Donte simplified the expression below.

4(1+3i)-(8-5i)
4+3i-8+5i
-4+8i

What mistake did he make?

Answer:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

Here we have a system of 3 equations with 3 variables:

4*x + 2*y + 1 = 1

2*x - y = 1

x + 3*y + z = 1

The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:

2*x - y = 1

2*x - 1 = y

Now that we have an expression equivalent to "y", we can replace this in the other two equations:

4*x + 2*(2*x - 1) + 1 = 1

x + 3*(2*x - 1) + z = 1

Now let's simplify these two equations:

8*x - 1 = 1

7*x - 3 + z = 1

Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:

8*x - 1 = 1

8*x = 1 + 1 = 2

x = 2/8 = 1/4

Now that we know the value of x, we can replace this in the other equation to find the value of z.

7*(1/4) -3 + z = 1

7/4 - 3 + z = 1

z = 1 + 3 - 7/4

z = 4 - 7/4

z = 16/4 - 7/4 = 9/4

z = 9/4

Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:

y = 2*(1/4) - 1

y = 2/4 - 1

y = 1/2 - 1

y = -1/2

Then the solution is:

x = 1/4

y = -1/2

z = 9/4

Answer:

?????????????????????????

Answer:

60m^2 is the answer im pretty sure

Step-by-step explanation:

yeah man thats it

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

Answer:alternate exterior angles

Step-by-step explanation:

Since they’re on the outside of the parallel lines that makes them exterior

Answer:

- (- (+) - ÷ )

+) (-) (+) (-)

= (+) (-)

Answer:

w ≈ 21.053 inches

l ≈ 28.353 inches

Step-by-step explanation:

Answer:

1042.5

Step-by-step explanation:

Given :-

Using Unitary Method :-

→ Cost of 1 m is P 69.95

→ Cost of 15m is P ( 69.5 * 15 ) = P 1042.5

Answer:

T = k * (A/W)

Step-by-step explanation:

9514 1404 393

Answer:

  30 grams

Step-by-step explanation:

The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.

  30 g of the radioactive rhodium will be left

Answer:

Sorry if this is wrong, but seeing the question I think the best answer following the question would be answer B, because for A it shows that 1 hour is 35 miles when it says 70 miles in 1 hour, not C because as the time rises so does the distance, and I checked D and it's wrong.

Step-by-step explanation:

Step-by-step explanation:

A. 2(x+4)=2x+8

=G

B. 3(2x-1)=6x-3

=I

C. 4(x+2)=4x+8

=J

D. 2(x+3)=2x+6

=K

E. 3(4x+1)=12x+3

=H

A - G

B - I

C - J

D - K

E - H

HOPE IT HELP

Completing the square gives

[tex]x^2-2x-2=(x-1)^2-3[/tex]

and comparing to [tex]y=x^2[/tex], the graph of [tex]y=x^2-2x-2[/tex] would be a horizontal shift to the right by 1 unit, and a vertical shift down by 3 units.

Hope this help!!!

Have a nice day!!!

Answer:

C. [tex]\frac{}{AB}[/tex]

Step-by-step explanation:

You can solve this in two ways, firstly by eliminating all the wrong answers, and secondly by just knowing that the horizontal line in [tex]_[/tex][tex]\frac{}{AB}[/tex] means that we are talking about a line.

This is how we solve this question by using the eliminating process.

(A. ∠C) is not the right answer because the ∠ sign lets us know that this answer represents an angle, not a line

(B. B) is not the right answer because it represent a point, not a line (in math we use a singular capital letter to represent points)

(D. ΔABC) is not the right answer because the Δ sign lets us know that the answer represents a triangle, not a line.

Therefore, the only option left is C. [tex]\frac{}{AB}[/tex]

Answer:

1 / 1365

Step-by-step explanation:

Given that :

Number of employees to choose from = 15

Number of employees to be chosen = 4

Probability of choosing You, Kyle, Carol and Adam

Recall ;

P(A) = number of required outcome / Total possible outcomes

Number of required outcome = 4C4

Total possible outcomes = 15C4

nCr = n! ÷ (n-r)!r!

Using calculator to save computation time :

15C4 = 1365

4C4 = 1

P(choosing you, Kyle, Carol and Adam) :

1 / 1365

Answer:

prime factorization of 225 = 32•52.

Step-by-step explanation:

The number 225 is a composite number so, it is possible to factorize it. 225 can be divided by 1, by itself and at least by 3 and 5.

A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.

