Find the number if:
4.5% of it is 23% of 4

Answer:

712,402,207

Step-by-step explanation:

;)

Answer: 711,142,207

Step-by-step explanation:

The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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Answer:

Step-by-step explanation:

£2.25 X 60 = £135

135 - 125= £10

£10/125 x 100 = 8%

Let Length of each Plan A workout be \( a\)

and Length of each Plan B workout be $b$

on Wednesday,

$5a+3b=7$

$2a+12b=19$

multiply equation one by $4$ and subtract equation two from it

to get,

$18a=9$ or $a=\frac12$

substitute $a$ in eq 2. to get $b$, $12b=18\implies b=\frac32$

Answer:

Negative correlation.

Step-by-step explanation:

Negative correlation means that as x increases, y decreases

Positive correlation means that as x increases, y also increases.

No correlation means that neither of the two above cases happens.

In the graph, we can see that on the right (when x is negative) the general y values are larger.

As x increases, the y-values decrease.

(Particularly, we could adjust these data with a linear equation with a negative slope)

Then this is a negative correlation.

Answer:

15ways

Step-by-step explanation:

This question bothers combination

Combination has to do with selection

Given

Total number of teams  = 6

champion and runner up = 2

number of ways is expressed as 6C2

6C2 = 6!/(6-2)!2!

6C2 = 6!/4!2!

6C2 = 6*5*4!/4!*2

6c2 = 30/2

6C2 = 15

Hence the number of ways they can be selected is 15ways

Mrs. Rosenblatt's class has an average grade of 87. After realizing she left out Joe's score of 65, the new mean will be lower than 87.

Explanation:

To find the new mean, we need to calculate the sum of all the grades in the class, including Joe's score of 65, and divide it by the total number of students in the class. Let's assume there are n students in the class.

The sum of all the grades in the class, including Joe's score, will be (87 * n) + 65, since the average grade before Joe's score was added was 87. Therefore, the new mean will be:

[(87 * n) + 65] / (n + 1)

Expanding this expression, we get:

(87n + 65) / (n + 1)

Simplifying this expression, we get:

(87n / (n + 1)) + (65 / (n + 1))

Since n is a positive integer, the value of (87n / (n + 1)) will be slightly less than 87. Therefore, the new mean will be slightly less than 87, reflecting the lower score added to the class average.

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12. 5x² - 180 = 0

5x² = 0 + 180

5x² = 180

x² = 180/5

x² = 36

x = √36

x = 6

13. 3x² - 100 = 332

3x² = 332 + 100

3x² = 432

x² = 432/3

x² = 144

x = √144

x = 12

14. ⅔x² - 8 = 16

⅔x² = 16 + 8

⅔x² = 24

2x² = 24 × 3

2x² = 72

x² = 72/2

x² = 36

x = √36

x = 6

15. ½x² - 5 = 5

½x² = 5 + 5

½x² = 10

x² = 10 × 2

x² = 20

x = √20

16. x² + 1 = 3x² - 13

1 + 13 = 3x² - x²

14 = 2x²

14/2 = x²

7 = x²

√7 = x

17. 2(x² + 4) = 10

2x² + 8 = 10

2x² = 10 - 8

2x² = 2

x² = 2/2

x² = 1

x = √1

x = 1

18. 3(x² - 1) = 9

3x² - 3 = 9

3x² = 9 + 3

3x² = 12

x² = 12/3

x² = 4

x = √4

x = 2

19. 2(x + 3)² = 8

2(x² + 3² + 2×x×3) = 8

2(x² + 9 + 6x) = 8

2x² + 18 + 12x = 8

2x² + 12x = 8 - 18

2x² + 12x = -10

2(x² + 6x) = -10

x² + 6x = -10/2

x(x + 6) = -5

x + 6 = -5/x

6 = -5/x - x

6 = -5/x - x²/x

6 = (-5 -x²)/x

6x = -5 - x²

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

\(\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}\)

and flows out at a rate of

\(\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}\)

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

\(\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))\)

Multiply both sides by the integrating factor, \(e^{t/180}\), and rewrite the left side as the derivative of a product.

\(e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))\)

\(\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))\)

Integrate both sides with respect to t (integrate the right side by parts):

\(\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt\)

\(\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C\)

Solve for A(t) :

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}\)

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

\(\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}\)

So,

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}\)

Recall the angle-sum identity for cosine:

\(R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)\)

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

\(R \cos(\theta) = -\dfrac{66,096,000}{32,401}\)

\(R \sin(\theta) = \dfrac{367,200}{32,401}\)

Recall the Pythagorean identity and definition of tangent,

\(\cos^2(x) + \sin^2(x) = 1\)

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

Then

\(R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}\)

and

\(\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)\)

so we can rewrite A(t) as

\(\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}\)

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

\(24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}\)

and

\(24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}\)

which is to say, with amplitude

\(2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}\)

