8. Solve the system using elimination.
3x - 4y = 9
- 3x + 2y = 9

Step-by-step explanation:

We need to prove that ,

cot x / csc x - csc x / cot x = - tan x sec x .

LHS :-

> cot x / csc x - csc x / cot x

> cos x / sin x ÷ csc x - sin x × csc x / cos x

> cosx - 1/ cos x

> cos² x - 1 / cos x

> - sin²x / cosx

> -sin x / cos x × sin x

> -tan x sin x

= RHS

Hence Proved !

Answer:

652 cases

Step-by-step explanation:

The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!

Answer:

(a) Temperature: Numerical

(b) Traffic congestion: Categorical

Step-by-step explanation:

Required

Determine the variable type

(a) Temperature

Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.

Hence, the variable is numerical

(b) Traffic congestion

From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....

Hence, the variable is categorical

tan graph and its tax because tax=0

Answer:

0.4444 = 44.44% probability that it is NOT raining

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Technician not detected.

Event B: Not raining.

Probability the technician is not detected:

0.3 of 0.25(raining).

0.08 of 0.75(not raining). So

[tex]P(A) = 0.3*0.25 + 0.08*0.75 = 0.135[/tex]

Probability the technician is not detected and it is not raining:

0.08 of 0.75. So

[tex]P(A \cap B) = 0.08*0.75 = 0.06[/tex]

Given that the technician will NOT be detected, what is the probability that it is NOT raining?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.135} = 0.4444[/tex]

0.4444 = 44.44% probability that it is NOT raining

Step-by-step explanation:

√19200cm²

=138.56cm

then the highest possible volume

=(138.56)³

=2660195.926cm³

The largest possible volume of the box is; V = 25600 cm³

Let us denote the following of the square box;

Length = x

Width = y

height = h

Formula for volume of a box is;

V = length * width * height

Thus; V = xyh

but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;

V = x²h

The box has an open top and as such, the surface are of the box is;

S = x² + 4xh

We are given S = 19200 cm². Thus;

19200 = x² + 4xh

h = (19200 - x²)/4x

Put (19200 - x²)/4x for h in volume equation to get;

V = x²(19200 - x²)/4x

V = 4800x - 0.25x³

To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;

dV/dx = 4800 - 0.75x²

At dV/dx = 0, we have;

4800 - 0.75x² = 0

0.75x² = 4800

x² = 4800/0.75

x² = 6400

x = √6400

x = 80 cm

From h = (19200 - x²)/4x;

h = (19200 - 80²)/(4 × 80)

h = (19200 - 6400)/3200

h = 4 cm

Largest possible volume = 80² × 4

Largest possible volume = 25600 cm³

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Answer:

5

Step-by-step explanation:

I'm going to call x, x1 because I want to use x as a variable.

So we have a ray with points (0,0) and (3x1,5) on it. This equation for this ray would be y=5/(3x1)×x.

We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.

We want these two lines' slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.

So we want to find x1 such that 5/(3x1)=1/3.

Cross multiply: 15=3x1

Divide both sides by 3: 5=x1

We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.

Another way:

If two vectors are perpendicular, then their dot product is 0.

The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).

Let's simplify:

6x-30.

We want this to be 0.

6x-30=0

Add 30 on both sides:

6x=30

Divide both sides by 6:

x=5

Answer:

The call more is cheaper than talk-now.

Step-by-step explanation:

The companies charge a flat fee plus an added cost for each minute or part of a minute used for two companies are as follows :

Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40

We need to find which company is cheaper if a customer talks for 50 minutes.

For call more,

C = 0.40(50) + 25 = 45 units

For talk-now,

C = 0.15(50) + 40 = 47.5 units

So, it can be seen that call more is cheaper than talk-now.

Answer:

m∠GHI = 160

Step-by-step explanation:

From the question given above, the following data were obtained:

m∠GHI = 14x + 6

m∠QHI = 130°

m∠GHQ = 3x – 3

m∠GHI =?

Next, we shall determine the value of x. This can be obtained as follow:

m∠GHI = m∠QHI + m∠GHQ

14x + 6 = 130 + (3x – 3)

14x + 6 = 130 + 3x – 3

Collect like terms

14x – 3x = 130 – 3 – 6

11x = 121

Divide both side by 11

x = 121 / 11

x = 11

Finally, we shall determine the value m∠GHI. This can be obtained as follow:

m∠GHI = 14x + 6

x = 11

m∠GHI = 14(11) + 6

m∠GHI = 154 + 6

m∠GHI = 160

Answer:

option B

Step-by-step explanation:

Sum of interior angles of a polygon with n sides:

                                                                          [tex]= (n - 2 )\times 180[/tex]

[tex]Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180[/tex]

[tex]Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ[/tex]

                      [tex][ \ because \ straight \ line \ angle = 180^\circ \ ][/tex]

That is ,

[tex]Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9[/tex]

OR

Sum of exterior angles of a regular polygon = 360

Given 1 exterior angle of the regular polygon is  40

Therefore ,

               [tex]n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9[/tex]

Answer:

9

Step-by-step explanation:

The amount of water released from the sprinkler for 80 minutes is 200 L

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of water from the sprinkler for 80 minutes be = A

Now , the value of A is given by the equation

A sprinkler releases water st a rate of 150 liters per hour

So , 60 minutes = 150 Liters of water

80 minutes = 1/60 hours

80 minutes = 1.333 hours

The amount of water released for 1.333 hours A = 150 x 1.333

On simplifying the equation , we get

The amount of water released for 1.333 hours A = 200 L

Therefore , the value of A is 200 L

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Answer:

Step-by-step explanation:

4*(n +5) - 2*(5 + 7n) = -70

4*n + 4*5 + 5*(-2) + 7n*(-2) = -70

4n + 20 - 10 - 14n = -70

4n - 14n + 20 - 10 = -70

- 10n + 10 = -70

Subtract 10 from both sides

-10n = -70 - 10

-10n = -80

Divide both sides by (-10)

n = -80/-10

n = 8

Step-by-step explanation:

sjbsbsbeekejebebheebebejekek

Answer:

Step-by-step explanation:

Answer:

s = -4

Step-by-step explanation:

Your goal is to manipulate the equation so you can isolate s

9s + 20 = -16

Subtract 20 from both sides to get:

9s = -36

Divide both sides by 9 so s is alone

you end up with s = -4

Answer:

s  = -4

Step-by-step explanation:

9s+20=−16

Subtract 20 from each side

9s +20 -20 = -16 -20

9s = -36

Divide by 9

9s/9 = -36/9

s  = -4

Hello!

[tex]\large\boxed{y = 13(2)^x}}[/tex]

y = abˣ

We know that at x = 0, b = 1 because any number to the power of 0 = 1.

Therefore:

13 = a(1)

13 = a

Now, plug in this value to solve for b:

y = 13bˣ

Substitute in the next point:

416 = 13(b)⁵

Divide both sides by 13:

32 = b⁵

Take the 5th root of both sides:

2 = b

Rewrite:

y = 13(2)ˣ

Answer:

The new volume is 3n^2+2n inches greater.

Step-by-step explanation:

Volume of a cube = s^3 where s is side of cube

Original volume = n^3

Volume of a Rectangular Prism = LBH

New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n

DIfference = New- original = 3n^2+2n

Answer:

[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]

Step-by-step explanation:

A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,

[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]

For finding the x intercept , equate the given function with 0, we have ;

[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]

Equate each factor with 0 ,

[tex]\sf \implies 2x = 0[/tex]

Divide both sides by 2 ,

[tex]\sf \implies\bf x = 0[/tex]

Again ,

[tex]\sf \implies ( x - 5)^2=0 [/tex]

Taking squareroot on both sides,

[tex]\sf \implies x - 5 = 0 [/tex]

Add 5 to both sides,

[tex]\sf \implies \bf x = 5[/tex]

Similarly ,

[tex]\sf \implies \bf x = -4 [/tex]

Hence the x Intercepts are -4 , 0 and 5 .

{ See attachment also for graph } .

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]

[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]

[tex]P(x=12)=0.00555[/tex]

Hence, the probability that exactly 12 buyers would prefer green

=0.00555

Hey there!

(4 + 21) - (1 - 71)

4 + 21 = 25

= 25 - (1 - 71)

1 - 71 = -70

= 25 - (-70)

= 25 + 70

= 95

Answer: 95

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

a) 1186

b) Between 1031 and 1493.

c) 160

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean of 1262 and a standard deviation of 118.

This means that [tex]\mu = 1262, \sigma = 118[/tex]

a) Determine the 26th percentile for the number of chocolate chips in a bag. ​

This is X when Z has a p-value of 0.26, so X when Z = -0.643.

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

[tex]-0.643 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -0.643*118[/tex]

[tex]X = 1186[/tex]

(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.

Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a p-value of 0.025, so X when Z = -1.96.

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

[tex]-1.96 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -1.96*118[/tex]

[tex]X = 1031[/tex]

97.5th percentile:

X when Z has a p-value of 0.975, so X when Z = 1.96.

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

[tex]1.96 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = 1.96*118[/tex]

[tex]X = 1493[/tex]

Between 1031 and 1493.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Difference between the 75th percentile and the 25th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -0.675*118[/tex]

[tex]X = 1182[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

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

[tex]0.675 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = 0.675*118[/tex]

[tex]X = 1342[/tex]

IQR:

1342 - 1182 = 160

Answer:

2x(4x-4+1)

Step-by-step explanation:

i hope it will help you

Answer:

x=1/2

Step-by-step explanation:

press the calculator

8x²-8x+2=0

x=1/2

min,x=1/2

min,y=0

Answer:

Point D

Step-by-step explanation:

The intersection(s) of lines represents where they cross or intersect. We can see that lines AD and DE cross or intersect as Point D, hence the answer being Point D.

Answer: Point D

Step-by-step explanation: The intersection of two figures is the set of points that is contained in both figures. In the diagram shown, D is the intersection of lines AD and DE because D is the point contained by both line AD and DE.

Answer:

4 places after the decimal.

the result is 0.0215

Step-by-step explanation:

I assume the expression is really

43 / (2⁴ × 5³)

this is the same as

(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)

since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5

the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5

the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5

the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5

in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.

and finally the fourth division to 0.5⁴.

0.5⁴ = (5/10)⁴ = 5⁴/10⁴

so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.

every divisible by 5 takes one of these powers away.

so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.

all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.

so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.

Answer:

(0.3049 ; 0.3751)

Step-by-step explanation:

The confidence interval for proportion can be obtained using the relation :

Phat ± Zcritical * [√phat(1-phat) / n]

phat = x / n

Sample size, n = 700

x = 238

phat = 238/700 = 0.34

Zcritical at 95% = 1.96

C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]

C.I = 0.34 ± 1.96 * 0.0179045

C. I = 0.34 ± 0.0350928

Lower boundary = 0.34 - 0.0350928 = 0.3049

Upper boundary = 0.34 + 0.0350928 = 0.37509

(0.3049 ; 0.3751)

Answer:

I think that answer would be B.

Step-by-step explanation:

Answer:

1600N

Step-by-step explanation:

Force = 400 N

Angle with horizontal = 60°

Displacement in horizontal direction = 8 m

work done formula when angle is included: Force * distance * cos(angle)

400 * 8 * cos(60)

= 400 * 8 * 1/2

= 1600N

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The attachment shows the ordered pairs (x, f(x)) and their graph.

Answer:

8.2 miles per minute

Step-by-step explanation:

Given

See attachment for graph

Required

The rate of Tyler's graph

This means that we calculate the slope (m) of the graph using:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

So, we have:

[tex](x_1 ,y_1) = (0,0)[/tex]

[tex](x_1 ,y_1) = (1,8.2)[/tex]

So, we have:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]

[tex]m = \frac{-8.2}{- 1}[/tex]

[tex]m = 8.2}[/tex]

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

[tex]\frac{vinegar}{oil}[/tex]  If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.

2x = 100 so

x = 50 ml of oil