He used 620 gallons of gas

9514 1404 393

Answer:

  160 cm³

Step-by-step explanation:

The ratio of the linear dimensions is the square root of the ratio of areas:

  scale factor B/A= √(64/144) = 8/12 = 2/3

The ratio of volumes is the cube of the scale factor:

  (volume B)/(volume A) = (2/3)³ = 8/27

Then the volume of pyramid B is ...

  volume B = (volume A) × (volume B)/(volume A)

  = (540 cm³) × (8/27) = 160 cm³ . . . . volume of pyramid B

_____

Equivalently, the ratio of volumes is the 3/2 power of the ratio of areas.

 Vb = Va(64/144)^(3/2) = (540 cm³)(4/9)^(3/2) = (540)(8/27) cm³ = 160 cm³

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

Evans would have $852.8

Step-by-step explanation:

Given

[tex]PV = \$800[/tex]

[tex]r = 3.25\%[/tex]

[tex]t = 2[/tex]

[tex]n = 1[/tex] --- annually'

Required

The future value

This is calculated using:

[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]

So, we have:

[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]

[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]

[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]

[tex]FV = 800 * (1 .0325)^2[/tex]

[tex]FV = 852.845[/tex]

[tex]FV = 852.8[/tex]

FV =

Answer:

Period: [tex]\pi[/tex]

Phase shift: n

Step-by-step explanation:

Tangent function:

Has the following format:

[tex]f(x) = \tan{ax - n}[/tex]

In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.

In this question:

[tex]f(x) = -4\tan{(x-n)}[/tex]

[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.

Answer:

A) 0.7696

B) 0.0474

C) Yes it's unusual

D) 0.05746

E) No, it is not unusual

F) No, it is not unusual

Step-by-step explanation:

This is a binomial probability distribution question.

We are told that 92.4% of those admitted graduated.

Thus; p = 92.4% = 0.924

From binomial probability distribution, q = 1 - p

Thus;

q = 1 - 0.924

q = 0.076

Formula for binomial probability distribution is;

P(x) = nCx × p^(x) × q^(n - x)

A) At least 11 graduated out of 12.

P(x ≥ 11) = P(11) + P(12)

P(11) = 12C11 × 0.924^(11) × 0.076^(12 - 11)

P(11) = 0.3823

P(12) = 12C12 × 0.924^(12) × 0.076^(12 - 12)

P(12) = 0.3873

P(x ≥ 11) = 0.3823 + 0.3873

P(x ≥ 11) = 0.7696

B) that exactly 9 of them graduated out of 12. This is;

P(9) = 12C9 × 0.924^(9) × 0.076^(12 - 9)

P(9) = 0.0474

C) We are not given significance level here but generally when not given we adopt a significance level of α = 0.05.

Now, exactly 9 out of 12 that graduated which is P(9) = 0.0474.

We see that 0.0474 is less than the significance level of 0.05. Thus, we can say that it is unusual to randomly select 12 students from the special programs and get exactly 9 that graduate

D) that at most 9 of them out of 12 graduated.

P(x ≤ 9) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)

This is going to be very long so I will make use of an online probability calculator to get the values of P(0) to P(8) since I already have P(9) as 0.0474.

Thus, we have;

P(0) = 0

P(1) = 0

P(2) = 0

P(3) = 0.00000001468

P(4) = 0.00000040161

P(5) = 0.00000781232

P(6) = 0.00011081163

P(7) = 0.00115477385

P(8) = 0.00877476184

Thus;

P(x ≤ 9) = 0 + 0 + 0 + 0.00000001468 + 0.00000040161 + 0.00000781232 + 0.00011081163 + 0.00115477385 + 0.00877476184 + 0.04741450256

P(x ≤ 9) = 0.05746

E) P(x ≤ 9) = 0.05746 is more than the significance level of 0.05, thus we will say it is not unusual.

F) from online binomial probability calculator, probability of getting only 9 out of 12 is more than the significance value of 0.05. Thus, we will say it is not unusual

Answer:

[tex]P(x < 4) = \frac{9}{50}[/tex]

Step-by-step explanation:

Given

[tex]n(S) = 50[/tex]

See attachment for distribution

Required

[tex]P(x < 4)[/tex]

This is calculated as:

[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]

Using the data on the frequency distribution table, we have:

[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]

[tex]P(x < 4) = \frac{9}{50}[/tex]

9514 1404 393

Answer:

  B

Step-by-step explanation:

If the probability of event "A" is 'p', then the probability of the event "not A" is

  P(not A) = 1 - P(A) = 1 - p

For p=0.5, this is ...

  P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B

Answer:

○B. 0.5 is the proof the outcome (not A).