Look at images below. : ]

Step-by-step explanation:

[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]

We have to find LCM

3 | 45,75,63

3 | 15,25,21

5 | 5,25,7

5 | 1,5,7

7 | 1,1,7

LCM=3×3×5×5×7=1575

The least common denominator for the group of denominators using the method of prime numbers is 1575.

LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers.  A factor is one of the numbers that multiplies by a whole number to get that number.

For the given situation,

The numbers are 45, 75, 63​

Prime factors of 45 = [tex]3,3,5[/tex]

Prime factors of 75 = [tex]3,5,5[/tex]

Prime factors of 63 = [tex]3,3,7[/tex]

Then the LCM can be found by, first take the common factors then multiple the remaining factors as,

⇒ [tex](3)(3)(5)(5)(7)[/tex]

⇒ [tex]1575[/tex]

Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.

Learn more about least common multiple here

https://brainly.com/question/24859913

#SPJ2

The estimated slope is approximately 2.344

The given table is presented as follows;

[tex]\begin{array}{ccc}Number \ of Bids &&Price \ in \ Dollars\\1&&23\\2&&34\\4&&44\\9&&46\\10&&50\end{array}[/tex]

The regression line formula to be considered = [tex]\bar u = b_0 + b\cdot \bar x[/tex]

The required parameter is;

The estimated slope

The method to find the estimate slope;

The least squares regression formula (method) is presented as follows;

[tex]\bar u = b_0 + b\cdot \bar x[/tex]

Where;

b₀ = The y-intercept

[tex]\mathbf{ b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right) }{\sum \left(x_i - \bar x\right )^2 } = The \ estimated \ slope}[/tex]

From MS Excel, we have;

[tex]\bar x[/tex] = 5.2, [tex]\bar u[/tex] = 39.4

[tex]\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right)[/tex] = 156.6

[tex]{\sum \left(x_i - \bar x\right )^2 }[/tex] = 66.8

Therefore;

The estimated slope, b = 156.6/66.8 ≈ 2.344 (by rounding the answer to three decimal places)

Learn more about regression line here;

https://brainly.com/question/23528764

Answer:

b. Kinsey must save $72 per month to achieve her goal.

Step-by-step explanation:

Goal over 16 months: $60 x 16 = $960

Collected after 11 months: $600

$360 ÷ 5 = $72

Kinsey must save $72 per month to achieve her goal. The answer we got by converting the sentence to Equation and solving.b is the required answer.

Kinsey has a plan to save $60 a month for 16 months so that she can purchase a new television. After 11 months Kinsey has saved $600. If the most that Kinsey can possibly save is $80 per month, which of the following statements given is true.

Two expressions with equal sign is called equation.

Goal over 16 months: $60 x 16 = $960

Collected after 11 months: $600

$360 still needed

5 months lefts

$360 ÷ 5 = $72

Therefore Kinsey must save $72 per month to achieve her goal.

To learn more about equations click here: https://brainly.com/question/19297665

#SPJ2

Answer:

A. QT ≅ AZ

Step-by-step explanation:

When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.

Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:

QP ≅ AR

PT ≅ RZ

QT ≅ AZ

The only correct one given in the options given above is QT ≅ AZ

[tex]\\ \sf\longmapsto 0.0000000015[/tex]

[tex]\\ \sf\longmapsto 0.0015\times 10^{-6}s[/tex]

[tex]\\ \sf\longmapsto 0.015\times 10^{-7}s[/tex]

[tex]\\ \sf\longmapsto 0.15\times 10^{-8}s[/tex]

[tex]\\ \sf\longmapsto 1.5\times 10^{-9}s[/tex]

Answer: 0.0000000015 = 1.5 × 10⁻⁹

Concept:

When converting an integer to scientific notation:

- If the number is ≥1, then count the moves of the decimal point to the right until the number is 0<number<10. The number of moves will be the exponent that is positive.

- For example: If converting 300, since there are two moves until it is left with 0<3<10. Thus, the scientific notation will be 3 × 10²

- If the number is <1, then count the moves of the decimal point to the left until the number is 0<number<10. The number of moves will be the exponent that is negative.

- For example: If converting 0.004, since there are three moves until it is left with 0<4<10. Thus, the scientific notation will be 4 × 10⁻³

Solve:

0.0000000015

The decimal point needs to move 9 times to the left to get a number that is between 0 and 10. The number is 1.5.