17) \(x+2x+1+3x=\boxed{6x+1}\)

18) \(17-a+5a-1+4ab=\boxed{4ab+4a+16}\)

19) \(2(3y-5+y+2)=\boxed{8y-6}\)

20) \(k^2 +k+k^2 -9k+23+k^2 +k+2k^2 -17=\boxed{5k^2 -7k+6}\)

\( \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 893(1 + \frac{41}{500} ) ^{1 \times 5} - 893 \\ \sf= 893 \times ( \frac{541}{500} ) ^{5} - 893 \\ \sf= 1324.30 - 893 \\ \sf = 431.30\)

Answer:

$431.30(approximate value)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer: 2 ≤ x < 7

Step-by-step explanation:

10 ≤ 3x + 4 < 25  ==> solve for x, so work to isolate the x variable

10-4 ≤ 3x + 4-4 < 25-4

6 ≤ 3x < 21

6/3 ≤ 3x/3 < 21/3

2 ≤ x < 7

Answer:

I believe it's [2, 7). It has to be solve differently.

Equation 6: x = (11y + 3z - 303) / 16

Equation 9: 811y + 387z = 2,745

What is Elimination?

The method of elimination is where you actually eliminate one of the variables by adding two equations. In this way, you remove one variable in order to solve for the other variable. In a system of two equations, since you have two variables, eliminating one greatly simplifies the process of solving for the other.

To solve the system of equations using elimination, we'll eliminate one variable at a time until we find the values of x, y, and z.

Multiply the second equation by 2 and the third equation by -3 to make the coefficients of z the same in both equations:

Equation 2: 2x - 12y - 12z = 6

Equation 3: 12x - 9y - 6z = -42

Add the first equation to the modified second equation and the modified third equation:

Equation 1 + Equation 2: -6x - 5y - 3z + 2x - 12y - 12z = 393 + 6

=> -4x - 17y - 15z = 399 (Call this Equation 4)

Equation 1 + Equation 3: -6x - 5y - 3z + 12x - 9y - 6z = 393 - 42

=> 6x - 14y - 9z = 351 (Call this Equation 5)

Multiply Equation 5 by 2 and subtract Equation 4 from it:

2 * Equation 5 - Equation 4: 12x - 28y - 18z - (-4x - 17y - 15z) = 702 - 399

=> 16x - 11y - 3z = 303 (Call this Equation 6)

Multiply Equation 4 by 16 and add it to Equation 6:

16 * Equation 4 + Equation 6: -64x - 272y - 240z + 16x - 11y - 3z = 16 * 399 + 303

=> -48x - 283y - 243z = 6,399 (Call this Equation 7)

Divide Equation 7 by -1 to simplify the coefficients:

Equation 7: 48x + 283y + 243z = -6,399

Now we have the following system of equations:

Equation 6: 16x - 11y - 3z = 303

Equation 7: 48x + 283y + 243z = -6,399

We can solve this system using further elimination or substitution. Let's solve it using substitution.

From Equation 6, solve for x:

16x = 11y + 3z - 303

x = (11y + 3z - 303) / 16

Substitute this value of x into Equation 7:

48[(11y + 3z - 303) / 16] + 283y + 243z = -6,399

Simplify the equation:

528y + 144z - 9,144 + 283y + 243z = -6,399

Combine like terms:

811y + 387z = 2,745 (Call this Equation 8)

Now we have the following system of equations:

Equation 6: x = (11y + 3z - 303) / 16

Equation 8: 811y + 387z = 2,745

We can solve this system by further substitution or using a numerical method. Let's solve it using substitution.

From Equation 6, solve for x:

x = (11y + 3z - 303) / 16

Substitute this value of x into Equation 8:

811y + 387z = 2,745

Simplify the equation:

811y + 387z = 2,745 (Call this Equation 9)

Now we have the following system of equations:

Equation 6: x = (11y + 3z - 303) / 16

Equation 9: 811y + 387z = 2,745

We can solve this system by further substitution or using a numerical method. Let's solve it using a numerical method such as Gaussian elimination or matrix inversion.

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Answer: 3rd brand.

Step-by-step explanation:

1st brand:

6 oz cost $1.25

The amount per ounce will be:

= $1.25/6

= $0.21

2nd brand:

8 oz cost $1.33

The amount per ounce will be:

= $1.33/8

= $0.17

3rd brand:

12 oz cost $1.50

The amount per ounce will be:

= $1.50/12

= $0.125

4th brand:

16 oz cost $2.10

The amount per ounce will be:

= $2.10/16

= $0.13

From the calculation, the 3rd brand of orange juice is the better but as it's cheaper than others.

Answer: y = -4x + 3

Step-by-step explanation:

   First, we will write 8x+2y=14 in slope-intercept form.

