Eric ran from school to the town monument and back again. On his way to the monument, he ran at 10kph and went back to school at 8kph. The entire trip took 2 hours and 15 minutes. How far is the monument from school?

Answer:

a) (i) 14.6cm (3 s.f.)

(ii) 77.6° (1 d.p.)

b) (i) see 4th picture

(ii) 16.3cm² (3 s.f.)

Step-by-step explanation:

Please see the attached pictures for full solution.

The model best fits the given situation will be exponential. Then the correct option is A.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

If the Principal P is invested at an annual interest of rate r, compounded k times a year for t years.  

Then the equation will be given as,

[tex]\rm A = P(1+ r)^{kt}[/tex]

Then the correct option is A.

More about the compound interest link is given below.

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Answer:

The third choice.

Step-by-step explanation:

This is a linear function.

The equation is y = (x - 5)(5x + 4) - 5x^2.

y = 5x^2 - 25x + 4x - 20 - 5x^2

y = 5x^2 - 5x^2 - 21x - 20

y = -21x - 20

That means this is a linear function, with a linear term of -21x and constant term of -20.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

180 grams

Step-by-step explanation:

2 people = 5 ounces

6 people= 5*3= 15 ounces

1 ounce= 28 grams

15 ounces= 15*28 grams= 420 grams

There is 240 grams already on the weight, so

420- 240= 180 grams more of diced onions are required

Answer:

[tex] \frac{80}{100} = \frac{4}{5} [/tex]

Answer:

$825.28

Step-by-step explanation:

First, we need to calculate the 15% off sale:

870(0.85) = 739.50

Now, we will calculate and add on the sales tax:

739.50(1.116) = 825.28

So, the final price of the dresser will be $825.28

Hence, the total cost of the dresser is $ [tex]15.138[/tex].

What is the percentage?

Percentages are generally defined as a ratio of any value to the whole value multiplied by [tex]100[/tex].

The symbol used to represent the percentage is %. Percentage means a number or a ratio represented in the form of fractions of [tex]100[/tex]. It is represented using the percentage sign ‘%’.

Here given that,

A dresser is normally priced at $[tex]870[/tex]. ​ ​This weekend however, there is a sale where everything is [tex]15[/tex]% off. ​ ​If the sales tax on items is [tex]11.6[/tex]%,

Firstly we will calculate the [tex]15[/tex]% off sale is

[tex]15[/tex]%[tex]=\frac{15}{100}\\\\[/tex]

[tex]15[/tex]%[tex]=0.15[/tex]

So,[tex]870(0.15) =130.5[/tex]

Then,

[tex]\frac{11.6}{100}=0.116[/tex] %

The sales tax on items is [tex]11.6[/tex]% is

[tex]130.5(0.116)=15.138[/tex] $

Hence, the total cost of the dresser is $ [tex]15.138[/tex].

To know more about the percentage

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Answer:6 ft

Step-by-step explanation:

Answer:

6ft

Step-by-step explanation:

Answer: No real solutions

Step-by-step explanation:

The discriminant can tell you how many solutions a quadratic equation has. The formula is b²-4ac. This also comes from the quadratic equation.

6²-4(1)(10)

36-40

-4

Since the discriminant is less that 0, there are no roots.

Answer:

The equation is C = 50s + 600. If C = 2750 we can write:

2750 = 50s + 600

2150 = 50s

s = 43 so the amount of students is 43.

For the last question, 90% of 46 = 0.9 * 46 = 41.4. Since 43 > 41.4, Vikas received his free trip.

Answer:

3n + 5

1. Substitute the numbers

3(5) + 5 = 15 + 5 = 20

2. Substitute the second number

3(6) + 5 = 18 + 5 = 23

This is because I realized I got the number of 4 last because I did 1*2 = 2.

Then I did 2*2 = 4.

So you have to multiply by two to get the next number. Or you can put it to the 4th or 5th exponent of 2.

1.  1

2.  1*2 = 2

3.  2*2 = 4

Answer:

t = 2,22 h

Step-by-step explanation:

At the beginning with the first processor, we download in 5 hours the whole movie, then in 1 hour, that processor downloads 1/5 of the movie.

If with the two processors we download the movie in 4 hours in 1 hour we download 1/4 of the movie.

In 1 hour with the two processors,  we get    1/4,  and in 1 hour with the old processor we get 1/5  

Then in 1-hour the old processor  plus contribution of the new one will download 1/4 of the movie or

 1/5  +  x   = 1/4

x  = 1/4 - 1/5

x(h) =  5 + 4 /20        x = 9/20    or   0,45 of the movie in  1 hour

Working along the new processor will do 0,45 ( 9/20) in 1 hour, to finish the whole movie it will need to download 11/20

If   in 1 hour download    9/20

            x                          11/20

x(r)   = (11/20) / (9/20)    = 11/9     x(r) =  1,22 (h)

Then total time for the new processor to download the movie is:

t = 1,22 + 1

t = 2,22 h

Answer:

y = -3/4

Step-by-step explanation:

1. Simplify all terms - 8y + 6 = ?

2. Set to two sides - 8y = -6

3. Solve - y = -6/8 = -3/4

Hope this helps:)

Answer:

hexagonal shape

Step-by-step explanation:

i am small child from American

sorry for answer

I'm 10 year old

I am born in Nepal

but develop in America

Answer:

[tex]Mean = 12[/tex]

[tex]Standard\ Deviation = 6[/tex]

Step-by-step explanation:

Given

Number of questions, n = 48

Probability of correct answer, p = 1/4

Required

- Find the mean

- Find the standard deviation

Using probability notations;

n = 48 and p = 1/4

Mean is calculated as follows;

[tex]Mean = np[/tex]

Substitute 48 for n and 1/4 for p

[tex]Mean = 48 * \frac{1}{4}[/tex]

[tex]Mean = \frac{48}{4}[/tex]

[tex]Mean = 12[/tex]

The Mean is 12

Calculating Standard Deviation (SD)

[tex]SD = \sqrt{np(1-p)}[/tex]

Substitute 48 for n and 1/4 for p

[tex]SD = \sqrt{48 * \frac{1}{4}(1-\frac{1}{4})}[/tex]

Solve the expression in the bracket

[tex]SD = \sqrt{48 * \frac{1}{4}(\frac{4-1}{4})}[/tex]

[tex]SD = \sqrt{48 * \frac{1}{4}(\frac{3}{4})}[/tex]

Open Bracket

[tex]SD = \sqrt{48 * \frac{1}{4}*\frac{3}{4}}[/tex]

[tex]SD = \sqrt{\frac{48 * 1 * 3}{4}}[/tex]

[tex]SD = \sqrt{\frac{144}{4}}[/tex]

[tex]SD = \sqrt{36}[/tex]

Take Square Root of 36

[tex]SD = 6[/tex]

The standard deviation is 6

Answer:

Perpendicular lines

Step-by-step explanation:

MN: (-4, 8) and (-4, -6), This line parallel to y-axis as as x-value doesn't change

KL: (-8, 2) and (6, 2), This line is parallel to x-axis as y-value doesn't change

The given lines are perpendicular as one is parallel to x, another one is parallel to y

Answer:

Step-by-step explanation:

Answer:

43.3 m

Step-by-step explanation:

you can use Tangent and calculator or table to find it.

tan ∅ = opp/adj

tan 61° = r/24

1.804 = r/24

r = 1.084 * 24 = 43.297 m

r = 43.3 m

Answer:

The correct option is 1.

Explanation:

The correct option is one because it means X is perpendicular to A and X is perpendicular to B.

If  the two lines are perpendicular to a same line,  then both lines are parallel to each other.

Here X⊥A and X⊥B. So, A║B.

Answer:

False

Step-by-step explanation:

A ball is a three dimensional object and it is spherical in shape.

Answer:

A ball is spherical

it's shaped like a sphere

Answer:

120 cm. .here u go..

Step-by-step explanation:

Circumference: 2πr

C=18 so r= 18/2π= 9π

Arc length = rθ 6=(9π)θ θ=6/9π

Convert to degrees by multiplying by 180/π



6/9π x 180/π = 120 degrees

Hope it helps!

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TYSM!

Answer:

[tex]P = \frac{5}{282} = 0.0177[/tex]

Step-by-step explanation:

First we need to find the total amount of apples in the crate:

Total = 10 + 14 + 4 + 18 = 46 apples

The probability of the first apple being a golden delicious apple is the number of those apples over the total number of apples:

[tex]P(golden) = \frac{N(golden)}{N(total)}[/tex]

[tex]P(golden) = \frac{4}{48} = \frac{1}{12}[/tex]

Then, the probability of the second apple being a granny Smith apple is the number of those apples over the total number of apples, but now the total number of apples is one less, because one apple was removed from the crate:

[tex]P(granny) = \frac{N(granny)}{N(total)-1}[/tex]

[tex]P(granny) = \frac{10}{47}[/tex]

The final probability we want is the product of those two probabilities:

[tex]P = P(golden) * P(granny) = \frac{1}{12} \frac{10}{47} = \frac{10}{564} = \frac{5}{282}= 0.0177[/tex]

Answer :

Given that the base of the triangle is x m, the height is 3m less than twice it's base then the height will be represented by the equation:

(2x-3) m

Thus the area will be:

Area=1/2bh

Area=1/2x(2x-3)=17.5

x^2-1.5x=17.5

Writing the above equation is quadratic form of ax^2+bx+c=0 we get:

x^2-1.5x-17.5=0

Answer:

C

Step-by-step explanation:

Equation A

16x - 7 = 11x - 32

(16x - 7) - 11x = (11x - 32) -11x

5x - 7 = -32

(5x - 7) + 7 = (-32) + 7

5x = -25

(5x)/5 = (-25)/5

x = -5

Equation B

-4x - 10 = 2x + 20

(-4x - 10) - 2x = (2x + 20) - 2x

-6x - 10 = 20

(-6x - 10) + 10 = (20) + 10

-6x = 30

(-6x)/-6 = (30)/-6

x = -5

Both Equation A and Equation B have a solution of -5.

Answer:

Altogether, Stevie and Michael made £480

Step-by-step explanation:

Since Stevie gets £120 more than Michael, Stevie gets the bigger ratio which is 5 and Michael gets the ratio 3

a:b=ax+bx

Stevie share =ax

Michael share=by

5:3=5x+3x

Stevie profit=Michael profit

*Stevie gets £120 more

5x+120=3x

5x-3x=120

2x=120

x=120/2

=60

x=60

Stevie=ax

=5*60

=£300

Michael=bx

=3*60

=£180

Altogether,

They made a profit of £180+£300

=£480

Answer:

Invariant points = 0

Step-by-step explanation:

When a point (h, k) is translated by a vector [tex]\binom{x}{y}[/tex], rule to be followed,

(h, k) → [(x + h), (y + k)]

Following this rule translated vertices of the rectangle OABC by a vector [tex]\binom{1}{3}[/tex] will be,

O(0,0) → O'(1, 3)

A(3, 0) → A'[(3 + 1), (0 + 3)]

           → A'(4, 3)

B(3, 3) → B'[(3 + 1), (3 + 3)]

           → B'(4, 6)

C(3, 0) → C'[(3 + 1), (0 + 3)]

           → C'(4, 3)

Therefore, every point on the perimeter of the square will get changed.

Number of invariant points = 0

Answer:

the result is a positive number not a negative number

Step-by-step explanation:

a - ( -b)

We know that subtracting a negative is like adding

a+b

This would result in a positive number

Answer:

No.

Step-by-step explanation:

Because it is a double negative, the difference will become positive.

For instance, 6 - (-4) = 10

(The subtraction and negative signs will become positive instead).