Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?

Answer:

Step-by-step explanation:

[tex] \sf{ - 7y = - 91}[/tex]

Divide both sides of the equation by -7

⇒[tex] \sf{ \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} }[/tex]

Calculate

⇒[tex] \sf{y = 13}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex] \boxed{\sf y = 13} [/tex]

Step-by-step explanation:

Solve for y:

[tex] \sf \implies - 7y = - 91[/tex]

Divide both sides of -7y = -91 by -7:

[tex] \sf \implies \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} [/tex]

[tex] \sf \frac{ - 7}{ - 7} = 1 : [/tex]

[tex] \sf \implies y = \frac{ - 91}{ - 7} [/tex]

[tex] \sf \implies y = \frac{ \cancel{ - 7} \times 13}{ \cancel{ - 7}} [/tex]

[tex] \sf \implies y = 13[/tex]

Answer:

5.6

Step-by-step explanation:

3.5 x 1.6

It all depends on where the parentheses are in the question.

(3) · (1/2) · (1.6)  =  2.4

or

(3-1/2) · (1.6)  =  5.6

Answer:

9 x =108

Step-by-step explanation:

Let the number of candies be x.

According to the question,

x=108/9

We can also write it as,

9 x=108

By the way ,each child will get 12 candies.

Thank you!

Answer:

45.35

Step-by-step explanation:

From the above question, we are told that the annual effective rate = 10% = 0.10

Note also that payment is been made every 2 years

Hence , we apply the formula of effective interest rate for a period of 2 years.

Effective Interest rate(j) = (1 + r)² - 1

= (1 + 0.10)² - 1

= 1.10² - 1

= 1.21

= 0.21

Present value of perpetuality = t/[j × j/(1 + r)²]

Where t = time in years = 2

r = 0.10

= 2/ [0.21 × 0.21/(1 + 0.10)²

= 54.87528

Present value at time t = 0

= 54.87528(1 + r)^-2

= 54.87528(1 + 0.10) ^-2

= 54.87528(1.10)^-2

= 45.35

Therefore, the present value at time (t) is 0 = 45.35

Answer: -4

At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.

Hope that helped,

-sirswagger21

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

Answer:

48 soldiers

Step-by-step explanation:

60 soldiers                    20 days

x soldiers                       100 days

60 x 20 = 1200 = 100x

Therefore x = 1200/100 = 12

60 - 12 = 48

Hope that helped!!! k

Answer:

30 Soldiers

Step-by-step explanation:

Given:

1) No of soldiers=60

No of days=20

2) No of days=100

No of soldiers=?

No of soldiers to leave=?

Solution:

Let us use the cross multiplication method.

Let x be the no of soldiers.

No of days                                     No of  soldiers

1) 20                                                     60

2) 100                                                    x

by cross multiplying,

20x=100 x 60

20x=600

x=600/20

x=30 soldiers

Therefore, No of soldiers to leave =60-30=30 soldiers

Answer:

1/5

Step-by-step explanation:

.7555555(repeating )

writing as a fraction

x = .755555555

10 x = 7.555555

Subtract the two

10x = 7.555555

-x =     .75555555

--------------------------

9x  =6.8

Divide each side by 9

x = 6.8/9

x = 68/90

Divide by 2

x = 34/45

We do the same  for .555555 repeating

y = .5555 repeating

10 y = 5.5 repeating

10y  = 5.5

-y =       .555

-------------------

9y = 5

y = 5/9

Subtract x - y

34/45 - 5/9

Get a common denominator

34/45 - 25/45

9/45

1/5

9514 1404 393

Answer:

  87°

Step-by-step explanation:

Call the circle center point X. The measure of arc FG is the measure of central angle FXG, which is the supplement of central angle GXH.

 arc FG = 180° -93° = 87°

Answer:

37 hours

Step-by-step explanation:

4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours

Answer:

37 hours

Step-by-step explanation:

4.5 hours = 4 hrs and 30 mins

8.75 hrs = 8 hrs and 45 mins

9.5 hrs = 9 hrs and 30 mins

10 hrs = 10 hrs and 0 min

4.25 hrs = 4 hrs and 15 mins

(30 + 45 + 30 + 15) mins = 2 hrs

Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours

Step-by-step explanation:

Recall that

[tex]\sin(-x) = -\sin x[/tex]

Therefore,

[tex]\csc(-x) = \dfrac{1}{\sin(-x)} = -\dfrac{1}{\sin x}[/tex]

so

[tex]\csc(-x)\tan x = \left(-\dfrac{1}{\sin x}\right)\left(\dfrac{\sin x}{\cos x}\right)[/tex]

[tex]\:\:\:\:\:\:\:\:\:= -\dfrac{1}{\cos x} = -\sec x[/tex]

Answer:

N=240;I%=5.6=-205000;PMT=;Fv=0;P/Y=12;C/Y=12;PMT:END

Step-by-step explanation:

A P E X

The group of values to be plugged into TVM solver is

N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.

