Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.

Answer:

3

Step-by-step explanation:

-2=0+x

x¹=-2 (purple one)

4=2x-2

2x=6

x²=3 (green one)

Answer:

36 x^3 - 32 x^2 + (x + 4) (x^2 - 6 x + 3).x^3 - 62 x + 12

Step-by-step explanation:

Answer:

x^6-2x^5-21x^4+48x^3-32x^2-62x+12

Step-by-step explanation:

Mark me as brainliest!!!!

[tex]\\ \sf\longmapsto \dfrac{4}{m+m}\times \dfrac{4}{m-m}[/tex]

[tex]\\ \sf\longmapsto \dfrac{4\times 4}{(m+m)(m-m)}[/tex]

[tex]\boxed{\sf (a-b)(a+b)=a^2-b^2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{16}{m^2-m^2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{16}{0}[/tex]

[tex]\\ \sf\longmapsto \infty[/tex]

Answer:

(16-m^4)/m^2

Step-by-step explanation:

=([tex]\frac{4}{m}[/tex]+m)([tex]\frac{4}{m}[/tex]-m)

=[tex]\frac{4+m^2}{m}[/tex]*[tex]\frac{4-m^2}{m}[/tex]  (LCM)

[tex]\frac{16-m^4}{m^2}[/tex] (a-b)(a+b)

Answer:

The selling price after the markup is $1.82

Step-by-step explanation:

$1.40 * .30 =

Multiply $1.40 times .30 (which is same as 30%)

$1.40 * .30 = $0.42

Add $1.40 and $0.42

= $1.82

Hope this helps.

Answer:

[tex]\frac{19351}{11220}[/tex]

Step-by-step explanation:

[tex]\frac{2640+3366+5049+3060+5236}{11220} = \frac{19251}{11220}[/tex]

9514 1404 393

Answer:

  (c)  On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.

Step-by-step explanation:

The x-coefficient is positive, so we can determine the shading from ...

  2x ... < ... (pay attention to the x-term and the inequality symbol)

That is, the solution region will have x values that are less than those on the (dashed) boundary line. Lower x-values are to the left, hence shading is on the left side of the boundary. (That's all you need to know here to make the correct choice.)

_____

Additional comment

If the choices are "above" or "below", then you will want to look at the y-term and the inequality symbol. If the coefficient of the variable of interest is negated (as it is for y here), then you need to consider the inequality symbol reversed: -y < ...   ⇔   y > .... Here, that means the shading is above the line. Since the slope of the line is positive, "left" and "above" are the same thing.

Answer:

c

Step-by-step explanation:

E2021

Answer:

Hey there!

All of the values: 0, 3, and 4 are in the domain.

This is because h(x) = (x - 3)^2 is a parabola, or a quadratic. By definition, the domain, or the possible x values of a parabola are infinite.

Hope this helps :)

Answer:

28

Step-by-step explanation:

Find the gcf

Answer:

a^2 - b^2 = (a-b)(a+b)

Step-by-step explanation:

x^2 -9

Rewriting as

x^2 - 3^2

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

x^2 - 3^2 = (x-3)(x+3)

Answer:

The chi - square test can be [tex]\approx[/tex] 0.667

Step-by-step explanation:

From the given data :

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis: The number of customers does  follow  a uniform distribution

Alternative hypothesis: The number of customers does not  follow  a uniform distribution

We learnt that: Carl recorded the number of customers who visited his new store during the week:

Day              Customers

Monday               17

Tuesday              13

Wednesday         14

Thursday              16

The above given data was the observed value.

However, the question progress by stating that : He expected to have 15 customers each day.

Now; we can have an expected value for each customer  as:

                      Observed Value                   Expected Value

Day                 Customers                        

Monday                17                                          15

Tuesday               13                                          15

Wednesday          14                                          15

Thursday               16                                         15

The Chi square corresponding to each data can be determined by using the formula:

[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]

For Monday:

[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Tuesday :

[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Wednesday :

[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

For Thursday:

[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

                   Observed Value   Expected Value    chi - square

Day                 Customers                        

Monday                17                     15                       0.2666666667

Tuesday               13                     15                       0.2666666667

Wednesday          14                     15                       0.06666666667

Thursday               16                    15                       0.06666666667

Total :                                                                        0.6666666668

The chi - square test can be [tex]\approx[/tex] 0.667

At level of significance ∝ = 0.10

degree of freedom = n - 1

degree of freedom = 4 - 1

degree of freedom = 3

At ∝ = 0.10 and df = 3

The p - value for the chi - square test statistics is 0.880937

Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis

Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.

Answer:.67

Step-by-step explanation:

Answer:a

a

   [tex]336.04 < \mu < 443.96[/tex]

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  [tex]0.4107 < p < 0.4293[/tex]

Step-by-step explanation:

From the question we are  told that

   The sample size  [tex]n = 19[/tex]

    The sample mean is  [tex]\= x = \$\ 390[/tex]

    The  standard deviation is  [tex]\sigma = \$ \ 120[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

           [tex]\alpha = 100 - 95[/tex]

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

    So  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  margin of error is mathematically represented as

      [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]

=>   [tex]E = 53.96[/tex]

The 95% confidence interval is  

     [tex]\= x - E < \mu < \= x + E[/tex]

=>   [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]

=>  [tex]336.04 < \mu < 443.96[/tex]

When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         [tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       [tex]\r p = \frac{210}{500}[/tex]

       [tex]\r p = 0.42[/tex]

Given that the confidence level is 0.99 the level of significance is  [tex]\alpha = 0.01[/tex]

The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

  Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]

=>   [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]

=>     [tex]E = 0.0093[/tex]

The 99% confidence interval  is

     [tex]\r p - E < p < \r p + E[/tex]

     [tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]

     [tex]0.4107 < p < 0.4293[/tex]

Answer:

A. 17 years

Step-by-step explanation:

Use the simple interest equation, I = prt, where I is the interest money gained, p is the starting amount of money, r is the interest rate in decimal form, and t is the time in years.

