An electronics store is selling mp3 players for 30% off. A customer purchases an mp3 player for $42. What was the price of that mp3 player before the reduction?

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:

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:

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

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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:

87

Step-by-step explanation:

Answer:

  y

Step-by-step explanation:

The expression

  y = f(x)

tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.

Answer:

6

Step-by-step explanation:

We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:

[tex]2^{1}=2[/tex]

[tex]2^{2}=4[/tex]

[tex]2^{3}=8[/tex]

[tex]2^{4}=16[/tex]

[tex]2^{5}=32[/tex]

[tex]2^{6}=64[/tex]

[tex]2^{7}=128[/tex]

[tex]2^{8}=256[/tex]

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover

Answer:

np = 81  , nQ = 99

Step-by-step explanation:

Given:

X - B ( n = 180 , P = 0.45 )

Find:

Sampling distribution has an approximate normal distribution

Computation:

nP & nQ ≥ 5

np = n × p

np = 180 × 0.45

np = 81

nQ = n × (1-p)

nQ = 180 × ( 1 - 0.45 )

nQ = 99

[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]

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:

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:

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:

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

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:    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:

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:

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:

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:

a) Fx=-5N  Fy=-5*sqrt(3) N   b) Fx= 5*sqrt(3) N    Fy=-5N

c) Fx=-5*sqrt(2) N    Fy=-5*sqrt(2)   N

Step-by-step explanation:

The arrow's F ( weight) component on axle x  is Fx= F*sinA  and on axle y is

Fy=F*cosA

a) The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(30)= -5 N      Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N

b) Now the x component  is co directed to axle x , and y component is opposite directed to axle y.

So x component is positive and y components is negative

So Fx = 10*sin(60)= 5*sqrt(3) N       Fy= -10*cos(60)= -10*1/2= -5 N

c)The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(45)= -5*sqrt(2)  N    

 Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N

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:

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:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

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:

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:

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/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:

-8

Step-by-step explanation:

8ʸ = 16ʸ⁺²

(2³)ʸ = (2⁴)ʸ⁺²

2³ʸ = 2⁴ʸ⁺⁸

3y = 4y + 8

y = -8

Answer:

A. -8

Step-by-step explanation:

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