We have 20  year loan then the number of periods will be

N = 20 x 12

N= 240

and, the Monthly payment is $510 then

PMT = - 510

and, Interest = 19.2%

and, PV = - 205, 000

Thus, N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.

Learn more about TVM here:

brainly.com/question/5566317

#SPJ7

Answer:

A service could be multiple things.

Step-by-step explanation:

Like, working as a scribe in a nursing home helping old people. Or, being part of a leadership club at school that funds food banks and things like that

Answer:

a

Step-by-step explanation:

Answer:

[tex]y = -x - 3[/tex]

Step-by-step explanation:

We are trying to get the equation [tex]3x + 3y = -9[/tex] into the form [tex]y = mx+b[/tex], aka slope-intercept form.

To do this we are trying to isolate y.

[tex]3x + 3y = -9[/tex]

Subtract 3x from both sides:

[tex]3y = -9 - 3x[/tex]

Rearrange the terms:

[tex]3y = -3x - 9[/tex]

Divide both sides by 3:

[tex]y = -x - 3[/tex]

Hope this helped!

[tex] \frac{5b^{5}c}{4c^4} \times \frac{8c}{b^4}[/tex]

[tex]\frac{40b^{5}c^2}{4b^{4}c^4}[/tex]

[tex]{10b^{5-4}c^{2-4}}[/tex]

[tex]10bc^-2[/tex]

[tex]\frac{10b}{c^2}[/tex]

Step-by-step explanation:

[tex] \frac{5 {b}^{5} c}{ 4{c}^{4} } \times \frac{8c}{ {b}^{4} } [/tex]

First reduce the expression with b⁴

b⁴ will cancel b^5 remaining with one b

That's

Next reduce 8 and 4 with their GCF which is 4

We have

Reduce the expression with c .

c will go into c⁴ remaining with c³

That's

Simplify the expression again with c

That's

Multiply the expression

We have the final answer as

Hope this helps you

Answer:

45/27=30/18=x/24

x = 30×24/18

or, x = 40

Answer:

? = 40

Step-by-step explanation:

Since the polygons are similar then the corresponding sides are in proportion, that is

[tex]\frac{?}{24}[/tex] = [tex]\frac{?}{24}[/tex] = [tex]\frac{30}{18}[/tex] ( cross- multiply )

18 ? = 720 ( divide both sides by 18 )

? = 40

Answer:

just devide it. after that ÷ with 100 per time

Step-by-step explanation: Let's begin by finding the

greatest common factor for the numbers 65 and 39.

I would make a factor tree and break up 65 and 39.

So 65 is 13 x 5 and 39 is 13 x 3.

Since the 13's match up, the greatest

common factor between 65 and 39 is 13.

For the variables, we use the smallest power on each of them.

So we use a^3 and b^4 to get 13a^3b^4 as our GCF.

Answer:

D

Step-by-step explanation:

To determine the range we must solve this inequality;

● 1200000<1800000-250x<1300000

Substract 1800000 from both sides.

● 1200000-1800000<1800000-250x<1300000-1800000

● -600000< -250x < -500000

Divide both sides by 250

● -600000/250 < -250x/250 < -500000/250

● -2400 < -x < -2000

Multiply both sides by -1 and switch the signs

● 2000 < x < 2400

The correct option is D. 2000<= x <= 2400

Given, the value of an airplane depends on the flight hours,

[tex]V= 1800000-250x[/tex], here x is the flight hours.

We have to calculate the range of x After one year.

Since, [tex]V= 1800000-250x[/tex]

[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]

Since the value of the plane is between $1,200,000 and $1,300,000. So,

[tex]x=\dfrac{1800000-1200000}{250}[/tex]

[tex]x=\dfrac{600000}{250}[/tex]

[tex]x=2400\\[/tex]

When V is 1300000 then x will be,

[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]

[tex]x=\dfrac{500000}{250}[/tex]

[tex]x=2000[/tex]

Hence the range of x will be from 2000 to 2400.