Plug in the values to solve for t:

417.69 = (630)(0.039)(t)

417.69 = 24.57t

17 = t

= 17 years

So, the correct answer is A, 17 years

Answer:

[tex]\bold{4\sqrt3 + i4}[/tex]

Step-by-step explanation:

Given complex number is:

[tex][2(cos10^\circ + i sin10^\circ)]^3[/tex]

To find:

Answer in rectangular form after using De Moivre's theorem = ?

i.e. the form [tex]a+ib[/tex] (not in forms of angles)

Solution:

De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.

As per De Moivre's theorem:

[tex](cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))[/tex]

So, the given complex number can be written as:

[tex][2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3[/tex]

Now, using De Moivre's theorem:

[tex]\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}[/tex]

So, the answer in rectangular form is:

[tex]\bold{4\sqrt3 + i4}[/tex]

Answer:

Step by step proof shown below.

Step-by-step explanation:

To prove the equation, you need to apply the Logarithm quotient rule and the Logarithm power rule. Here's how the quotient rule looks like.

[tex]log_b(x/y) = log_b(x) - log_b(y)[/tex]

And here's how the power rule looks like

[tex]log_a(x)^n = nlog_a(x)[/tex]

First let's apply the quotient rule.

[tex]\frac{f(x+h)-f(x)}{h} = \frac{log_a(x+h)-log_a(x) }{h} = \frac{log_a(\frac{x+h}{x} )}{h}[/tex]

Now we can do some quick simplification, and apply the power rule.

[tex]\frac{1}{h} log_a(1 + \frac{h}{x} ) = log_a(1+\frac{h}{x} )^\frac{1}{h}[/tex]

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

b.) 0.30

Step-by-step explanation:

15/50 = 0.3

Answer:

Answer is (x - 1)² = 4

Step-by-step explanation:

[tex]{ \tt{ {x}^{2} - 2x - 3 = 0}} \\ [/tex]

By completing squares:

[tex]{ \tt{ {x}^{2} - 2x + { (\frac{2}{2} )}^{2} - 3 - {( \frac{2}{2}) }^{2} = 0 }} \\ { \tt{( {x}^{2} - 2x + 1) = 4}} \\ { \tt{(x - 1) {}^{2} = 4 }}[/tex]

[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]

Answer:

0.801

Step-by-step explanation:

Answer:

0.801

Step-by-step explanation:

801/1000 = 0.801

Answer:

d the answer is d

Step-by-step explanation:

Set up a ratio:

6/11 = x/26

Cross multiply:

11x = 156

Divide both sides by 11:

X = 14.18 feet ( round answer as needed.)

Answer:

2.63%

Step-by-step explanation:

11.3/100*23.3/100*100%

On a number​ line, the coordinates of​ X, Y,​ Z, and W are −7​, −2​, 2​, and 7​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and

Answer:

1. x 55

2. y 117

x 51

3.x39

y116

4.x 18

5.x 48

y 14

for the last one I'm not sure. please give 5 start

Answer:

C

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Here r = 18 cm , thus

A = π × 18² = 324π ≈ 1017.9 cm² → C

Answer:

C.) 1017.9 cm²

Step-by-step explanation:

For a given circle

radius (r) = 18 cm

Now,

Area of Circle

= πr²

= 3.14 × (18)² cm

= 3.14 × 324 cm

= 1017.9 cm²

Answer:

  -3

Step-by-step explanation:

If these numbers are part of an arithmetic progression, their differences are the same:

  (x -7) -(2x +1) = (2x +1) -(x +3)

  -x -8 = x -2

  -6 = 2x

  -3 = x

___

The numbers in the sequence are 0, -5, -10.

Answer:

x = -3.

Step-by-step explanation:

As it is an Arithmetic Progression the differences between successive terms are common, so:

2x + 1 - (x + 3) = x - 7 - (2x + 1)

2x - x + 1 - 3 = x - 2x - 7 - 1

x - 2 = -x - 8

2x = -8 + 2 = -6

x = -3.

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

y = - 1/2x + 5

Comparing with the general equation above

Slope / m = -1/2

Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line

That's

Slope of the perpendicular line = 2

Equation of the line using point (–1, –2) and slope 2 is

y + 2 = 2( x + 1)

y + 2 = 2x + 2

y = 2x + 2 - 2

We have the final answer as

Hope this helps you

Answer:

C) y = 2x

Step-by-step explanation:

I got it right in the test !!

Answer:

the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.

Step-by-step explanation:

From the given information:

Sample size n = 200

The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.

∴

The population proportion [tex]p_o[/tex] = 1/2 = 0.5

NOW;

[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]

[tex]\sigma _p = \sqrt{0.00125}[/tex]

[tex]\sigma _p = 0.035355[/tex]

However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.

we use the Excel function as computed as follows in order to determine the z probability  = NORMSINV (0.9)

z value = 1.281552

Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)

[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

1.28 × 0.035355 = X - 0.5

0.0452544= X - 0.5

0.0452544 + 0.5 = X

0.5452544 = X

X [tex]\approx[/tex] 0.545

X = 54.5%

[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

- 1.28 × 0.035355 = X - 0.5

- 0.0452544= X - 0.5

- 0.0452544 + 0.5 = X

0.4547456 = X

X [tex]\approx[/tex] 0.455

X = 45.5%

Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.