Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer

Answer:1

Step-by-step explanation:

Answer:

D. x(2x − 3)/ 7

Step-by-step explanation:

[tex]To- divide- by -a -fraction, multiply- by -its -reciprocal.\\\frac{2x-3}{x} *\frac{x^{2} }{7} \\Cancel- the- common -factor -of x\\(2x-3)\frac{x}{7}\\ Apply- the- distributive- property.\\2x\frac{x}{7} -3\frac{x}{7}\\ Multiply ; 2x\frac{x}{7}\\ \frac{2x^2}{7} -3\frac{x}{7}\\ Combine -3- and; \frac{x}{7} \\\frac{2x^2}{7} + \frac{-3x}{7}\\ Move- the- negative- in- front -of -the- fraction.\\\frac{2x^2}{7} - \frac{3x}{7} \\Simplify- terms.\\ x\frac{(2x-3)}{7}\\[/tex]

Answer:

8x

Step-by-step explanation:

Answer:

Step-by-step explanation:

-6y+4x=z

-6y=z-4x

y=(z-4x)/-6

Answer:

[tex]y=\frac{z-4x}{-6}[/tex]

Step-by-step explanation:

Answer: 6811

Step-by-step explanation:

in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17

--

so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811

Answer:

2 total roots

x = -1/3, 3/4

Step-by-step explanation:

We can use the discriminant b² - 4ac to find how many roots a polynomial has.

Answer:

Step-by-step explanation:

Edginuity 2021

Answer:

7

Step-by-step explanation:

[tex]1.5x = 10.5 \\ x = \frac{10.5}{1.5 } \\ x = 7[/tex]

Hope it helps!

Answer:

7

Step-by-step explanation:

We need to transpose the equation which will give us: x = 10.5 ÷ 1.5

After the division, we get 7

For a check up: 1.5 × 7 = 10.5

Hope this helps and please mark as the brainliest.

Answer:

0.3032

Step-by-step explanation:

Use binomial probability.

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

P = ₆C₃ (0.45)³ (0.55)³

P = 0.3032

Answer:

3.6miles

Step-by-step explanation:

Given:

distance of tent from the closest point on shore-line, d=3miles.

distance between shoreline point and coral reef, x=2miles

The shortest distance (say l) that the visitor runs towards the reef in order to swim a minimum distance which takes least time.

[tex]\therefore l^2=d^2+x^2\\l=\sqrt{3^2+3^2} \\l=3.6\ miles[/tex]

Now on reaching at the shore at this point the visitor will have to swim the least distance due east to reach coral reef.

The radioactive compound has a half-life of around 3.09 hours.

The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:

Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,

100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.

At time 6 hours, the amount of the substance present is,

100 mg × (1 - 3%) = 97 mg.

Given that the amount of material available determines how quickly something degrades,

The half-life can be calculated as follows:

[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]

Therefore, the half-life of the radioactive substance is approximately 3.09 hours.

Learn more about half-life:

brainly.com/question/24710827

#SPJ12

Answer:

[tex]y = 5x-15[/tex]

Step-by-step explanation:

Parallel ⇒ So the slopes will definitely be equal

So,

Slope = m = 5

Now,

Point = (x,y) = (4,5)

So, x = 4, y = 5

Putting these in the slope intercept form to get b

[tex]y = mx +b \\[/tex]

5 = (5)(4) + b

5 = 20 + b

b = -20+5

b = -15

So, Putting m and b in the slope intercept form to get the required equation,

[tex]y = 5x-15[/tex]

Answer:

7.5* 10^8

Step-by-step explanation:

(1.5 x 10^5)(5 x 10^3)

Multiply the numbers

1.5*5=7.5

Add the exponents

10 ^(5+3) = 10^8

Put back together

7.5* 10^8

This is in scientific notation

Answer:

9 1/2

Step-by-step explanation:

Answer:

[tex]\frac{3x}{32}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}\times \frac{1}{4}x[/tex]

[tex]\frac{3\times \:1\times \:x}{8\times \:4}[/tex]

[tex]=\frac{3x}{32}[/tex]

Answer:

[tex]180[/tex]

Step-by-step explanation:

[tex]6 \times 2 \times 3 \times 5[/tex]

[tex]12 \times 15[/tex]

[tex]=180[/tex]

Steps to solve:

6 * 2 + 3 - 5

~Multiply

12 + 3 - 5

~Add

15 - 5

~Subtract

10

Best of Luck!

Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

Answer:

9 people

Step-by-step explanation:

37, 39, 41, 46, 61, 63, 69, 77, 80

9 people waited more than 36 minutes.

Answer:

You have found 24 nickels.

Step-by-step explanation:

Let N be the number of nickles, D be the number of dimes and Q be the number of quarters. The number of coins and their face values are given by the following expressions, respectively:

[tex]N+D+Q=72\\0.05N+0.10D+0.25Q=10.20[/tex]

As of now we have three variables and two expressions, the final expression needed to solve the linear system is given by the amount offered by the coin dealer:

[tex]10N+20D+15Q=1,060[/tex]

Solving the linear system:

[tex]N+D+Q=72\\5N+10D+25Q=1,020\\10N+20D+15Q=1,060\\\\10N-10N+20D-20D+15Q-50Q=1,060-(2*1,020)\\-35Q=-980\\Q=28\\\\5N-10N+10D-10D+25Q-10Q=1,020-720\\-5N+15Q=300\\-5N=300-(15*28)\\N=24[/tex]

You have found 24 nickels.

Answer:

P-value = 0.00028

Step-by-step explanation:

The statician performs an hypothesis test for the mean difference.

As the alternative hypothesis is Ha: μd ≠ 0, we know that it is a two-tailed test.

The test statistic is t=6.163.

For a two-tailed test and 8 degrees of freedom, this corresponds to a P-value of:

[tex]\text{P-value}=2\cdot P(t>6.163)=0.00028[/tex]

This P-value is smaller enough to reject the null hypothesis at almost any significance level.

Answer:

3.2

Step-by-step explanation:

Rounded to the nearest 10

Answer:

57.0°, 123.0°

84.0°, 96.0°

56.9,

Step-by-step explanation:

Given:

a = 36, c = 48, ∠A = 39°

∠B1 is larger than ∠B2

Find attached the diagram.

We would apply sine rule to find ∠C

a/sinA = c/sinC

36/sin39° = 48/sinC

36sinC = 48sin39

sinC = 48sin39/36 = 48(0.6293)/36

sin C = 0.8391

C = arcsin(0.8391)

C= 57.045

∠C1 = C = 57.0° (1 decimal place)

For sine rule, angles which give same value are x and (180-x)

If C= x = 57.0°

180-x = 180 - 57.0° = 123°

∠C2 = 123.0°

sin57° = sin123° = 0.8387

∠A + ∠B + ∠C = 180° (sum of angles I'm a triangle)

39.0 + ∠B +57.0 = 180°

∠B = 180-(39+57)

∠B = 84.0°

∠B1 = 84.0°

∠B2 = 180-∠B1 = 180°-84.0°

∠B2 = 96.0°

∠B1 is smaller than ∠B2

b/sinB = c/sinC

b1/sinB1 = c1/sinC1

b/sin84 = 48/sin57

b = 48sin84/sin57

b = 56.9

The measure of C is 57.0 and the measure of B is 84.0 degrees

The given parameters are:

[tex]\mathbf{a = 36cm}[/tex]

[tex]\mathbf{c = 48cm}[/tex]

[tex]\mathbf{\angle A = 39^o}[/tex]

The measure of angle Ais calculated using the following sine formula

[tex]\mathbf{\frac{a}{sin\ A} = \frac{c}{sin\ C}}[/tex]

So, we have:

[tex]\mathbf{\frac{36}{sin\ 39} = \frac{48}{sin\ C}}[/tex]

Evaluate sin 39

[tex]\mathbf{\frac{36}{0.6293} = \frac{48}{sin\ C}}[/tex]

Cross multiply

[tex]\mathbf{sin\ C \times 36 = 48 \times 0.6293}[/tex]

[tex]\mathbf{sin\ C \times 36 = 30.2064}[/tex]

Divide both sides by 36

[tex]\mathbf{sin\ C= 0.8391}[/tex]

Take arc sin of both sides

[tex]\mathbf{C = sin^{-1}(0.8391)}[/tex]

[tex]\mathbf{C = 57.0}[/tex]

The value of B is:

[tex]\mathbf{B = 180 - A - C}[/tex]

So, we have:

[tex]\mathbf{B = 180 - 39 - 57.0\\}[/tex]

[tex]\mathbf{B = 84.0}[/tex]

Hence, the measure of C is 57.0 and the measure of B is 84.0 degrees

Read more about sine equations at:

https://brainly.com/question/14140350

Step-by-step explanation:

If a triangle is rotated 90° about the origin.

The rule that describes the transformation is

(x, y) → (–y, x)

Answer:

Integer

Step-by-step explanation:

Integer :a number which is not a fraction; a whole number that can be Positive or negative

Hope this helps.. Good Luck

Answer:

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159

Step-by-step explanation:

According to the given data we have the following:

mean = μ= 22

standard deviation = σ = 2

n = 100

μx = 22

σx=σ/√n=2/√100=0.2

Therefore, P( x < 21.8)=P(x-μx)/σx<(21.8-22)/0.2

=P(z<-1)

= 0.159

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159

Segment AB will move further away from point P (since both A and B move away from P). So it's not possible for AB and A'B' to be on the same line. In fact, these two line segments are parallel.

In contrast, AC and A'C' are on the same line. Points A and C move away from P, but line AC goes through P, which means A'C' does as well. It's not possible for AC and A'C' to be parallel.

Check out the diagram shown below.

Side note: point P is the only point that does not move. This is known as the fixed point.

Answer:

Step-by-step explanation:

| − | = | + 9I

THERE ARE TWO POSSIBILITIES

2x-1=4x+9                          and              2x-1=-4x-9

2x-4x=9+1                            and           2x+4x=-9+1

-2x=10                                   and            6x=-8

x=-5                                and                  x=-8/6

x=-5                               and                     x=-4/3

SOLUTION SET ={-5,-4/3}

[tex]\frac{2x-1}{3}-\frac{3x}{4}=\frac{5}{6}\\ taking LCM\\\frac{8x-4-9x}{12}=\frac{5}{6}\\\frac{-1x-24}{12}=\frac{5}{6}\\ by cross multiplication\\6(-1x-4)=12*5\\-6x-24=60\\-6x=60+24\\-6x=84\\\\x=-14\\soltion set {-14}[/tex]

[tex]10+\sqrt{10m-1}=13\\\sqrt{10m-1}=13-10\\\\\sqrt{10m-1}=3\\ taking square on both sides\\10m-1=3^2\\10m-1=9\\10m=9+1\\10m=10\\m=1[/tex]  

the number of solution to a linear equation is 1

2(x - 4) = 6 then x is ----7

Solution of | + | = − is ---------13/3,5/3

Answer:

The 90% confidence interval of the true proportion of people who watched educational television is (0.7117, 0.8283)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 200, \pi = \frac{154}{200} = 0.77[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.96\sqrt{\frac{0.77*0.23}{200}} = 0.7117[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.96\sqrt{\frac{0.77*0.23}{200}} = 0.8283[/tex]

The 90% confidence interval of the true proportion of people who watched educational television is (0.7117, 0.8283)

[tex]32500[/tex]

[tex]0.00604[/tex]

[tex]2.4 \times 10^6[/tex]

[tex]1.47 \times 10^{-3}[/tex]

Answer:

A) 32500

B) 0.00604

C) [tex]2.4 * 10^6[/tex]

D) [tex]1.47 * 10^{-3}[/tex]

Answer:

  15 minutes

Step-by-step explanation:

Betty mows at 3 times the speed that Bullwinkle does, so is equivalent to having 3 Bullwinkles in her place. That makes the lawn get mowed as though 4 Bullwinkles were working, so it will take 1/4 the time it takes Bullwinkle to mow the whole yard. 1/4 of 60 minutes is 15 minutes.

Working together, Betty and Bullwinkle will take 15 minutes to mow the lawn.

Answer:

[tex]t=\frac{5.2-5}{\frac{0.8}{\sqrt{40}}}=1.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=40-1=39[/tex]  

Thep value for this case would be given by:

[tex]p_v =P(t_{(39)}>1.58)=0.061[/tex]  

Since the p value is higher than the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that true mean is not significantly higher than 5.

Step-by-step explanation:

Information provided

[tex]\bar X=5.2[/tex] represent the sample mean

[tex]s=0.8[/tex] represent the sample standard deviation

[tex]n=40[/tex] sample size  

[tex]\mu_o =5[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true mean is higher than 5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{5.2-5}{\frac{0.8}{\sqrt{40}}}=1.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=40-1=39[/tex]  

Thep value for this case would be given by:

[tex]p_v =P(t_{(39)}>1.58)=0.061[/tex]  

Since the p value is higher than the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that true mean is not significantly higher than 5.

Answer:

9x-11

Step-by-step explanation:

-5+2(x-3)+7x

Distribute

-5 +2x -6 +7x

-11 +9x

9x-11

Answer:

[tex]= 9x - 11 \\ [/tex]

Step-by-step explanation:

[tex] - 5 + 2(x - 3) + 7x \\ - 5 + 2x - 6 + 7x \\ - 5 - 6 + 2x + 7x \\ - 11 + 9x \\ = 9x - 11[/tex]