. Using this line of thought we know that -5i and 5i cannot be roots of the equation, since they're complex.

Answer:    x1=1   x2=-2  and x3=2

Step-by-step explanation:

1st   x1=1 is 1 of the roots , so

F(1)=1-1-4+4=0 - true

So lets divide x^3-x^2-4x+4 by (x-x1), i.e  (x^3-x^2-4x+4) /(x-1)=(x^2-4)

x^2-4 can be factorized as (x-2)*(x+2)

So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)

So there are 3 dofferent roots:

x1=1   x2=-2  and x3=2

Answer:

  p(mean < 2000) ≈ 0.81

Step-by-step explanation:

Your table gives the probability the value is between z=0 and z=0.88. You want the probability the value is between -∞ and 0.88, so you have to add the probability it is between -∞ and zero. You must add 0.5 to the table value.

  p(Z < 0.88) = 0.5 +0.3106 = 0.8106

_____

Comment on table values

You probably need to do some interpolation of your table values to get accuracy to 4 significant digits. All of the calculators I use give the probability for a Z-score of 0.88388 to be about 0.8116, not 0.8106.

When working with a "half" table, you need to be aware of what the table is giving you and what you're trying to use it for. A quick sketch of the problem may be helpful. (see below)

Answer:

2,967.92 ( dollars )

Step-by-step explanation:

The amount the bond is worth, should be the present value of the bond, other wise known as PV. If it is given that Google.com bond will pay $ 4,500 ten years from now, it should be that the future value, otherwise known as FV, is 4,500 dollars.

Consider the given. There is a 4.25 percent discount rate, a time span of 10 years ( tenor / time ) and of course a future value of 4,500 dollars. Using this, we can calculate the present value -

[tex]PV = FV / ( ( 1 + rate )^{time} ),\\PV = 4,500 / ( 1 + 4.25 / 100 )^{10}\\----\\( Calculations ) PV = ( About ) 2,967.92 ( dollars )\\Solution = 2968 ( dollars )[/tex]

As you can see, through simple calculations the solution should be that the bond worth is about $ 2,967.92

Answer:

1 cup per drink per student.

20 oz. left over

Step-by-step explanation:

given; 2 gallons for 100 students

1 cup holds 3 oz.

first, convert 2 gallons to oz.

1 gal = 160 oz.

2 gallons * 160 oz per 1 gal = 320 oz.

320 oz / 100 students = 3.2oz.

but 1 cup can only hold 3 oz.

therefore 3.2 - 3 = 0.2 oz * 100 = 20 oz. left over.

hope it helps.

Answer:

Step-by-step explanation:

[tex] \frac{8 {x}^{4} }{16 {x}^{7} } [/tex]

Reduce the fraction with 8

[tex] \frac{ {x}^{4} }{2 {x}^{7} } [/tex]

Simplify the expression

[tex] \frac{1}{2 {x}^{3} } [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

100

Step-by-step explanation:

The number, when decreased by 40%, is equal to 100.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

Let the number be x then the number is calculated as:-We can see that the number is decreased by 40% then the remaining part is 60%

x ( 60% ) = 60

x ( 60 / 100 ) = 60

x = 100

Hence, the number, when decreased by 40%, is equal to 100.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

Answer:

D. [tex]3^3 - 4^2[/tex]

Step-by-step explanation:

Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2

Answer:

Lateral Surface Area = 15.072 [tex]mm^2[/tex]

Step-by-step explanation:

Given that:

Base of Cylinder has radius, r = 1.2 mm

Height, h = 2 mm

To find:

Lateral Surface area of cylinder = ?

Solution:

We know that total surface area of a cylinder is given by:

[tex]TSA = 2\pi r^2+2\pi rh[/tex]

Here [tex]2\pi r^2[/tex] is the area of two circular bases of the cylinder and

[tex]2\pi rh[/tex] is the lateral surface area.

Please refer to the attached image for a better understanding of the Lateral and Total Surface Area.

So, LSA = [tex]2\pi rh[/tex]

[tex]\Rightarrow LSA = 2 \times 3.14 \times 1.2 \times 2\\\Rightarrow LSA = 6.28 \times 2.4\\\Rightarrow LSA = 15.072\ mm^2[/tex]

So, the answer is:

Lateral Surface Area of given cylinder = 15.072 [tex]mm^2[/tex]

Answer:

LSA  =   24.1

Step-by-step explanation:

I just did this, I dont know how to upload my work, but It marked it as right and gave me the green check mark. The answer is 24.1

Answer:

The point estimate of the population​ proportion is 0.78.

The margin of error of the interval is of 0.135 = 13.5%.

The number of individuals in the sample with the specified​ characteristic is 1170.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction of these two bounds divided by 2.

In this question:

Lower bound: 0.645

Upper bound: 0.915

Point estimate of the population​ proportion

[tex]p = \frac{0.645 + 0.915}{2} = 0.78[/tex]

The point estimate of the population​ proportion is 0.78

Margin of error for the following confidence​ interval

[tex]M = \frac{0.915 - 0.645}{2} = 0.135[/tex]

The margin of error of the interval is of 0.135 = 13.5%.