Thus, the scientific notion of 0.0000000015 will be 1.5 × 10⁻⁹

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4(x+4) =2x-18

4x+16=2x‐18

4x–2x= –18 –16

2x= – 34

x= –34/2

x= – 17

I hope I helped you^_^

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

Part A)

About 0.51% per year.

Part B)

About 0.30% per year.

Part C)

About 28.26%.

Step-by-step explanation:

We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:

[tex]f(t) = 10.72(0.9t+10)^{0.3}\text{ where } 0 \leq t \leq 20[/tex]

Where t is measured in years with t = 0 being the year 2000.

Part A)

Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:

[tex]\displaystyle f'(t) = \frac{d}{dt} \left[ 10.72\left(0.9t+10\right)^{0.3}\right][/tex]

Rewrite:

[tex]\displaystyle f'(t) = 10.72\frac{d}{dt} \left[(0.9t+10)^{0.3}\right][/tex]

We can use the chain rule. Recall that:

[tex]\displaystyle \frac{d}{dx} [u(v(x))] = u'(v(x)) \cdot v'(x)[/tex]

Let:

[tex]\displaystyle u(t) = t^{0.3}\text{ and } v(t) = 0.9t+10 \text{ (so } u(v(t)) = (0.9t+10)^{0.3}\text{)}[/tex]

Then from the Power Rule:

[tex]\displaystyle u'(t) = 0.3t^{-0.7}\text{ and } v'(t) = 0.9[/tex]

Thus:

[tex]\displaystyle \frac{d}{dt}\left[(0.9t+10)^{0.3}\right]= 0.3(0.9t+10)^{-0.7}\cdot 0.9[/tex]

Substitute:

[tex]\displaystyle f'(t) = 10.72\left( 0.3(0.9t+10)^{-0.7}\cdot 0.9 \right)[/tex]

And simplify:

[tex]\displaystyle f'(t) = 2.8944(0.9t+10)^{-0.7}[/tex]

For 2002, t = 2. Then the rate at which the percentage is changing will be:

[tex]\displaystyle f'(2) = 2.8944(0.9(2)+10)^{-0.7} = 0.5143...\approx 0.51[/tex]

Contextually, this means the percentage is increasing by about 0.51% per year.

Part B)

Evaluate f'(t) when t = 17. This yields:

[tex]\displaystyle f'(17) = 2.8944(0.9(17)+10)^{-0.7} =0.3015...\approx 0.30[/tex]

Contextually, this means the percetange is increasing by about 0.30% per year.

Part C)

For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:

[tex]\displaystyle f(17) = 10.72(0.9(17)+10)^{0.3}=28.2573...\approx 28.26[/tex]

So, about 28.26% of the American population in 2017 are age 55 and older.

Answer:

d) you can reach a large audience with one communication

Step-by-step explanation:

common sense

It looks like you're asked to compute

[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz[/tex]

where C is parameterized by ⟨t, t, t⟩ with 0 ≤ t ≤ 1.

In other words, x = y = z = t, so dx = dy = dz = dt, and the integral reduces to

[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz = \int_0^1 t\,\mathrm dt + t\,\mathrm dt + t\,\mathrm dt \\\\ = 3 \int_0^1 t\,\mathrm dt \\\\ =\frac32t^2\bigg|_{t=0}^{t=1} \\\\ =\boxed{\frac32}[/tex]

Answer:

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.

At the null hypothesis, we test if the proportion is of at least 64%, that is:

[tex]H_0: p \geq 0.64[/tex]

At the alternative hypothesis, we test if the proportion is of less than 64%, that is:

[tex]H_1: p < 0.64[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

64% is tested at the null hypothesis:

This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]

A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.

This means that [tex]n = 900, X = 0.61[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]

[tex]z = -1.88[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.

Looking at the z-table, z = -1.88 has a p-value of 0.0301.

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Answer:

slope is undefined

Step-by-step explanation:

(9, 1 ) and (9, - 4 )

Since the x- coordinates of the 2 points are 9, then the line is vertical and parallel to the y- axis with slope being undefined.

Slope is the change in y over the change in x.

