Given f() = -4x + 3, find f(-3)

[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]

Check the picture below.

Answer:

D. x>5

Step-by-step explanation:

[tex]3x + 2 < 4x - 3 \\ = 3x - 4x < - 3 - 2 \\ = - x < - 5 \\ = x > 5[/tex]

Answer:

2827.43 cm^2

Step-by-step explanation:

Hope this helped! <3 Have a great day :) Brainliest please?

Multiply 80 by number of copies sold and add to her salary:

P = 80N + 1700

Now replace N with 26:

P = 80(26) + 1700

P = 3,780

Answer:

P=1,700+80n

Total Pay if Yoko sells 26 Copies; 3,780

Hope This Helps! :) Please Mark Brainliest!

Answer:

multiply 3 or *3 that is 2*3=6

Answer:

x = - 9, y = -1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}x-2y=-7\\ -3x-2y=29\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=-7+2y[/tex]

[tex]\begin{bmatrix}-3\left(-7+2y\right)-2y=29\end{bmatrix}[/tex]

[tex]\begin{bmatrix}21-8y=29\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-7+2y[/tex]

[tex]\mathrm{Substitute\:}y=-1[/tex]

[tex]x=-7+2\left(-1\right)[/tex]

[tex]x=-9[/tex]

[tex]\mathrm{Thus, Answer:x=-9,\:y=-1}[/tex]

[RevyBreeze]

Answer:

x = -9, y = -1

Step-by-step explanation:

Solution:

If x = -7+2y

Then

-3(-7+2y)-2y=29

Simplify

21 - 8y = 29

And if x = -7+2y

Simplify

y = -1

x = -7+2(-1)

x = -9

Hence, x = -9 and y = -1

~lenvy~

Answer:

C. tanS = 5/12, tanT = 12/5

Step-by-step explanation:

Tangent has NOTHING to do with hypotenuse, do we can easily eliminate answer choices involving 13, the hypotenuse. For angle S, the opposite side measures 5 and the adjacent side measures 12. For angle T, the opposite side measures 12 and the adjacent side measures 5. See this below algebraically

tanθ = opp/adj

tanS = 5/12

tanT = 12/5

I hope this helps!

225

[tex]15\times 15[/tex]

__________________________________________________

Calculate

[tex]15\times 15[/tex]

__________________________________________________

Calculate the product or quotient

[tex]225[/tex]

I hope this helps you

:)

Answer:

[tex]\sf 4.9 \times 10^{11}[/tex]

Step-by-step explanation:

Given expression: [tex]\sf (7 \times 10^5)^2[/tex]

Apply exponent rule [tex]\sf (ab)^2=a^2 \cdot b^2[/tex] :

[tex]\sf \implies 7^2 \times (10^5)^2[/tex]

[tex]\sf \implies 49 \times (10^5)^2[/tex]

Apply exponent rule  [tex]\sf (a^b)^c=a^{bc}[/tex] :

[tex]\sf \implies 49 \times 10^{5 \cdot 2}[/tex]

[tex]\sf \implies 49 \times 10^{10}[/tex]

Scientific notation:  [tex]\sf a \times 10^n[/tex]

where  [tex]\sf 1\leq a < 10[/tex] and n is an integer

We can write 49 as [tex]\sf 4.9 \times 10=4.9 \times 10^1[/tex]

[tex]\sf \implies 4.9 \times 10^1\times 10^{10}[/tex]

Apply exponent rule [tex]\sf a^ba^c=a^{b+c}[/tex]

[tex]\sf \implies 4.9 \times 10^{11}[/tex]

Answer: 28.6

Step-by-step explanation:

To round 28.6 to the nearest tenth consider the hundredths’ value of 28.6, which is 0 and equal or more than 5. Therefore, the tenths value of 28.6 increases by 1 to 7.28.6 rounded to the nearest tenth = 28.6 hope that helps

Answer:

x - 1

Step-by-step explanation:

The graph touches the x-axis at x = 1, its factor would be (x - 1)

Using the normal distribution and the central limit theorem, it is found that the probability is of 0.1368 = 13.68%.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem:

The mean and the standard error are given by:

[tex]\mu = p = 0.47[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.47(0.53)}{61}} = 0.0639[/tex]

The probability that less than 40% of the sample are looking to buy an SUV is the p-value of Z when X = 0.4, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.4 - 0.47}{0.0639}[/tex]

Z = -1.095

Z = -1.095 has a p-value of 0.1368.

0.1368 = 13.68% probability that less than 40% of the sample are looking to buy an SUV.

To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that

P(M) = P(F) = 50/100 = 1/2

P(U) = 60/100 = 3/5

P(M | U) = 2/3

P(E) = 40/100 = 2/5

P(F | E) = 3/4

8a. This follows immediately from the given information. Specifically,

P(E) = 1 - P(U) = 1 - 3/5 = 2/5

8b. By definition of conditional probability,

P(A | B) = P(A and B) / P(B)   ⇒   P(A and B) = P(A | B) P(B)

It follows that

P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5

8c. Using Bayes' rule/the definition of conditional probability,

P(U | F) = P(U and F) / P(F) =  P(F | U) P(U) / P(F)

Since F and M are mutually exclusive,

P(F | U) = 1 - P(M | U)

and so

P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5

8d. Here we assume gender and employment status are independent, so for instance

P(F and E) = P(F) P(E)

We then have by the inclusion/exclusion principle that

P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)

We also have by the law of total probability

P(F) = P(F and U) + P(F and E)

so

P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)

By the assumed independence,

P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)

P(F or U) = P(F) P(E) + P(U)

P(F or U) = 1/2 • 2/5 + 3/5 = 4/5

9.

a. This is mostly a matter of counting the ways a given type of stamp can fall out.

[tex]P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}[/tex]

since there are 20 non-green stamps.

[tex]P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}[/tex]

since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.

[tex]P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}[/tex]

since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}[/tex]

which follows from the inclusion/exclusion principle.

b. There is a total of 10 used stamps, so the probability of at least 1 going missing is

[tex]P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}[/tex]

By definition of conditional probability,

[tex]P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}[/tex]

However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and

[tex]P(C \mid A) = P(C) = \dfrac{415}{506}[/tex]

c. A and C are independent if and only if

[tex]P(A \cap C) = P(A) P(C)[/tex]

We know

[tex]P(C \cap A) = P(C)[/tex]

so if A and C are independent, then

[tex]P(C) = P(A) P(C)[/tex]

but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.

Applying the appropriate circle theorems involving angles formed by chords and tangents, we have:

1. x = 75°; y = 85°, z = 210°

2. x = 38°

3. x = 143°

The angle formed outside a circle when two tangents intersect equals half of the positive difference of the intercepted arcs, based on the angles of intersecting tangents theorem.

The angles of intersecting chords theorem states that, half the sum of the intercepted arcs equals the vertical angle formed by two chords in a circle.

According to the inscribed angle theorem, the measure of an inscribed angle in a circle = 1/2(measure of intercepted arc)

1. x = 180 - 105 (opposite angles in a cyclic quadrilateral are supplementary)

x = 75°

y = 180 - 95 = 85°

z = measure of intercepted arc HEF = 2(105) [inscribed angle theorem]

m(HEF) = 210°

2. x = 1/2(218 - 142) [angles of intersecting tangents theorem]

x = 1/2(76)

x = 38°

3. x = 1/2(146 + 140) [angles of intersecting chords theorem]

x = 1/2(286)

x = 143°

Learn more about circle theorems on:

https://brainly.com/question/26403793

The volume of a sphere is the amount of space in it

The volumes of the spheres are 24416.64, 113.04 and 310181.76

The volume of a sphere is calculated using:

V = 4/3 πr^3

When the radius, r = 18, we have:

V = 4/3  * 3.14 * 18^3

V = 24416.64

When the radius, r = 3, we have:

V = 4/3  * 3.14 * 3^3

V = 113.04

When the radius, r = 42, we have:

V = 4/3  * 3.14 * 42^3

V = 310181.76

Hence, the volumes of the spheres are 24416.64, 113.04 and 310181.76

Read more about volumes at:

https://brainly.com/question/1972490

Answer:

Since the least number of digits in the number is 2 decimal places

Round 3.0478 to 2 dp

3.05+4.92=7.97

B is the answer

Step-by-step explanation:

Give brainliest please

Answer:

B

Step-by-step explanation:

Answer:

2 + n < 14 is the inequality please

Answer:

B

Step-by-step explanation:

b because everything must cost less than 80 and

< 80 means the unknown number will be less than 80.

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

They are equal

Make them into mixed numbers

10/4 = 2 2/4 you can put this into its simplest form so 2 1/2

5/2 = 2 1/2

Answer:

Investement P

Step-by-step explanation:

Answer: I dont know if im right for sure but the answer should be 4

Step-by-step explanation

8 goes into 2 4 times (8 divided by 2 = 4)

Each child ate 2 pieces (4-2=2)

so therefore for it to be 2 pieces left over there were 4 kids I think.

Answer:

11

Step-by-step explanation:

So each pizza has 8 equal slices but we don't know the amount pizzas but we can find it by doing this ⬇️

1 pizza= 8 slices

3 pizzas = x

you cross multiply it and it will end up as 3×8= 24 slices.

now each kid ate 2 pieces and there was a leftover of 2

therefore, 24-2= 22 pieces divided 2 is 11

or; 3×8=24-2=22÷2=11

Step-by-step explanation:

it is 300,000 for a 3 day contract

Answer:

Square, purple triangle, and red arrow

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To turn the fraction of 1 1/2 to decimal would be : 1.50 add fifty percent because you have to add 6 to 12 and six is half, so you add half. Half of 150 is 75 so add them you get 225 and as a fraction, that's 2 1/4. Already you have the first part done. Since there is only one answer with 2 1/3 your answer has to be D.

Answer:

43 x 43  units      1849 units^2

Step-by-step explanation:

The largest area will be a square (equla sides)

   172 / 4 = 43

a square IS a rectangle

43  x   43

Answer:

She has 1 and 1/12 pounds of fruit already and she needs 1 and 11/12 pounds more to have 3 total pounds

The direction will be resultant

Now

The number of handshake that took place is 28.

In any situation where order of an outcome does not matter, mathematical combination (C) are use calculate the total outcomes of an event.

8 people are to shake each other once. The concept to be use to derive the number of hands that took place is Combination.

The formulae of Combination for this Scenario is n(n-1)/2n(n−1)/2 .

The number of people (n) is 8.

\begin{gathered}Total handshake = n(n-1)/2\\Total handshake = 8 * (8-1)/2\\Total handshake = 8 * 7/2\\Total handshake = 56/2\\Total handshake = 28\end{gathered}Totalhandshake=n(n−1)/2Totalhandshake=8∗(8−1)/2Totalhandshake=8∗7/2Totalhandshake=56/2Totalhandshake=28

In conclusion, the number of handshake that took place is 28.

Answer:

28

Step-by-step explanation:
3 people
A B C
AB
AC
BC
3 total

4 people
A B C D
AB
AC
AD
BC
BD
CD
6 total

this can be modeled with
n*(n - 1)/2
8*(8 - 1)/2
8*3.5
28

Answer:

what do you want to ask brother...

Step-by-step explanation:

or you post this by mistake.....

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

We should solve according to the order of operations, PEMDAS.

#1) Parentheses

#2) Subtraction

#3) Addition