The number of individuals in the sample with the specified​ characteristic

78% of 1500

0.78*1500 = 1170

The number of individuals in the sample with the specified​ characteristic is 1170.

Answer:

  6/(49π) ≈ 0.03898 m/min

Step-by-step explanation:

  V = πr²h . . . . formula for the volume of a cylinder

  dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

  dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

  dh/dt ≈ 0.03898 m/min

Answer:

4 inches

Step-by-step explanation:

We can set up a proportion to find out the length value (assuming x is the length of the frame)

[tex]\frac{3}{x} = \frac{9}{12}[/tex]

We multiply 12 and 3...

[tex]12\cdot3=36[/tex]

And divide by 9...

[tex]36\div9=4[/tex]

So, the length of the frame is 4 inches.

Hope this helped!

Answer:

Step-by-step explanation:

4 inches

Answer:

Solution,

Circumference of circle = 615.44 units

Radius = ?

Now,

Circumference of circle = 615.44

[tex]2\pi \: r = 615.44[/tex]

[tex]2 \times 3.14 \times r = 615.44[/tex]

[tex]6.28r = 615.44[/tex]

[tex]r = \frac{615.44}{6.28} [/tex]

[tex]r = 98 \: units[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The interval is constructed at 93% confidence.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between these two bounds, divided by 2.

Confidence interval of proportions concepts:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have that:

2050 people, so n = 2050.

Lower bound: 0.878

Upper bound: 0.903

[tex]\pi = \frac{0.878 + 0.903}{2} = 0.8905[/tex]

[tex]M = \frac{0.903 - 0.878}{2} = 0.0125[/tex]

Confidence level:

We have to find z.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.0125 = z\sqrt{\frac{0.8905*0.1095}{2050}}[/tex]

[tex]0.0069z = 0.0125[/tex]

[tex]z = \frac{0.0125}{0.0069}[/tex]

[tex]z = 1.81[/tex]

[tex]z = 1.81[/tex] has a pvalue of 0.965.

That is:

[tex]]1 - \frac{\alpha}{2} = 0.965[/tex]

[tex]\frac{\alpha}{2} = 0.035[/tex]

[tex]\alpha = 2*0.035[/tex]

[tex]\alpha = 0.07[/tex]

Finally

[tex]1 - \alpha = 1 - 0.07 = 0.93[/tex]

The interval is constructed at 93% confidence.

Answer/Step-by-step explanation:

*The six raw data values in the second row are for teens are: 14, 15, 15, 15, 16, and 16

*There are 6 raw data values in the 20's represented in the 3rd row. They are: 25, 25, 27, 28, 28, and 28

*There are 3 raw data values in the 30's that are represented in the 4th row. They are: 35, 36, and 36.

*There are 0 raw data values in the 40's represented in the 5th row.

*There are 21 raw data values in the entire data set. They are:

1, 2, 3, 7, 9, 14, 15, 15, 15, 16, 16, 25, 25, 27, 28, 28, 28, 35, 36, 36, and 50.

Answer:

a

Step-by-step explanation:

hope this helps

Answer:

Systematic Sampling

Step-by-step explanation:

Systematic sampling is a form of sampling in which the researcher applies probability sampling such that every member of the group is selected at regular intervals or periods. The researcher picks a random starting point and after an interval must have elapsed, another sample member is chosen. This sampling method is similar to that disclosed in the question because it has the key qualities.

For example, an interval is given after the 1000th soda is tested for quality.  This means that the interval for testing can accommodate 1000 sodas after which the first member is tested again. So, this is a Systematic sampling method.

Answer:

[tex]18x^2+85x+18 = 0[/tex]

Step-by-step explanation:

Given Equation is

=> [tex]2x^2+7x-9=0[/tex]

Comparing it with [tex]ax^2+bx+c = 0[/tex], we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = [tex]-\frac{b}{a}[/tex]

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]

Sum of Roots = [tex]\frac{\alpha^2+\beta^2 }{\alpha \beta }[/tex]

Sum of Roots = [tex]\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }[/tex]

Sum of roots = [tex](\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}[/tex]

Sum of roots = [tex]\frac{49}{4} + 9 /\frac{-9}{2}[/tex]

Sum of Roots = [tex]\frac{49+36}{4} / \frac{-9}{2}[/tex]

Sum of roots = [tex]\frac{85}{4} * \frac{2}{-9}[/tex]

Sum of roots = S = [tex]-\frac{85}{18}[/tex]

Product of Roots = [tex]\frac{\alpha }{\beta } \frac{\beta }{\alpha }[/tex]

Product of Roots = P = 1

The Quadratic Equation is:

=> [tex]x^2-Sx+P = 0[/tex]

=> [tex]x^2 - (-\frac{85}{18} )x+1 = 0[/tex]

=> [tex]x^2 + \frac{85}{18}x + 1 = 0[/tex]

=> [tex]18x^2+85x+18 = 0[/tex]

This is the required quadratic equation.

Answer:

α/β= -2/9      β/α=-4.5

Step-by-step explanation:

So we have quadratic equation  2x^2+7x-9=0

Lets fin the roots  using the equation's  discriminant:

D=b^2-4*a*c

a=2 (coef at x^2)   b=7(coef at x)  c=-9

D= 49+4*2*9=121

sqrt(D)=11

So x1= (-b+sqrt(D))/(2*a)

x1=(-7+11)/4=1   so   α=1

x2=(-7-11)/4=-4.5    so  β=-4.5

=>α/β= -2/9       => β/α=-4.5

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Given that μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems, the hypothesis are

For null,

H0: μ1 − μ2 = - 10

For alternative,

Ha: μ1 − μ2 < - 10

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 115.6

x2 = 129.3

s1 = 5.04

s2 = 5.32

n1 = 8

n2 = 8

t = (115.6 - 129.3)/√(5.04²/8 + 5.32²/8)

t = - 2.041

Test statistic = - 2.04

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [5.04²/8 + 5.32²/8]²/[(1/8 - 1)(5.04²/8)² + (1/8 - 1)(5.32²/8)²] = 45.064369/3.22827484

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.030

Since alpha, 0.01 < the p value, 0.03, then we would fail to reject the null hypothesis.

Answer:

2-x=-3x-12+6

2-x=-3x-6

8=-3x+x

8=-2x

x=-4

hope it's clear

mark me as brainliest

Answer:

Option B is the correct option.

Step by step explanation

2 - x = -3 ( x + 4) +6

Distribute -3 through the paranthesis

2 - x = - 3x - 12 + 6

Calculate

2 - x = - 3x - 6

Move variable to LHS and change its sign

2 - x + 3x = -6

Move constant to R.H.S and change its sign

- x + 3x = -6 - 2

Collect like terms and simplify

2x = -8

Divide both side by 2

2x/2 = -8/2

Calculate

X = -4

Hope this helps....

Good luck on your assignment..

Answer:

At a significance level of 0.02, there is not enough evidence to support the claim that the percentage of readers that own a laptop is significantly different from 45%.

P-value = 0.06

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of readers that own a laptop is significantly different from 45%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.45\\\\H_a:\pi\neq 0.45[/tex]

The significance level is 0.02.

The sample has a size n=370.

The sample proportion is p=0.4.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.45*0.55}{370}}\\\\\\ \sigma_p=\sqrt{0.000669}=0.026[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.4-0.45+0.5/370}{0.026}=\dfrac{-0.049}{0.026}=-1.881[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z<-1.881)=0.06[/tex]

As the P-value (0.06) is greater than the significance level (0.02), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.02, there is not enough evidence to support the claim that the percentage of readers that own a laptop is significantly different from 45%.

Answer:

1. There is no difference in amount of items that people are able to remember before and after being taught the memory device.

2. There is no difference between performance of men and women on memory test.

Step-by-step explanation:

Test 1:

The hypothesis for the two-way ANOVA test can be defined as follows:

H₀: There is no difference in amount of items that people are able to remember before and after being taught the memory device.

Hₐ: There is difference in amount of items that people are able to remember before and after being taught the memory device.

Use MS-Excel to perform the two-way ANOVA text.

Go to > Data > Data Analysis > Anova: Two-way with replication  

A dialog box will open.

Input Range: select all data

Rows per sample= 10

Alpha =0.05

Click OK

The ANOVA output is attaches below.

Consider the Columns data:

The p-value is 0.199.

p-value > 0.05

The null hypothesis will not be rejected.

Conclusion:

There is no difference in amount of items that people are able to remember before and after being taught the memory device.

Test 2:

The hypothesis  to determine whether or not men and women perform differently on the memory test is as follows:

H₀: There is no difference between performance of men and women on memory test.

Hₐ: There is a difference between performance of men and women on memory test.

Consider the Sample data:

The p-value is 0.075.

p-value > 0.05

The null hypothesis will not be rejected.

Conclusion:

There is no difference between performance of men and women on memory test.

Answer:

Step-by-step explanation:

c= 2(pi)r

Area = (pi)r^2

28.26 = (pi) r^2

r =[tex]\sqrt{9}[/tex] = 3

circumference = 2 (3.14) (3)

                        = 18.8 in

Answer:  approx 18.8 in

Step-by-step explanation:

The area of the circle is

S=π*R²   (1)   and the circumference of the circle is C= 2*π*R      (2)

So using (1)  R²=S/π=28.26/3.14=9

=> R= sqrt(9)

R=3 in

So using (2) calculate C=2*3.14*3=18.84 in or approx 18.8 in

Answer:

i think the answer is option 1           3

Step-by-step explanation:

i say this bc 3/4 times 4 is 3

hope this helps

if this is the correct answer plz mark brainliest.

Answer:

[tex]\boxed{11.78}[/tex]

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer:

d. $125, $135, $150, $130

Step-by-step explanation:

$125, $135, $150, $130

Range of the above set of numbers:

$150 - $125 = $25

Mean of numbers:

$125 + $135 + $150 + $130 = $540

540 ÷ 4 = $135