An atom of silicon is approximately 0.00000000025 meters wide. How do you express that number in scientific notation? O 25 10-10 meters O 2.5 × 10-11 meters O 2.5 1010 meters O 2.5 x 10-10 meters​

(a) The function f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto).

(b) The inverse function of f is f⁻¹(x) = ∛((x + 2)/4).

(a) To show that the function f: R → R defined by f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto):

Injectivity: Suppose we have two values x₁ and x₂ in the domain such that f(x₁) = f(x₂). We need to prove that x₁ = x₂. So, let's assume 4x₁³ - 2 = 4x₂³ - 2. By simplifying, we get 4x₁³ = 4x₂³.

Dividing both sides by 4 gives us x₁³ = x₂³.

Taking the cube root of both sides gives x₁ = x₂. Therefore, the function f is injective.

Surjectivity: For surjectivity, we need to show that for every y in the codomain (R), there exists at least one x in the domain (R) such that f(x) = y. Let's take an arbitrary y ∈ R.

We need to find an x such that f(x) = y. Solving the equation 4x³ - 2 = y for x, we have x = ∛((y + 2)/4). Thus, for any y in the codomain, there exists an x in the domain such that f(x) = y. Therefore, the function f is surjective.

(b) To find f⁻¹(x) (the inverse function of f), we interchange the roles of x and f(x) in the original function equation and solve for x.

Start with y = 4x³ - 2 and solve for x:

y + 2 = 4x³

x³ = (y + 2)/4

x = ∛((y + 2)/4)

Thus, the inverse function of f is f⁻¹(x) = ∛((x + 2)/4).

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We know that the probability of an event or other is additive, so we will have that the probability that sneakers or boots will be the favorite shoe of the next reader is:

So, the probability is 70%.

The probability that Z falls between 1.05 and 2.13 is 0.1307.

We know that a standard normal distribution has a mean of 0 and a standard deviation of 1. We want to find the probability that the random variable Z falls between 1.05 and 2.13.

To solve this problem, we need to find the area under the standard normal curve between the Z-scores of 1.05 and 2.13. We can use a standard normal table or calculator to find this probability.

Using a standard normal table, we can find the probability of Z being less than 2.13 and subtract the probability of Z being less than 1.05.

The value for Z = 2.13 can be looked up in the standard normal table and we find that the corresponding probability is 0.9838.

The value for Z = 1.05 can also be looked up and we find that the corresponding probability is 0.8531.

Therefore, P(1.05 ≤Z≤2.13) = P(Z ≤ 2.13) - P(Z ≤ 1.05) = 0.9838 - 0.8531 = 0.1307.

Therefore, the probability that Z falls between 1.05 and 2.13 is 0.1307.

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Answer:

$312.5

Step-by-step explanation:

#250÷8=$31.25

#$31.25*10=$312.5

You have to show the picture of what your talking about. Please do so if you want someone to answer your question.

Step-by-step explanation:

Interior angles of a 5-gon    sum to   ( 5-2)(180 = 540 degrees

smallest angle =x

largest angle = x + 4d    

          where d is the arithmetic sequence common difference

x + 4d     -x     =  44    shows d = 11

then    x    + x+d    + x+2d   + x+3d   + x + 4d = 540

      5x + 10d = 540      we know d = 11

       5x + 10(11) = 540

         5x = 430

           x = smallest angle = 86 degrees

The smallest interior angle of the pentagon is 86 degrees. This was found by setting up an equation involving the common difference "d" in the arithmetic sequence of angles and solving for "x."

Let's denote the five interior angles of the pentagon as follows:

Let the smallest angle be "x" degrees.

The other four angles form an arithmetic sequence, so we can represent them as x + d, x + 2d, x + 3d, and x + 4d, where "d" is the common difference between the angles.

Now, we know that the difference between the largest angle and the smallest angle is $44^\circ$. Therefore, we can write the equation:

(x + 4d) - x = $44^\circ$

Simplify and solve for "d":

4d = $44^\circ$

Now, divide both sides by 4 to find the value of "d":

d = $44^\circ / 4 = $11^\circ

Now that we know the common difference "d" is $11^\circ", we can find the smallest angle "x" by using the equation for the sum of angles in a pentagon, which is 540 degrees:

x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 540

Simplify and solve for "x":

5x + 10d = 540

5x + 10($11^\circ) = 540

5x + $110 = 540

Now, subtract $110 from both sides:

5x = 540 - $110

5x = $430

Finally, divide by 5 to find the smallest angle "x":

x = $430 / 5 = $86

So, the smallest angle of the pentagon is $86 degrees.

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Yes, it is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. By dilating the photo, it will be enlarged to fit the frame. Dilating a photo involves scaling it up or down to fit a particular size.

This is possible since dilating a photo is done proportionally. This implies that if the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same. Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame. It is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. Dilating a photo involves scaling it up or down to fit a particular size. This is possible since dilating a photo is done proportionally. If the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same.Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame. By dilating the photo, it will be enlarged to fit the frame.The process of dilating a photo can also be represented as a mathematical equation. The equation is as follows:y = kx where:y is the new height of the photo x is the original height of the photo k is the scale factor If the scale factor, k, is greater than 1, the photo will be enlarged, while if the scale factor is less than 1, the photo will be reduced. Therefore, if the scale factor, k, is 2, then the height of the photo will be multiplied by 2, resulting in a photo that is 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame.

In conclusion, it is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. Dilating a photo involves scaling it up or down to fit a particular size. This is done proportionally, meaning that if the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same. Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame.

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Answer: x= -1, 3, 0

I know these are right because I just took the test

The given expression is undefined for the values -1,3 and 0.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The expression is \(\dfrac{x-1}{x^2-2x-3}+\dfrac{5}{2x^2+2x}\).

The expression is not defined as points -1,3 and 0 check all the points.

At x = - 1

\(E=\dfrac{-1-1}{(-1)^2-2(-1)-3}+\dfrac{5}{2(-1)^2+2(-1)}\\E=\dfrac{-2}{0}+\dfrac{5}{0}\)

The expression is not defined. Similarly, you can check for points 3 and 0 the expression is not defined.

Therefore, the given expression is undefined for the values -1,3 and 0.

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

A Type II error would occur in the case where we do not conclude malathion is effective when in fact it was effective.

This means that we fail to reject the null hypothesis (that Malathion has no effect on reducing the number of beetles) when in reality, the alternative hypothesis (that Malathion does reduce the number of beetles) is true.

In other words, we incorrectly accept the null hypothesis and miss detecting a true effect of Malathion.

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Answer:y= x + 7 +10

Step-by-step explanation:

Answer:

its y = x-5 -10

Step-by-step explanation:

b on edge 2020

Answer:$300

divide any one of the outcomes and it should equal 300. something that might help is removing the zeros. 6 divided by 2 is 3. you them add the zeros you took off back on and get 300.

Answer:

Wheres the polygon ?

Step-by-step explanation:

\((i)\\\\2A = \begin{pmatrix}3x \times 2 & 1 \times 2 & 5 \times 2\\0\times 2 & 2x \times 2 & -3 \times 2\end{pmatrix} = \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix}\\\\\\(ii)\\\\2A + B = C\\\\\implies \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix} + \begin{pmatrix}y & 0 & -4\\1 & -3y & 2\end{pmatrix} = \begin{pmatrix}31& 2 & 6\\1 & 17& -4\end{pmatrix}\)

\(\implies \begin{pmatrix}6x+y & 2+0 & 10-4\\0+1 & 4x-3y & -6+2\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\\\implies \begin{pmatrix}6x+y & 2 & 6\\1 & 4x-3y & -4\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\text{System of equations},\\\\6x +y =31,~~ 4x -3y = 17\\\\\\(iii)\\\\6x +y-31 =0 \\\\4x-3y -17=0\\\\\text{Solving by cross multiplication method}\\\\\\\dfrac x{1(-17) - (-31)(-3)} = \dfrac y{4(-31) - 6(-17)} = \dfrac 1{6(-3) - 4(1)}\)

\(\implies \dfrac{x}{-17 -93} = \dfrac{y}{-124 +102} = \dfrac 1{-18-4}\\\\\\\implies -\dfrac{x}{110} = -\dfrac{y}{22} = -\dfrac 1{22}\\\\ \implies \dfrac{x}{110} = \dfrac{y}{22} = \dfrac 1{22}\\\ \\\text{Hence,}\\\\\\x=\dfrac{110}{22}=5,~~~~ y= \dfrac{22}{22} =1\)

Answer:

  (i)

  \(2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right]\)

  (ii) 6x+y=31; 4x-3y=17

  (iii) (x, y) = (5, 1)

Step-by-step explanation:

The matrix 2A is written by multiplying each element of A by 2.

