Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5km from home and their walking speed is 4 kilometres per hour. A On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home?

Answer:

[tex]\sf \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

Angles are measured in a counterclockwise direction from the positive x-axis (initial side).

Therefore, if an angle's terminal side is on the positive y-axis, the angle will be 90° or [tex]\sf \dfrac{\pi}{2}[/tex] radians.

See attached diagram for visual explanation.

If the angle was [tex]\pi[/tex] then the terminal side would be on the negative x-axis.

If the angle was [tex]\dfrac32\pi[/tex] then the terminal side would be on the negative y-axis.

If the angle was [tex]2\pi[/tex] then the terminal side would be on the positive x-axis and the angle would be one complete revolution of the circle.

If he sold the 459 shares of rayje clothiers that you purchased yesterday. The amount of profit is: d. $6,306.66.

Using this formula

Profit=Net change×Number of shares sold

Where:

Net change=$13.74

Number of shares sold=459 shares

Let plug in the formula

Profit=$13.74×459 shares

Profit=$6,306.66

Therefore the amount of profit is: d. $6,306.66.

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Answer:

x=2

Step-by-step explanation:

To test when the function f(x) over takes the function g(x)

I just plugged in the x values

X f(x) g(x)

1 6 6

2 12 16

3 18 30

4 24 48

We can see from this table that f(x) is greater than g(x) starting from x=2

Therefore I think x=2 is your answer.

Hope this helps! :)

Answer:

[tex]v = 2064.2 {cm}^{3} [/tex]

Step-by-step explanation:

we first consider the formula for the volume of a sphere

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

we were given diameter of 15.7cm.

we can find the radius by dividing the diameter by 2

because two times a radius makes a diameter.

[tex] \frac{15.7}{2} = 7.9cm[/tex]

we have the radius as 7.9cm.

and we know pi (π) to be 3.14 or 22/7.

but in this case, we use 3.14.

now let's substitute the values in the formula

[tex]v = \frac{4}{3} \times 3.14 \times {7.9}^{3} [/tex]

and we will get

[tex]v = 2064.19 {cm}^{3} [/tex]

but the nearest 10th will be

[tex]v = 2064.2 {cm}^{3} [/tex]

Answer: is 2026.3 cm ^3

Step-by-step explanation:

=》 Solution;

solving,

x+2x+6x+18=180

or, 9x + 18 = 180

or, x + 18 = 180/9

or, x + 18 = 20

or, x = 20 - 18

or, x = 2

therefore, value of x is 2

now,

i) x = 1 X x = 1 X 2 = 2

ii) 2x = 2 X x = 2 X 2 = 4

iii) 6x = 6 X x = 6 x 2 = 12

The hypothesis illustrates that C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

Using a graphing calculator and calculated the t-interval of the jellybean sample using a 99% confidence level:

tInterval 9.68,1.23,125,0.99

It resulted in 9.68 ± 0.287805.

Therefore, we're 99% confident that the weight number of jellybeans would lie between 9.3922 oz and 9.9678 oz.

Therefore, the researcher failed to reject the null hypothesis.

Complete question:

A weight of 9.45 oz lies within this range, therefore, it is possible that the candy company's claim is true.

A candy company claims that their bags of jellybeans have a mean weight of 9.45 oz. 125 randomly chosen bags of jellybeans were sampled, and it was discovered that their mean weight was 9.68 oz, with a standard deviation of 1.23 oz. Test this hypothesis using a 99% confidence level.

A- Reject the null hypothesis. There is not enough evidence to oppose the company's claim.

B- Reject the null hypothesis. There is enough evidence to oppose the company's claim.

C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

D- Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.

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Answer:

627 miles north

747 miles east

Step-by-step explanation:

Bearing angles are measured east of north, so in (N, E) coordinates, the final position of the plane is ...

 (1.5 h)(650 mi/h)(cos(50°), sin(50°)) = (975cos(50°), 975sin(50°)) mi

 = (626.72, 746.89) mi

The plane will be 627 miles north and 747 miles east of its point of departure.

Answer:

x = 2

y = -3

Step-by-step explanation:

y = x - 5  -------------------(I)

x + y = -1 ----------------(II)

Substitute y = x -5 in equation (II)

x + (x - 5) = -1

x + x - 5 = -1   {Combine like terms}

   2x - 5 = -1 {Add 5 to both sides}

        2x  = -1 + 5

         2x = 4 {Divide both sides by 2}

           x = 4/2

x = 2

Substitute x = 2 in equation (I)

y = 2 - 5

y = -3

Answer:

m∠A = 139°

Step-by-step explanation:

Since knowing that:

Supplementary angles = 180 degree

Thus we put that in both equation:

( 7x - 15 ) + ( 2x - 3 ) = 180

Combine like terms & use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Hence,  Angle A will have a measure of 7x - 15 which means  7 ×  22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

Check Answer by add 139 and 31 which equal 180

~lenvy~

Answer:

a

Step-by-step explanation:

 Answer: a and b bc that are in the negative-positive quad

Answer:

28

Step-by-step explanation:

in order to find first quartile find median:

median =32

since there are 6 data points lets split the data set into 2 groups of 3 data points each

the median of the first group is the first quartile and the median of the second group is the third quartile

group 1: 16 28 28

median=28

1st quartile=28

The theorem simply states that diagonals of a parallelogram bisect each other is proven as OA = OC.

