PLEASE HELP ASAP
TRIGONOMETRY

Answer:

$102

Step-by-step explanation:

2% of $100 = 0.02 * $100 = $2

The increase is $2.

$100 + $2 = $102

Answer: $102

Answer:

100 x 0,2 x 1 year(12/12 months)

=$102 after a year

Answer:

8.31

8.3

8.301

8.03

8.031

I think that's the answer.. not sure th

Answer:

$12,375

$12820.50

Step-by-step explanation:

To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49

Hence,

Lower bound = $27.50

Upper bound = $28.49

Therefore. Cost of making 450 chairs ;

27.50 * 450 = $12,375 (lower bound)

28.49 * 450 $12820.50 (upper bound)

Answer:

Last one

Step-by-step explanation:

Answer:Analyze the results of the correlation using the given residual plot.

Residual

Step-by-step explanation:

Answer:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

[tex]V = l * b * h[/tex]

Make h the subject of the formula

[tex]h = \frac{V}{lb}[/tex]

The surface area (S) of the aquarium is:

[tex]S = lb + 2(lh + bh)[/tex]

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

[tex]C = 7 * lb + 1 * 2(lh + bh)[/tex]

[tex]C = 7lb + 2(lh + bh)[/tex]

[tex]C = 7lb + 2h(l + b)[/tex]

Substitute [tex]\frac{V}{lb}[/tex] for h in the above equation

[tex]C = 7lb + 2*\frac{V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{b} + \frac{2V}{l}[/tex]

Differentiate with respect to l and with respect to b

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex]

[tex]C_b=7l - \frac{2V}{b^2}[/tex] [tex]=0[/tex]

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

[tex]7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}[/tex]

[tex]7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}[/tex]

By comparison:

[tex]l =b[/tex]

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex] becomes

[tex]7l - \frac{2V}{l^2}=0[/tex]

[tex]7l = \frac{2V}{l^2}[/tex]

Cross Multiply

[tex]7l^3 = 2V[/tex]

Solve for l

[tex]l^3 = \frac{2V}{7}[/tex]

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]

Recall that: [tex]l =b[/tex]

[tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]

Also recall that:

[tex]h = \frac{V}{lb}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}[/tex]

Apply law of indices

[tex]h = \sqrt[3]{\frac{49V^3}{4V^2}}[/tex]

[tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

The dimension that minimizes the cost of material of the aquarium is:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Answer:

Step-by-step explanation:

perimeter = 4(10x) = 40x units

if x = 12, perimeter = 480x units

Answer:

it is 222

Step-by-step explanation:

1440 divided by 20 :)

Answer:

c) inversely

Step-by-step explanation:

In Mathematics an inverse relationship can be defined as a relationship between two variables, in which an increase in the value of one variable leads to a decrease in the value of the other variable i.e as the value of one variable becomes large, the value of the other variable becomes small.

Mathematically, an inverse relationship is given by the formula;

A = K/B

Where;

A and B are the variables.

K is the constant of proportionality.

Hence, if an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.

Answer:

a - Mutual

b - (x+21)+(2x+3)=90

c - 3x +24 =90

3x=90-24

3x=66

X=22

Answer:

d i hope please be d please please

Answer:

426.7pi

Step-by-step explanation:

V = 1/3 pi r2h

1/3 × 22/7× 8 × 8 × 20

426.7 pi

Answer:

Let's assume the fraction is 1/1

decreasing 1 by 10% = .9

decreasing 1 by 50% = .5

So the fraction becomes .9/.5 = 1.8

So its value increases by 180%

Step-by-step explanation:

Answer:-257.8

Step-by-step explanation:

Answer:

(6³×2^6)÷2³=6³×2^(6-3)=6³×2³=(6×2)³=12³is your answer(1728)

Answer:

24

Step-by-step explanation:

8 * 3 = 24

12 * 2 = 24

(the star is the multiplication sign)

Hope this helps :)

You have 2 points with the same x value of 2 and 2 points with the same y value of 4.

You now need 2 points with the same x value of 4 ( you are given 1) and 2 y values of 1 ( you are given 1.

The missing point would need to be (4,1)

The width would be x2-x1 = 4-2 = 2 units

The length would be y2-y1 = 4-1 = 3 units

Area = 3x 2 = 6 square units

Answer:

65

Step-by-step explanation:

Answer:

6 units to the right, 3 units down

Step-by-step explanation:

where is the question I dont see it

Answer:

Step-by-step explanation:

It’s 20

Answer:

0.0011 = 0.11% probability of selling less than 3 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A real estate agent has 17 properties that she shows.

This means that [tex]n = 17[/tex]

She feels that there is a 50% chance of selling any one property during a week.

This means that [tex]p = 0.5[/tex]

Compute the probability of selling less than 3 properties in one week.

This is

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{17,0}.(0.5)^{0}.(0.5)^{17} \approx 0[/tex]

[tex]P(X = 1) = C_{17,1}.(0.5)^{1}.(0.5)^{16} = 0.0001[/tex]

[tex]P(X = 2) = C_{17,2}.(0.5)^{2}.(0.5)^{15} = 0.0010[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011[/tex]

0.0011 = 0.11% probability of selling less than 3 properties in one week.

Answer:

Q.1 a²+10a+24

splitting the middle.

a²+6a+4a+24

=a(a+6)+4(a+6)

(a+6)(a+4)

Q.2 x²+9x+18

splitting the middle

x²+6x+3x+18

x(x+6)+3(x+6)

(x+6)(x+3)

Answer:

x > -20

Step-by-step explanation:

-x < 20

When dividing by negative numbers, flip the inequality.

x > -20

inclusive -> open circle

greater than -> to the right

open circle at -20 going to the right

Answer:

Never:

Step-by-step explanation:

because its more understandable we know this because it wouldnt be always

Answer:

[tex]\theta=41.18^{\circ}[/tex]

Step-by-step explanation:

Given that,

The height of the tree, h = 14 ft

The height of the shadow, b = 16 ft

We need to find the angle of elevation of the sun from the ground. Let the angle be θ. We can use trigonometry to find it. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{14}{16}\\\\\theta=41.18^{\circ}[/tex]

So, the required angle of elevation of the sun is equal to [tex]41.18^{\circ}[/tex].

Answer:

182.82812

Step-by-step explanation:

Answer:

By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.

Hope this helps(and also if you have a more refined wording please put it in the comments)!

Answer:

By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.

Answer:

Step-by-step explanation:

From the given information:

[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]

A)

[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]

[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]

B)

[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]

[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]

C)

[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]

[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]

D)

[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]