Need help on polynomial expressions

Answer:

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Step-by-step explanation:

Represent the bus average speed with x and the motorcycle average speed with y

Given

[tex]x = y + 2[/tex]

Distance covered by bus = 165 miles

Distance covered by motorcycle in same time = 155 miles

Required

Determine the speed of each

Average Speed is calculated as;

[tex]Average\ Speed = \frac{Distance}{Time}[/tex]

Since the two are measured with the same time, represent time with T

For the bus

[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes

[tex]x = \frac{165}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{165}{x}[/tex]

For the motorcycle

[tex]y = \frac{155}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{155}{y}[/tex]

Since, T = T; we have that

[tex]\frac{165}{x} = \frac{155}{y}[/tex]

Cross Multiply

[tex]165y = 155x[/tex]

Substitute [tex]x = y + 2[/tex]

[tex]165y = 155(y+2)[/tex]

Open Bracket

[tex]165y = 155y - 310[/tex]

Collect Like Terms

[tex]165y - 155y = 310[/tex]

[tex]10y = 310[/tex]

Divide both sides by 10

[tex]y = 31[/tex]

Recall that [tex]x = y + 2[/tex]

[tex]x = 31 +2[/tex]

[tex]x = 33[/tex]

Hence;

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Answer:

Hello,

Step-by-step explanation:

Q1:

[tex]\left\{\begin{array}{ccc}x&=&t+\dfrac{1}{t} \\\\y&=&t-\dfrac{1}{t} \\\end{array}\right.\\\\\left\{\begin{array}{ccc}x^2&=&t^2+\dfrac{1}{t^2} +2\\\\y^2&=&t^2+\dfrac{1}{t^2} -2\\\end{array}\right.\\\\\\x^2-y^2=4: \ equilater\ hyperbola.\\[/tex]

Q2:

1)

[tex]\left\{\begin{array}{ccc}x&=&2t^2} \\\\y&=&4t \\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}t&=&\dfrac{y}{4} \\\\x&=&2*(\dfrac{y}{4})^2 \\\end{array}\right.\\\\\\\boxed{x=\dfrac{y^2}{8}} :\ parabola\ with\ x-axis\ as\ axis\ of\ symmetry[/tex]

2)

[tex]y=\dfrac{25}{x} \\[/tex]

equilater hyperbola (centre (0,0))

Answer: $ 11,232.00

Step-by-step explanation:

Given:  Amount = $ 10,800

Interest Rate = 8%   =0.08

Time in Months= 6.00

Formula :

Interest on Note = (Amount)× (Interest Rate) × ((Time in Months) /12)

= (10800)× (0.08)× (6/12)

= $432

The amount of the borrower's check =(Amount + Interest on Note)

= $ (10,800+432)

= $ 11,232.00

Hence, The amount of the borrower's check = $ 11,232.00

The fence would be the perimeter of the shape.

Perimeter = 17 + 17 + 14 + 14 = 62 meters.

Multiply the price per meter by total meters:

25 x 62 = 1550

For fencing , we have to find the perimeter of rectangle.

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Formula \: \: Using \: = \: 2 \: ( \: L + B \: )}}}}}\end{gathered}[/tex]

Perimeter of rectangle = 2 ( L + B )

Perimeter of rectangle = 2 ( 17 m + 14 m )

Perimeter of rectangle = 2 ( 31 m )

Perimeter of rectangle = 62 m.

Hence, the perimeter of rectangle is 62 m.

For Fencing Cost = perimeter × rate of fencing per metre

Fencing Cost = 62 × 25

Fencing cost = 1,550

Hence, the cost of fencing of a rectangular plot is 1,550

Answer:

BC = 13.4

Step-by-step explanation:

its a law of cosines S-A-S

a² = b² + c² - 2bc cosA

a² = 12.6² + 4.6² - ( 2 * 12.6 * 4.6 * cos 90 )

a² = 179.92

a = sqrt (179.92)

a = 13.4

Answer:

No, the sale price wasn't consistent with the ad

Step-by-step explanation:

The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

330

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

We are rounding the number 326 to the nearest tens.

The '2' is in the tens place, and the '6' is to the right of the digit.

Since the '6' is greater than or equal to 5, then we would round up.

326 ≈ 330

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

[tex]\large \boxed{\$10000.00}[/tex]

Step-by-step explanation:

We can use the formula for continuously compounded interest.

[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]

Answer:

a) Your answer for part a (I got 3/28) is wrong.

Odds are always expressed as ratios after calculating. Therefore, the odds in favour of receiving a gift = 3:22

b) Your answer in part b(I got 7/9) is correct.

The probability of the box having a toy is 7/9.

Step-by-step explanation:

The question above has to do with odds and probability.

It is important to note that odds are expressed in the form of ratios while probabilities are expressed as fractions.

a) At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift.(I got 3/28)

The formula for calculating odds from probability is Odds = Probability / (1 - Probability).

Probability = 3/25

Odds =(3/25)/(1 - 3/25)

= (3/25)/22/25

= 3/25 ÷ 22/25

= 3/25 × 25/22

= 3/22

Note that odds are always expressed as ratios.

Therefore, the odds in favour of receiving a gift = 3:22

Your answer for part a (I got 3/28) is wrong.

The correct answer is 3:22

b) A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9.

The formula for calculating probability from odds is P = Odds / (Odds + 1).

Odds = 7/2 or 7:2

We convert the odds to fraction when calculating

Probability = Odds / (Odds + 1).

Probability = (7/2)/ (7/2 + 1)

Probability = (7/2)/9/2

Probability = 7/2 ÷ 9/2

= 7/2 × 2/9

= 7/9

Probability is always expressed as a fraction.

Therefore, the probability of the box having a toy is 7/9.

Your answer in part b(I got 7/9) is correct.

9514 1404 393

Answer:

  C)  462

Step-by-step explanation:

The presenters can be chosen 11C6 = 462 different ways.

__

If the teacher were concerned about the order of the presentations, the number of possibilities goes up to 11P6 = 332,640 different ways.

the corresponding angles should be equal

so, [tex] 5x+15=90 \implies 5x=75\implies x=15^{\circ}[/tex]

Answer:

A

Step-by-step explanation:

f(x)→g(x)

(0, 0) → (3, -4)

Therefore it increases it x-axis from 0 to 3

And decreases in y-axis from 0 to -4

Answer:

Answer: negative

Y= -500x + 4,500

Step-by-step explanation:

Answer:

C. negative

B. Y= -500x + 4,500

I just did it

Answer: (iii) Profit The marked price of an article is 15% above its selling price and the cost price is 25% less tha its marked price. Find the discount percent and gain percent.​

Step-by-step explanation:

Answer:

does the answer help you?

Answer:

A) 0.12. Yes. Choosing a green and blue M&M is possible

B) 0.43. Yes. Choosing a yellow and red M&M is possible

C) 0.78

Step-by-step explanation:

First of all, the summation of the distribution of all colours is;

Σ(all colors ) = 22% + 20% + 23% + 10% + 6% + 6% + 13% = 100%, or 1.

Thus;

a) P(green candy or blue candy) is;

P(GREEN ∪ BLUE) = P(G) + P(BL)

P(GREEN ∪ BLUE) = 6%+6%

P(GREEN ∪ BLUE) = 12% or 0.12

Now, due to the fact that we have to choose ONE candy and only ONE candy at random, then they are mutually exclusive: Yes. Choosing a green and blue M&M is possible

b)P(yellow candy or red candy is;

P(YELLOW ∪ RED) = P(Y) + P(R)

P(YELLOW ∪ RED) = 20% + 23% = 43% or 0.43

Yes. Choosing a yellow and red M&M is possible

c) P(NOT PURPLE)

the probability of having a purple is;

P(PURPLE) = 22% or 0.22

So, the Probability of NOT having a PURPLE is 1 - 0.22 = 0.78

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

y = 11x - 20

Step-by-step explanation:

y = 4(x - 5) + 7x

y = 4x - 20 + 7x

y = 11x - 20

Answer:

A. It will definitely be a t-test

Step-by-step explanation:

T-test is a type of inferential statistic test which used to determine whether there is a significant difference between mean of two group sets or variables.The t-test technique is widely used in hypothesis testing in statistics.  When the model building for game play is determine through regression analysis, it will require t-test to be conducted to reach a conclusion.

Answer:

a) forming a bell

b) 5

c) 4.7

d) mean

is the correct answer

pls mark me as brainliest

Answer:

[tex]-1 \frac{3}{4}[/tex]

Step-by-step explanation:

Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)

Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from  [tex]\frac{3}{4}[/tex].

To subtract this, we can break up [tex]2\frac{1}{2}[/tex]  into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)

We land up at [tex]-1 \frac{3}{4}[/tex].

Hope this helped!

Answer:

So this is giving us the slope the slope is y=-7x+150

Step-by-step explanation:

It is giving us the Y intercept which is $150  because thats how much he starts out with

It is giving us the slope -7 dollars because he is spending that everyday

Answer:

hello your question is incomplete below is the complete question

Find the minimum sample size n needed to estimate μ For the given values of​ c, σ​, and E. c=0.98​, σ=6.5​, and E=22 Assume that a preliminary sample has at least 30 members.

Answer : 48

Step-by-step explanation:

Given data:

E = 2.2,

std ( σ ) = 6.5

c ( level of confidence ) = 0.98

To find the minimum sample size

we have to first obtain the value of  [tex]Z_{a/2}[/tex]  

note : a can be found using this relation :

( 1 - a ) = 0.98 ----- equation 1

a = 1 - 0.98 = 0.02

hence:  a/2 = 0.01

This means that P( Z ≤ z ) = 0.99  the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33

P( Z ≤ 2.33 ) = 0.99

To obtain the sample size n

[tex]n = (\frac{std*z}{E} )^{2}[/tex]

n = [tex](\frac{6.5*2.33}{2.2} )^2[/tex] =  (6.88409)^2

Therefore n ≈ 48

Answer:

A

Step-by-step explanat

Answer:

Nine thousandths = 0.009

Step-by-step explanation:

thousandths =  1/1000 = 0.001

nine thousandths = 9/1000 = 0.009

Answer:

.009

Step-by-step explanation:

9 thousandths as a decimal is 9/1000.  Which is the same 0.009

Answer: 6

Step-by-step explanation:

Answer:

716.75 m^3

Step-by-step explanation:

Volume of a cylinder:

=> PI x R^2 x H

H = Height

R = Radius

=> PI x 3.9^2 x 15

=> PI x 15.21 x 15

=> PI x 228.15

=> 228.15 PI

           or

=> 228.15 x 3.14159

=> 716.75 m^3