  \(2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right]\)

__

Variables are seen in elements (1, 1) and (2, 2) of the matrices A and B, so the simultaneous equations can be chosen from those elements of the equation 2A+B=C.

__

A graphing calculator shows the solution to be (x, y) = (5, 1).

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

We know that the section formula states that if a point P(x,y) lies on line segment AB joining the points A(x

1

,y

1

) and B(x

2

,y

2

) and satisfies AP:PB=m:n, then we say that P divides internally AB in the ratio m:n. The coordinates of the point of division has the coordinates

P=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let C(1,1) divides the line segment AB joining the points A(−2,7) and B(x

2

,y

2

) in the ratio 3:2, then using section formula we get,

C=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

⇒(1,1)=(

3+2

3x

2

+(2×−2)

,

3+2

3y

2

+(2×7)

)

⇒(1,1)=(

5

3x

2

−4

,

5

3y

2

+14

)

⇒1=

5

3x

2

−4

,1=

5

3y

2

+14

⇒5=3x

2

−4,5=3y

2

+14

⇒3x

2

=5+4,3y

2

=5−14

⇒3x

2

=9,3y

2

=−9

⇒x

2

=

3

9

,y

2

=−

3

9

⇒x

2

=3,y

2

=−3

Hence, the point B(x

2

,y

2

) is B(3,−3).

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

The total sample size that is needed is 402.

Given that,

South :

Proportion, p = 0.189

Alpha = 1 - 95%

        = 0.05

Z Critical value = 1.96

[ UseExcel Function : " =NORMSINV(1-(0.05/2)) " ]

Margin of Error should be less than 0.05

Sample Size Formula is

Sample Size, n = (Z2)*p*(1-p)/(E2)

                      = (1.962)*0.189*(1-0.189)/(0.052)

                      = 235.53

                      = 236

Northeast :

Proportion, p = 0.123

Alpha = 1 - 95%

        = 0.05

Z critical value = 1.96

[ UseExcel Function : " =NORMSINV(1-(0.05/2)) " ]

Margin of Error should be less than 0.05

Sample Size Formula is

Sample Size, n = (Z2)*p*(1-p)/(E2)

                      = (1.962)*0.123*(1-0.123)/(0.052)

                      = 165.75

                      = 166

Therefore, total sample Size needed is 236 + 166 = 402

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The value of 42° 18' - 23° 56' is 18° 22'.

To perform the calculation 42° 18' - 23° 56', we need to subtract the minutes and degrees separately.

For the minutes:

18' - 56' = -38' (since 18' is smaller than 56')

For the degrees:

42° - 23° = 19°

Combining the degrees and minutes, we have:

19° - 38'

Since the minutes result in a negative value, we need to borrow 1 degree from the 19°. Thus, the final result is:

18° 22'

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Answer:

corresponding angles, alternate exterior angles

Step-by-step explanation:

when you have to parallel lines cut be a transversal, you get different pairs of angles that are either equal or supplementary (add to 180).

For example, corresponding angles are congruent, and alternate exterior angles are congruent.

Answer:

∠DAB = ∠DBA

Then AD=DB from above statement

A spurious correlation is a correlation between two variables that appears to be causally linked but is actually due to the influence of a third variable that is not considered. The correct answer is  spurious correlation.

Spurious correlations are correlations that exist between two variables, but they are not actually causally related to one another, despite the fact that they appear to be causally related at first glance. The relationship between two variables may be accounted for by a third variable that was previously overlooked or not considered, causing the original correlation to be explained away. Spurious correlations are commonly found in science and research, and they can lead to misleading results if not properly identified and accounted for. It is critical to account for all potential confounding variables in order to establish causal links between variables and avoid spurious correlations. Therefore, researchers must carefully consider all variables that might influence the relationship between two variables to avoid drawing inaccurate conclusions.

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Answer:

(4,19)

Step-by-step explanation:

Cuz if u substitute these values in for the x and y in the equation, the equation would be true:

1.) 19 = 7(4) - 9

2.) 9 ≠ 7(54) - 9

3.) 30 ≠ 7(-3) - 9

4.) 15 ≠ 7(2) - 9

As you can see, 1st equation is the only equation that's true.

Hope this helps!

Answer:

Dilation

Step-by-step explanation:

Option B