From the information, OA = OC and OB = OD. In both triangles AOD and BOC, AD = BC since opposite angles are equal.

Also, ADO = CBO since alternate interior angles are equal. Also, DAO = BCO.

Therefore, OA = OC

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Check the picture below.

Using compound interest, it is found that Claire will have $6,186 in her account when Henry's money has tripled in value.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For Henry, we have that r = 0.0675, n = 12. The time it takes for the amount to triple is t when A(t) = 3P, hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]3P = P\left(1 + \frac{0.0675}{12}\right)^{12t}[/tex]

[tex](1.005625)^{12t} = 3[/tex]

[tex]\log{(1.005625)^{12t}} = \log{3}[/tex]

[tex]12t\log{(1.005625)} = \log{3}[/tex]

[tex]t = \frac{\log{3}}{12\log{(1.005625)}}[/tex]

t = 16.32.

Then, for Claire, we have that the parameters are as follows:

P = 2300, r = 0.0625, n = 1, t = 16.32.

Hence, the amount is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 2300\left(1 + \frac{0.0625}{1}\right)^{16.32}[/tex]

A(t) = 6186.

Claire will have $6,186 in her account when Henry's money has tripled in value.

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1) 720 inches³

2) 900 inches³

3) 120 inches³

hope it helps...!!!

Answer:

2 quarts .

Step-by-step explanation:

4 quarts make a gallon but two is already added

Answer:

2 quarts

Step-by-step explanation:

Answer:

5 1/2

Step-by-step explanation:

2x2=

4

2 x 1/2 =

1

2 x 1/4=

1/2

1+1/2=

1 1/2+4 =

5 1/2

Answer:

I believe it would be 8 11/20 ft³

Step-by-step explanation:

The z-score is the number of standard deviations while the data value is away from the mean.

The Z-score is said to be a kind of numerical measurement that is known to show or depicts the value's relationship one has to the mean of a group of values.

WE have given a mean: 4.9 median: 6 mode: 6 variance: 4

The Z-score is often measured usually in terms of standard deviations that arise from the mean. It means that if a Z-score is 0, it shows that the data point's score is the same as the mean value.

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Answer:

standard deviations, mean.

Step-by-step explanation:

EDGE2022

Answer:

ok so 23 percent more means thats its the oringaly price times 1.23 so

0.75*1.23=9.225

92 cents per apple

Hope This Helps!!!

Answer:

  120 cubes

Step-by-step explanation:

This kind of problem can be easier to work if you rewrite the prism dimensions in terms of cube dimensions. For 2 cm cubes, the prism dimensions are ...

As always, the volume of the rectangular prism is the product of its dimensions:

  V = (6)(10)(2) = 120 cubes

120 2-cm cubes will fit int the rectangular prism.

Answer:

-47

Step-by-step explanation:

28+ ___=-19

28+x= -19

-28 -28

_________

X= -47

28+-47= -19

you have to subtract from the $92.74 the $10 of the monthly fee, and then that is divided by the additional amount per minute, so that gives us the result I use it 1379 minutes

Answer:

Answer below!

Step-by-step explanation:

Alright I'm not too sure on what the question is asking for per your instructions, but I've written out my best explanation on how to use distributive property to solve this equation.

So first, what is the process of distributive property? It basically states whatever is in the parenthesis is multiplied by the outside number.

In simpler terms, each character in the parenthesis is multiplied by the number standing outside of the parenthesis.

So we can go...

(3 x 4x) - (3 x 5) = (12x) - (15)

And there's your answer, 12x - 15! Unless you know what x means, you'll probably just stop there.

Hope this was helpful!

Step-by-step explanation:

16, 48, 144

hmmm.

the first thing that comes to mind : it cannot be an addition, as the difference between the 2nd and 3rd numbers is much bigger than the difference between the 1st and 2nd numbers.

so, we try multiplication.

and I see : 16×3 = 48

aha !

48×3 = 144

ok, we found it. the sequence is clearly created by multiplying always the previous number by 3.

so, we have 2 main choices to get the 6th term :

1. simply calculate 144 ×3×3×3 (3 times to get from the 3rd to the 6th term).

2. define the sequence formula and calculate for the 6th term.

1.

144 × 3×3×3 = 144 × 27 = 3,888

2.

a1 = 16

a2 = a1×3 = 16×3 = 48

a3 = a2×3 = a1×3×3 = 16×9 = 144

an = a1 × 3^(n-1) = 16 × 3^(n-1)

a6 = 16 × 3⁵ = 16 × 243 = 3,888

Answer:

1890 in³

Step-by-step explanation:

The formula to find the volume of a triangular prism: 1/2 x b x h x l, where b is the base, h is the height and l is the length.

1) Substitute the given values in the image into the formula above.

= 1/2 x 18 x 7 x 30

= 1/2 x 126 x 30

= 1/2 x 3780

= 1890

Answer:

187 in^2

Step-by-step explanation:

hope this helps!