Slope = (-4 - 1) / (9 -9) = -5/0 you cannot divide by 0,so the slope is undefined. This means it is a vertical line

Answer:

Rational number

Step-by-step explanation:

Given

[tex]5\frac{3}{8}[/tex]

Required

The subset it belongs to

Express as improper fraction

[tex]5\frac{3}{8} = \frac{43}{8}[/tex]

The above number is rational because it is represented by the division of 2 integers, i.e. 43 and 8 are integers

Express as decimals

[tex]5\frac{3}{8} = 5.375[/tex]

The above number cannot be classified as integers or whole because it has decimal parts

Answer:

3x=63

Step-by-step explanation:

3 coins means a coin is x and total expenditure is equal to 63

Answer:

1130

Step-by-step explanation:

1109+7 = 1116

1116+7 = 1123

Adding 7 each time

1123+7 = 1130

[tex]\\ \sf\longmapsto \sqrt{10}\times \sqrt{15}[/tex]

[tex]\\ \sf\longmapsto \sqrt{10\times 15}[/tex]

[tex]\\ \sf\longmapsto \sqrt{2\times 5\times 3\times 5}[/tex]

[tex]\\ \sf\longmapsto \sqrt{5\times 5\times 6}[/tex]

[tex]\\ \sf\longmapsto 5\sqrt{6}[/tex]

None of the above should be 4th option

Answer:

A

Step-by-step explanation:

The first term of the sequence is 4, the common difference is 3. So the equation of this sequence is 4+(n-1)*3 or 1+3*n. Plug in n=100

Answer:

11:7

Step-by-step explanation:

Solution

Here

7a-11b=0

a:b=?

we know that

a=7

b=11

ans =11:7

Hence proved

Answer:

[tex]thank \: you[/tex]

Answer:

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]

The maximum monthly profit realizable is $38,200.

Answer:

Step-by-step explanation:

3*(2k + 3) - 8k + 5 + 5           Remove the brackets on the left

6k + 9 - 8k + 5 + 5                Combine like terms

6k-8k+9 + 5 + 5

-2k + 19

Step-by-step explanation:

X= -4,-2,2,4 (respectively)

Y=4,-4 (respectively)

hope it helps

Answer:

384 kmph

Step-by-step explanation:

x=3

Step-by-step explanation:

x+2=5

x=5-2

x=3

Answer:

question is not proper

Step-by-step explanation:

question is

Answer:

Find the value of x:-

To find Y, use Pythagorean theorem:- [tex]c^{2} =a^{2} +b^{2}[/tex]

[tex](2.1)^{2} =y^{2} +(1.4)^{2}[/tex]

[tex]2.1^{2}=4.41[/tex]

[tex]1.4^{2} =1.96[/tex]

[tex]4.41=y^{2} +1.96[/tex]

subtract 1.96 from both sides

[tex]2.45=y^{2}[/tex]

[tex]y=1.5652[/tex]

Now, to find x:-

[tex]x=y+y[/tex]

[tex]= 1.5632+1.5652[/tex]

[tex]x=3.1 \: ft[/tex]

~OAmalOHopeO

Answer:

3645

Step-by-step explanation:

f(1)=5

f(2)=3*5=15.

f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645

9514 1404 393

Answer:

  perimeter ≈ 12.4 units

Step-by-step explanation:

The side adjacent to the angle is given. The relationships useful for the other two sides are ...

  Tan = Opposite/Adjacent

  Cos = Adjacent/Hypotenuse

From these, we have ...

  opposite = 5·tan(22°) ≈ 2.02

  hypotenuse = 5/cos(22°) ≈ 5.39

Then the perimeter is ...

  P = a + b + c = 2.02 + 5 + 5.39 = 12.41

The perimeter of ∆ABC is about 12.4 units.

Answer:

False

True

True

Step-by-step explanation:

Angle 1 cannot be equal to angle 4. Even by just viewing one can see that they can't be equal.

Angle 1 and 2 when combined give a 90 degree angle going from a to c.

Angle 3 and 4 form a 180 degree angle.

HOPE THIS HELPED

Answer:

x+ 4

Step-by-step explanation:

      ____x__+4___

x+2 | [tex]x^2 + 6x + 8[/tex]

        [tex]x^2 + 2x[/tex]

        ------------

                [tex]4x + 8\\[/tex]

                 [tex]4x + 8\\[/tex]

                  --------

                     0

Answer:

x+4

Step-by-step explanation: