10. How many different combinations are there of the digits 46987?

Answer:

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

Given a negative square root √(-x);

From our knowledge of complex numbers, we know that

i^2 = -1 and vise versa

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.

If A × A = B

Then √B = A.

Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.

2 × 2 = -2 × -2 = 4

3 × 3 = -3 × - 3 = 9

And so on.

So, the square root of 4 = 2 or -2

The square root of 9 = 3 or -3

But if one of the numbers is positive while the other is negative, then the result is negative.

2 × -2 = -4

3 × -3 = -9

Clearly, √(-4) ≠ 2 ≠ -2

√(-9) ≠ 3 ≠ -3

It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.

Let i² = -1, then we have that

√(-1) = i.

This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.

-A = -1 × A

So, √(-A) = √(-1 × A)

= √(-1) × √A

= i × √A

= i√A

Example, to simplify √(-16)

√(-16) = √(-1 × 16)

= √(-1) × √16

= i × ±4

= ±4i

Answer:

Temperature after 1 minute = 184 ° F

Step-by-step explanation:

starting temperature = 200 °F

rate of decrease = 8% per minute

Temperature lost = 8% of 200 = 8/100 × 200 = 0.08 × 200 = 16 °F

It therefore means that after 1 minute, the cup of coffee loses 16 °F,

∴ Temperature after 1 minute = (starting temperature) - (lost temperature)

= 200 - 16 = 184 °F

Answer:

6m = b

Step-by-step explanation:

The area of triangle when angle and sides are given = 1/2* sin angle*ab

Area = 1/2 * sin 30 * 4*b

Area = 6m²

6 = 1/2 * sin 30 * 4*b

(6*2)/(sin 30 * 4)= b

12/(0.5*4) = b

12/2 = b

6m = b

Answer:

1/8 but idk im not good with math

Step-by-step explanation:

Answer:

16-25

Step-by-step explanation:

Step  1  :

           2

Simplify   —

           5

Equation at the end of step  1  :

  24    2

 ——— +  —

 100    5

Step  2  :

            6

Simplify   ——

           25

Equation at the end of step  2  :

  6    2

 —— +  —

 25    5

Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.

This is best done in polar coordinates:

[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]

so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].

The lamina is then the set of points

[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]

Now compute the integral: the mass of the lamina is

[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]

Answer:

The area of the region is 25,351 [tex]units^2[/tex].

Step-by-step explanation:

The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then

                                   [tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]

where [tex]F[/tex] is an antiderivative of [tex]f[/tex].

A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if

                                                    [tex]F^{'}(x)=f(x)[/tex]

The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.

To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:

Apply the Fundamental Theorem of Calculus

[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]

[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]

[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]

Answer: (11/8)

Step-by-step explanation:

I will answer this in English.

a person collects 7/4 of an amount, spends 1/4 and lends 1/8. What fraction of the amount collected is left?

If the amount is A, then he collects:

C = (7/4)*A

Now, he spends 1/4 and lends 1/8 of the amount A, so the fraction left is:

Left = (7/4)*A - (1/4)*A - (1/8)*A

now i will write 7/4 as 14/8 and 1/4 as 2/8.

left = (14/8)*A - (2/8)*A - (1/8)*A  = ((14 - 2 - 1)/8)*A = (11/8)*A

The answer is [ 2 2 1]

look at the attached picture

Hope it helps

Good luck on your assignment

Answer:

Maths anxiety

Step-by-step explanation:

In a typical research study, there are basically 2 types of variables involved, which are the dependent and the independent variable.

The dependent variable is affected by other factors or the independent variable involved in the study. The dependent variable would change is the independent variable is manipulated, changed or varied.

The dependent variable in Joe's dissertation is MATHS ANXIETY, which is dependent on the gender of students. Gender is the independent variable as he wants to find out if there's any difference in maths anxiety between males and females.

The dependent variable is Math Anxiety which is dependent on gender of the students.

Answer:

Yes I believe the answer will be the same.

Step-by-step explanation:

Answer:

1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller

Step-by-step explanation:

Answer:

9x^3-21x^2+19x-6

Step-by-step explanation:

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6

9x^3-21x^2+19x-6

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6 is the answer to the question

Answer:

Not correct

Step-by-step explanation:

Sample 8 has one free throw, sample 9 has 3 free throw success,

sample 10 has 3 free throw success

sample 11 has 5 free throw success

sample 12 has 5 free throw success

sample 13 has 2 free throw success

sample 14 has 1 free throw success;

See one sample should contain 15 free throw and the probability of success should be 0.7

Let's look at sample 8

Total no of success is 1

Total no of free throws 15

Probability is 1/15 = 1/15 * 100 =6.67%

Similarly you can do so for the others.

Explanation:

The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.

320 + 25 + c = 430

         345 + c = 430

345 - 345 + c = 430 - 345

c = 85

The cost of the coat was $85.

Answer:

$85 for the coat

Step-by-step explanation:

1 dress = $80

4 dress =$80×4

=$320

sweater=$25

coat=?

4 dresses plus the sweater cost :

$320+$25=$345

The cost of all the item $430

cost of the coat :

$430-$345=$85

Answer:

Step-by-step explanation:

If they earned $440 in 40 hours

This means they earned 440÷40=11 in one hour

Sam makes x-2 amount of money per hour so the difference between Sam's and Joe's salary is $2

Find two numbers that add up to Ten and can subtract to make a difference of 2 (I am starting with ten as it is easier) 6+4=10 6-4=2

So to make 6 and. 4 add to make a 11 we need to add a 0.5 to each of them so 6.5+4.5=11 and 6.5-4.5= $2.

Therefore Joe makes $6.50 an hour and Sam makes £4.50

Answer:

2nd branch > 1st branch > 3rd branch

or

[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]

Step-by-step explanation:

Length of First branch = [tex]\frac{2}{3}[/tex] foot

Length of second branch = [tex]\frac{2}{2}[/tex] foot

Length of third branch = [tex]\frac{2}{8}[/tex] foot

Let us convert the fractions in decimal forms:

[tex]1.\ \dfrac{2}{3} = 0.67[/tex]

[tex]2. \dfrac{2}{2} = 1[/tex]

[tex]3.\ \dfrac{2}{8} = \dfrac{1}{4}=0.25[/tex]

It can be clearly seen that 1 is the largest value among the three values.

So, 2nd branch is the largest.

Now, let us have a look at the values of first and third branches:

0.67 and 0.25.

Clearly, 0.67 is greater than 0.25.

So, the correct order is:

2nd branch > 1st branch > 3rd branch

OR

We can use other method to see it.

Here, all the 3 fractions have same numerator.

So, denominator can help us decide the which fraction has a large value.

If numerator is same, the larger denominator will have smaller fractions.

The denominators are 2, 3 and 8.

8 > 3 > 2

So, the answer is

2nd branch > 1st branch > 3rd branch

or

[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]

Answer:

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 22, \sigma = 5.1[/tex]

Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?

The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{24 - 22}{5.1}[/tex]

[tex]Z = 0.39[/tex]

[tex]Z = 0.39[/tex] has a pvalue of 0.6517

1 - 0.6517 = 0.3483

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Answer:

D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Step-by-step explanation:

The scale factor is equal to 1. Hence, the quadrilateral A'B'C'D' will be identical to quadrilateral ABCD, whose vertices are the same.

The algebraic expression of the dilation is:

[tex](x',y') = (x,y)[/tex]

Besides, the coordinates of the new quadrilateral are A'(3, 3), B'(5, 3), C'(7, 1), and D'(1, 1)

And quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Therefore, the right answer is D.

Answer: D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Step-by-step explanation: just did a test with this question and got it right. Hope this helped! thx for the points :D

Answer:

2.5 ft

Step-by-step explanation:

As radius is perpendicular to tangent ,

LT [tex]\perp[/tex]KT

By pythagoras theorem:

LT² = LK² - KT²

LT² = (6.5)² - 6²

LT² = 42.25 - 36

LT² = 6.25

LT = 2.5 ft

LT = radius = 2.5 ft

Answer:

1 = D 75 inches

2 = A 27

Step-by-step explanation:

1 - 6.3 times 12 = 75.6

2 - 6 times 9 = 54

54/2 = 27

:)

Answer:

The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Step-by-step explanation:

We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.

Let X = Chipotle meals having calories

So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])

Now, the 68-95-99.7 rule states that;

So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;

                               [tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]

                                        =  -2

Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.

SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Answer:

A=9404

Step-by-step explanation:

Answer:

9404

Step-by-step explanation:

Answer:

x= 13.7 (nearest tenth)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

(-5,13)

Step-by-step explanation:

because t=3

[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]

Answer:

The answer is c

Step-by-step explanation:

The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

The congruent triangles are:

Triangle MNO and Triangle NMO

The above means that:

Sides MN and NO or MN and MO are equal

So, the triangles are isosceles triangles

However, it is possible that sides NO and MO are congruent

Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

Read more about congruent triangles at:

https://brainly.com/question/1675117

Answer:

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

  f(n) = -n^2 -3n +5

Step-by-step explanation:

Suppose the formula is ...

  f(n) = an^2 +bn +c

Then we have ...

  f(1) = 1 = a(1^2) +b(1) +c

  f(2) = -5 = a(2^2) +b(2) +c

  f(3) = -13 = a(3^2) +b(3) +c

__

Here's a way to solve these equations.

Subtract the first equation from the second:

  -6 = 3a +b . . . . . 4th equation

Subtract the second equation from the third:

  -8 = 5a +b . . . . . 5th equation

Subtract the fourth equation from the fifth:

  -2 = 2a

  a = -1

Then substituting into the 4th equation to find b, we have ...

  -6 = 3(-1) +b

  -3 = b

and ...

  1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation

  5 = c

The formula is ...

  f(n) = -n^2 -3n +5

Step-by-step explanation:

3 + 15 + 75 + 375 + 1,875

This is a geometric series.  The first term is 3, the common ratio is 5, and the number of terms is 5.

∑₁⁵ 3 (5)ⁿ⁻¹

∑₀⁴ 3 (5)ⁿ

3 + 12 + 48 + 192 + 768

This is a geometric series.  The first term is 3, the common ratio is 4, and the number of terms is 5.

∑₁⁵ 3 (4)ⁿ⁻¹

∑₀⁴ 3 (4)ⁿ

4 + 32 + 256 + 2048 + 16,384

This is a geometric series.  The first term is 4, the common ratio is 8, and the number of terms is 5.

∑₁⁵ 4 (8)ⁿ⁻¹

∑₀⁴ 4 (8)ⁿ

2 + 6 + 18 + 54 + 162

This is a geometric series.  The first term is 2, the common ratio is 3, and the number of terms is 5.

∑₁⁵ 2 (3)ⁿ⁻¹

∑₀⁴ 2 (3)ⁿ