The correct option is D. 2000<= x <= 2400.

For more details on range follow the link:

https://brainly.com/question/10185991

Answer:

$935.76

Step-by-step explanation:

BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?​

Step 1

We find the Present value factor of sum

The formula =

(1 + i)^n

Where

i = maturity rate = 9% = 0.09

n = number of years = 10 years

Present Value = ( 1 + 0.09)^-10

= 0.4224

Step 2

We find the present value factor of annuity

The formula is given as:

1 - (1+i)^-n / i

i = maturity rate = 9% = 0.09

n = number of years = 10 years

= 1 - (1 + 0.09)^-10 /0.09

= 1 - 0.4224 /0.09

= 0.5775 /0.09

= 6.417

Step 3

The bond's current market price is calculated as:

= PV factor of Sum × Par Value + PV factor of annuity × coupon payment

Coupon payment is calculated as:

= Coupon interest × par value

= 8% × 1000

= 80

Hence,

= 0.4224 × 1,000 + 6.417 × 80

= 422.4 + 513.36

= 935.76

In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:

[tex]\$935.76[/tex]

We find the Present value factor of sum, by the formula of:

[tex](1 + i)^n[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]

We find the present value factor of annuity, by the formula as:

[tex]1 - (1+i)^{-n} / i[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]

The bond's current market price is calculated as:

[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]

Coupon payment is calculated as:

[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]

So continue the calcule;

[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]

See more about market place at brainly.com/question/24518027

Answer:

The sample required is  [tex]n = 135[/tex]

Step-by-step explanation:

From the question we are told that

     The  standard deviation is  [tex]\sigma = 9[/tex]

      The margin of error is [tex]E = 2[/tex]

Given that the confidence level is  99%  then the level of  significance is mathematically evaluated as

         [tex]\alpha = 100-99[/tex]

        [tex]\alpha = 1 \%[/tex]

        [tex]\alpha = 0.01[/tex]

Next we will obtain the critical value  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference  math dot armstrong dot edu) , the value is  

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58[/tex]

The  sample size is mathematically represented as

          [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

substituting values

           [tex]n = [ \frac{ 2.58 * 9 }{2} ]^2[/tex]

            [tex]n = 135[/tex]

Answer:x2.2

Step-by-step explanation:

Answer:

105.12 ft²

Step-by-step explanation:

Let's first find the area of the rectangle.

[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².

To find the area of the semi-circle, we find the area of a whole circle and divide by two.

The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.

[tex]3.14\cdot4^2[/tex]

[tex]3.14\cdot16[/tex]

[tex]50.24\div2=25.12[/tex]

Add 80 and 25.12:

[tex]80+25.12=105.12[/tex]

Hope this helped!

Answer:

Option B, parallel

Step-by-step explanation:

for the first line,

[3-(-1)]/[11-9]

= 4/2 = 2

for the second line,

(0-(-4))/(-4-(-6))

= 4/2 = 2

Both has same slope so they're parallel but it doesn't seem like they are the same line

Answer:

[tex]\large \boxed{\sf No}[/tex]

Step-by-step explanation:

There are 365 days in 1 year.

The average person lives for about 78 years.

Multiply 78 by 365 to find the value in days.

[tex]78 \times 365= 28470[/tex]

The average person lives for about 28470 days.

Answer:

Option C

The graph of g is vertically shifted 5 units down

⇛6(2 - 6x) = -24

⇛12 - 36x = -24

⇛-36x = -24 - 12

⇛-36x = -36

⇛x = -36/-36

⇛x = 1

Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom   n  - 1     df = 22 - 1     df = 21

As the question mentions " different " that means,  a two-tail test

At 0,01 significance level     α  = 0,01       α/2  =  0,005

and t(c)  = 2,831

Test Hypothesis

Null Hypothesis                      H₀          μ  =  μ₀

Alternative hypothesis           Hₐ          μ  ≠  μ₀

To calculate t(s)

t(s)  =  (  μ  -  μ₀ ) /σ/√n

t(s)  =  (  433,50 - 385 ) / 86,92 / √22

t(s)  =  2,6171

Comparing   t(c)   and t(s)

t(s) < t(c)

Then  t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim