A road is 450 metres long . It takes a woman 5 minutes to walk along the road . Work out the average speed of the woman . Give your answer in metres per second .​

Answers

Answer 1
theres 60 seconds in a minute. If it takes her 5 minutes, multiply 60 by 5. you will get 300. then all you will do is divide the meters by 300 seconds. you will get the answer of 1.5 metres per second.

Related Questions

Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x)-sin(x)sin*y))dx+cos(x)cos(y)dy=0 g

Answers

The differential equation

[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]

is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].

We have

[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]

[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]

and [tex]M_y=N_x[/tex], so the equation is indeed exact.

Now, the solution [tex]f[/tex] satisfies

[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]

Integrating with respect to [tex]x[/tex], we get

[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]

[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]

and differentiating with respect to [tex]y[/tex], we get

[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]

[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]

Then the general solution to the exact equation is

[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]

3 *(x-7)*(x+7)-(x-1)*(3x+2)=13

Answers

The value of x will be 158. The value of x is obtained by simplifying the equation.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Identity used;

(x+a)(x-a) = x² - a²

Given expression;

3(x-7)(x+7) - (x-1)(3x+2) = 13

Solving the equation step by step;

[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]

Hence, the value of x will be 158.

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How many other states have a similar law? all 50 states 48 states 40 other states 52 states

Answers

Answer:

all 50 states

Step-by-step explanation:

The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Answers

The equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52  milligram remains

How to determine the equation?

The missing information in the question is:

[tex]f(t)=m(0.5)^{\frac th}[/tex]

When the mass is 50 mg, it means that:

m = 50

So, we have:

[tex]f(t)=50(0.5)^{\frac th}[/tex]

When 10 years remain in the life of the substance, it means that:

t = 10

So, we have:

[tex]f(t)=50(0.5)^{\frac {10}h}[/tex]

The half life is 5.3. So, we have

[tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex]

Evaluate the equation

f(t) = 13.52

Hence, the required equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52  milligram remains

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Answer:c

Step-by-step explanation:

I want to verify my work answer for the below SSAT question.

Thank you

Cindy throws a rock in the air. The rock's height, y, in feet, with respect to time, x, in seconds can be modeled by the function y=-2x^2+10x+28. When does the rock hit the ground in seconds

My work:
y=-2x^2+10x+28
0= -2(x^2-5x-14) (While knowing that the zero is supposed to be there, I don't understand why 0= -2(x^2-5x-14) )
(x-7)(x+2)
(-7,+2)
I put 2 as the answer, but when checking it was 7?

What part did I do wrong?

Answers

Answer:

7

Step-by-step explanation:

You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may  assume that the ground is y=0, unless the problem says otherwise.

Ok so where you went wrong is that when you factored out and got

(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have

x-7 = 0

and

x+2 = 0

and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.

This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.

Good luck with your exam !

Answer:

7 seconds

Step-by-step explanation:

Given function:

[tex]y=-2x^2+10x+28[/tex]

where:

y = height above the ground (in feet)x = time (in seconds)

To find the time when the rock hits the ground, set the equation to zero and solve for x.

First, simplify by factoring out the common term  -2:

[tex]\implies -2(x^2-5x-14)=0[/tex]

Divide both sides by -2:

[tex]\implies x^2-5x-14=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=1 \cdot -14=-14[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2

Rewrite b as the sum of these two numbers:

[tex]\implies x^2-7x+2x-14=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x-7)+2(x-7)=0[/tex]

Factor out the common term (x - 7):

[tex]\implies (x+2)(x-7)=0[/tex]

Therefore:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies x-7=0 \implies x=7[/tex]

As time cannot be negative, the rock hits the ground in 7 seconds.

11. Find the amount of interest on $600, if a bank is paying 5.5% interest.
[A] $30 [B] $3.30
[C] $330
[D] $33
[E] $23

Answers

B) 3.30 Since 600/100= 6 x 5.5= 3.30
B 3.30 is the answer

Price of an article is marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894. Find the cost price, marked price and profit percentage.​

Answers

Step-by-step explanation:

here is your answer. where are you from

The cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

For example, if you say 678, we must also know the whole number, but if you say 80%, it becomes evident. The percentage is the same as the amount of that value but ranges from 1 to 100.

Let's say

Cost of article = c

Given,

Marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894

1.4c - 0.15×(1.4c) = 26894

c = Rs 22600

So,

Marked price = 1.40c = Rs 31640

Profit percentage = ( 26894 - 22600)22600 = 19%.

Hence cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

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Name
Two-Variable Statistics
Relationship between Two Categorical Variables - Marginal and Joint Relative Frequency -
Part 2
Warm Up
Complete the table and calculate the percent for each total.

Answers

The completed table is given below,

the percentage of girls in the class is 47.62%,

the percentage of boys in the class is (100-47.62)% = 52.38%,

the percentage of students that love Math is 36.5%,

the percentage of students that love Reading is 22%, and

the percentage of students that love Science is 41.27%

To make comparison and statistical analysis easier, numerical data is systematically and logically represented in tabulations as rows and columns. Grouping relevant data together makes comparison easier and aids in statistical analysis and interpretation.

To put it another way, tabulation is the process of organizing data and presenting it in a tabular format. Depending on the type of categorization, it might be double, complicated, or simple.

The below table yields that

The total number of students is 315

The fraction of girls in the class is 150/315 = 0.4762

So, the percentage of girls in the class is 47.62%

Hence the percentage of boys in the class is (100-47.62)% = 52.38%

The fraction of students that love Math is 115/315 = 0.365

So, the percentage of students that love Math is 36.5%

The fraction of students that love Reading is 70/315 = 0.22

So, the percentage of students that love Reading is 22%

The fraction of students that love Science is 130/315 = 0.4127

So, the percentage of students that love Science is 41.27%

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Why is it just as likely that the cube will show an even number as an odd number?

Answers

A standard numbered cube (die) has six faves numbered 1, 2, 3, 4, 5, 6
Three are even 2, 4, 6 and three are odd 1, 3, 5
P(even) = 3/6
P(odd) = 3/6
So for a fair die an odd number is equally likely as an even number

Please help! Consider the function y = 9-x^2, where x ≥ 3
What is the inverse of the function? What is the domain of the inverse? Show all of your work
(hint: swap x and y in the domain as well as the function)

Answers

Using it's concept, it is found that the inverse function is [tex]y = \sqrt{9 - x}[/tex], and the domain is [tex]x \leq 9[/tex].

How to find the inverse function?

The inverse of a function y = f(x) is found exchanging x and y and isolating y. The domain of the inverse is the range of the original function f(x).

In this problem, the function is:

y = 9 - x²

Then, we exchange and isolate y, hence:

[tex]x = 9 - y^2[/tex]

[tex]y² = 9 - x[/tex]

[tex]y = \sqrt{9 - x}[/tex]

The domain is [tex]9 - x \geq 0 \rightarrow x \leq 9[/tex], as looking at the graph of y = 9 - x², the range is [tex]y \leq 9[/tex].

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A television has increased in price by 5%
the new price is £194.25. what was the original price?

Answers

Answer:

let the original price be X

now new price = original price + increment

increment = 5 % of X = X/20

new price = 194.25

now, 194.25 = X + X / 20 = 21X / 20

X = 194.25 * 20 / 21

X = 185

original price = 185

consider an investment of $6000 that earns 4.5% interest.


How long would it take for the investment
to reach $15,000 if the interest is
compounded monthly? Round your
answer to the nearest tenth.

Answers

Answer:

20.4 years (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

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

where:

A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Given:

A = $15,000P = $6,000r = 4.5% = 0.045n = 12 (monthly)

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf 2.5=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}[/tex]

[tex]\implies \sf t=20.40017123[/tex]

Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.

A hot air balloon is descending.
The height of the balloon n minutes after it starts to descend is hn
metres.
The height of the balloon (n +1) minutes after it starts to descend, hn + 1 metres, is given by
hn + 1 = K×hn
+ 20 where K is a constant.
The balloon starts to descend from a height of 1200 metres at 09 15
At 09 16 the height of the balloon is 1040 metres.
Work out the height of the balloon at 09 18

Answers

Answer:

The height of the balloon at 09 18 =  788.4 meters.

Step-by-step explanation:

As the hot air balloon is descending.

and the height of the balloon n minutes after it starts to descend is [tex]h_{n}[/tex]

meters.

The height of the balloon (n +1) minutes after it starts to descend, [tex]h_{n+1}[/tex]meters, is given by

[tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex] where K is a constant

Here the balloon starts to descend from a height of 1200 meters at 09 15

So [tex]h_{n}[/tex]=1200 meters

At 09 16 the height of the balloon is 1040 meters.

So  [tex]h_{n+1}[/tex]= 1040 meters

the height of the balloon at 09 18 = [tex]h_{n+3}[/tex] meters

now  [tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex]

k = [tex]\frac{h_{n+1 }-20 }{h_{n} }[/tex]

k= (1040 - 20) ÷ 1200

k = 0.85

Now [tex]h_{n+2}[/tex] = (0.85 × 1040) +20 =904 meters

Similarly  [tex]h_{n+3}[/tex] = (0.85 × 904) +20 = 788.4 meters.

Therefore the height of the balloon at 09 18 =  788.4 meters.

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Given the matrices A and B shown below, find -A + 1/3B

Answers

Step-by-step explanation:

1. first multiply -1 times all elements of matrix A

2. then multiply 1/3 by all elements of matrix B

3. then add each corresponding entries to get the result.

from step 1. matrix A will be

-4 -2. -1. -3

-2. 0. 1. -3

step 2. matrix B will be

3. -1. -2. -4

3. -10. 10. -1

add each corresponding elements to get

-1. -3. -3. -7

1. -10 11. -4

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation? 6x2 5x - 4 = 0 6x2 5x 4 = 0 62x 5 x = 4 6 x2 5x = 4

Answers

Answer:

The answer would be 6x^2 + 5x - 4 = 0

PLEASE HURRY
Which of the following can be used to evaluate the series


e d g e

Answers

Answer:

1 55

2 455

3554

Step-by-step explanation:

nfn

Marcia bought a car for £34500 and sold it for £29700. what was her percentage loss?
can i have an explanation please :)

Answers

Answer:

cost of car = 34500

selling price = 29700

amount of loss = 34500 - 29700 = 4800

loss percentage = (loss amount ÷ cost price ) * 100

= 13.913 ≈ 14% loss

Cos(5 π/3)=___

A. √3/2
B. -√2/2
C. 1/2
D. √2/2

Answers

Answer:

i think the answer is C. 1/2

One possible integer of x for which 1/4 < k/10 < 1/3 is true?

Answers

Answer:

[tex]\fbox {x = 3}[/tex]

Step-by-step explanation:

Decimal form of the lower and higher limits :

1/4 = 0.251/3 = 0.33...

Hence, the best one which lies in the middle of the limits would be 0.3.

Now, equate the middle part :

x/10 = 0.3x = 3

AP Calculus AB Question from A, P .E* X
(Will give branliest if correct)

Answers

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

What is the domain of a function as a result of a binary operator

Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):

f(x):

Domain - [-3, 3]

g(x):

Domain - (- ∞, + ∞)

If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:

(f/g)(x):

Domain - [-3, 1/3) ∪ (1/3, 3]

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

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What is the range of the relation in the table below?

Answers

The range of the relation is {0, 2, 4}

How to determine the range?

The range of the relation are the y values

From the table, we have:

y values = 0, 2, 4, 2, 0

Remove the repetition

y values = 0, 2, 4

Hence, the range of the relation is {0, 2, 4}

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What is the value of x?



Enter your answer in the box.

...°

Answers

X=111

A 7 sided shape all the interior angles should add to 900 so if you add all the angles given you get 789 then subtract that from 900

This is direct proportion .

I need help in question 2 only one of the questions then I can do the rest tysm
Il give

Answers

Answer:

(a) 2.5

Step-by-step explanation:

(a) Since y is directly proportional to x we can write y and x in terms of the following equation:

y = cx where c is a constant
and c = y/x ...(1)
or,

x = y/c ...(2)

For (a)
y = 8 when x = 2 ==> c = y/x = 8/2 =4 from (1)

From (2) we get x = 10/4 = 2.5

The other questions can be solved in a similar fashion



what is the value when 18times of the difference of 15 and 12 divided by 6

Answers

The answer is 9! 15-12=3 and 3x18 is 54 and 54/6 is 9.

Set up a proportion to solve for x in the following similar triangles

Answers

Answer:

[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]

Select the two binomials that are factors of 49x^2 - 36
A. 7x + 12
B. 7x - 3
C. 7x + 6
D. 7x - 6

Answers

By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)

How to find the factors of subtraction of squares

A subtraction of squares is a binomial which satisfies the following property:

a² - b² = (a - b) · (a + b)     (1)

If we know that a² = 49 · x² and b² = 36, then we have the following factors:

49 · x² - 36 = (7 · x - 6) · (7 · x + 6)

By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)

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Type the correct answer in the box

Answers

Answer:

[tex]log\boxed{7}[/tex]

Step-by-step explanation:

[tex]log\frac{14}{3}+log\frac{11}{5}-log\frac{22}{15}[/tex]

[tex]=log\bigg(\frac{14}{3}*\frac{11}{5}\bigg)-log\frac{22}{15}[/tex]

[tex]=log\bigg(\frac{14*11}{3*5}\bigg)-log\frac{22}{15}[/tex]

[tex]=log\bigg(\frac{154}{15}\bigg)-log\frac{22}{15}[/tex]

[tex]=log\bigg(\frac{154}{15}\div\frac{22}{15}\bigg)[/tex]

[tex]=log\bigg(\frac{154}{15}\times\frac{15}{22}\bigg)[/tex]

[tex]=log\bigg(\frac{154}{22}\bigg)[/tex]

[tex]=log\boxed{7}[/tex]

What is the additive inverse of x=-1317, and verify -(-x) = x ?

Answers

Answer:

1317 is the additive inverse of x = -1317.

Step-by-step explanation:

Additive inverse of a number which when added to the original number gives zero as the result.

Additive inverse of x = -1317

-1317 + 1317 = 0

1317 is the additive inverse of x = -1317.

Verification of -(-x) = x

L. H. S

-(-x) = -{-(-1317)}

= - 1317

R. H. S

x = -1317

Thus, L.H.S. = R.H.S

-(-x) = x

Verified

Graph of y = log(-x)?

Answers

Answer:

lklklkj

Step-by-step explanation:

67890-

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answers

The correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given expression:-

2.3p – 10.1 = 6.5p – 4 – 0.01p

The same expression will be calculated as:-

Multiply the given expression by 100 we will get our answer.

E = 100 (s 2.3p – 10.1 = 6.5p – 4 – 0.01p )

E = 230p – 1010 = 650p – 400 – p

Therefore  the correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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