8x+2y=14

2y = -8x + 14

y = -4x + 7

   Next, we will take this new slope-intercept form equation, y = -4x + 7, and use the slope from it to substitute the coordinate point given to find the y-intercept of the equation we are trying to find.

y = -4x + b

(-5) = -4(2) + b

-5 = -8 + b

b = 3

   Lastly, we will write our equation with a slope of -4 and a y-intercept of 3.

         y = -4x + 3

The evaluation of  the function requested in fraction in lowest terms is \(\frac{4}{5}\)

This question can be associated to the trigonometry questions, which implies that the figure that was given in the question is a right triangle,  whereby the ratio sine  can be defined as ;

\(\\\\ sin(x) = \frac{opposite}{hypotenuse}\)

In this case we can se that the x is the angle and  the opposite leg tht can be associated to angle A measures 28, as it can be seen the hypotenuse measures 35 which implies that ;

\(sin(A) = \frac{28}{35}\)

\(\frac{4}{5}\)

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Two expressions with an equal sign is called as Equation. If the difference between two numbers is 12. The first number is 5 less than twice the second number then the two numbers are 29 and 17.

Two expressions with an equal sign is called as Equation.

Let the two numbers be a and b.

Given equation is a-b=12 .....(1) and

The first number is 5 less than twice the second number i.e a=2b-5

Substitute a in (1)

2b-5-b=12

b-5=12

b=17

b=17 is the second number.

Now we have to find first number so

a=2b-5...(2)

Substitute b=17 in (2)

a=2(17)-5

=34-5

=29

Therefore the two numbers are 29 and 17.

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The number of ways can the selection be made is 84.

Given:

an executive hires 3 office workers from 8 applicants.

a ) .

Number of ways = C ( 8 , 3 )

C ( n , r ) = n! / ( n - r ) ! r!

C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!

= 8! / 5! * 3 !

= 8 * 7 * 6 * 5! / 5! * 3!

= 56 * 6 / 3!

= 56 * 6 / 3 * 2 * 1

= 56 * 3 / 2 * 1

= 28 * 3 / 1

= 28 * 3

= 84 ways

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Answer:

84 counters

Step-by-step explanation:

⅖ + ½ = 7/10

10 - 7 = 3

280 ÷ 10 × 3 = 84

Answer:

28

Step-by-step explanation:

1/2×280=140(red counters)

2/5×280=112(yellow counters)

140+112=252

280-252=28(green counters)

Answer:

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Step-by-step explanation:

\( 5x^2 - 2 = 4x \)

\( 5x^2 - 4x - 2 = 0 \)

\( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

\( x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)} \)

\( x = \dfrac{4 \pm \sqrt{16 + 40}}{10} \)

\( x = \dfrac{4 \pm 2\sqrt{14}}{10} \)

\( x = \dfrac{2 \pm \sqrt{14}}{5} \)

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Answer:

Answer:

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

Step-by-step explanation:

5x^2 - 2 = 4x5x

2

−2=4x

5x^2 - 4x - 2 = 05x

2

−4x−2=0

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=

2a

−b±

b

2

−4ac

x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)}x=

2(5)

−(−4)±

(−4)

2

−4(5)(−2)

x = \dfrac{4 \pm \sqrt{16 + 40}}{10}x=

10

4±

16+40

x = \dfrac{4 \pm 2\sqrt{14}}{10}x=

10

4±2

14

x = \dfrac{2 \pm \sqrt{14}}{5}x=

5

2±

14

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

Answer:

C and H

Explanation:

All others are not the same shape, they tend to be pointing in different directions.

Answer:

a c h g f

Step-by-step explanation:

False.

For a square matrix A, the vectors in the column space of A (col(A)) are not necessarily orthogonal to the vectors in the null space of A (nul(A)). The column space consists of all possible linear combinations of the columns of A, while the null space consists of all vectors that satisfy the equation Ax = 0.

Orthogonality between col(A) and nul(A) would imply that any vector in col(A) is perpendicular to any vector in nul(A), which is generally not the case. There may exist some specific scenarios where col(A) and nul(A) have orthogonal vectors, but it is not a general property.

Therefore, the statement that vectors in the column space of a square matrix A are orthogonal to vectors in the null space of A is false.

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8x + 7 = -25

=>  8x = -25 - 7 = -32

=> x = -32/8 = -4

Answer:

-4=x

Step-by-step explanation:

8x+7(-7)=-25(-7)

8x(/8)=-32(/8)

-4=x

The diagram that shows all the lines of symmetry is diagram B.

We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).

With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.

So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.

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The distance between N and PS is 3.2.

What is the midpoint of the segment?

Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.

From the below figure,

N is the intersection of the red and blue circles.

I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).

Then the formula for the red circle is:

             (x-2)² + (y-4)² = 4.

The formula for the blue circle is

                  x² + y²- 16 = 0.

Solving for x and y yields intersections

               (0, 4) and (3.2, 2.4),

the first being S and the latter being N.

Hence, the distance between N and PS is 3.2.

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To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.

In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.

Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.

The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.

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