Given the following functions, evaluate each of the following:

Answer:

1. 20 km/hr (60km / 3h)

2. 70 m/hr (170m / 2h)

3. 6.5 hr (260cm / 40km)

4. 4.5 s (72cm / 16cm)

5. 184 km (46km * 4h)

Step-by-step explanation:

We'll use d = distance, t = time, s = speed.

Speed over time can be found by dividing distance by time

s = d / t

We can take this formula and manipulate it to find either distance or time if we know two of the values. Keeping in mind division and multiplication cancel each other.

If we wanted to find d for instance we can multiply both sides by t to get

s * t = d

For time we can divide both sides of the above formula by s to get

t = d / s

Answer:

1. 20 km/h

2. 70 m/h

3. 6.5 h

4. 4.5 s

5. 184 km

Step-by-step explanation:

For first two questions, you can use the following formula:

[tex]\displaystyle \large{s = \frac{d}{t}}[/tex]

I denote ‘s’ be speed, ‘d’ be distance and ‘t’ be time. Some books may use ‘v’ for speed instead of ‘s’ but I use ‘s’ variable instead so it makes the equation easier to memorize.

Therefore, speed = distance/time

( 1 ) The first question is given both distance be 60 km and time be 3 hours. Therefore:

[tex]\displaystyle \large{s=\frac{60}{3}}\\\displaystyle \large{s=20 \ \ \sf{km / h}}[/tex]

So for the first question, the speed is 20 km/h

( 2 ) The second is given both distance be 140 m and time be 2 hours. Therefore:

[tex]\displaystyle \large{s=\frac{140}{2}}\\\displaystyle \large{s=70 \ \ \sf{m / h}}[/tex]

Therefore, speed is 70 m/h

For the third and four questions, we will be finding time. From the speed formula:

[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]

Multiply both sides by t.

[tex]\displaystyle \large{st=d}[/tex]

Divide both sides by s.

[tex]\displaystyle \large{t=\frac{d}{s}}[/tex]

Therefore, time = distance/speed

( 3 ) The question is given speed be 40 km/h and distance be 260 km. Therefore:

[tex]\displaystyle \large{t=\frac{260}{40}}\\\displaystyle \large{t=\frac{13}{2} \ \ \sf{h}}\\\displaystyle \large{t = 6\frac{1}{2} \ \ \sf{h}}\\\displaystyle \large{t= 6.5 \ \ \sf{h}}[/tex]

Therefore, time is 6.5 h

( 4 ) The question is given speed be 16 cm/s and distance be 72 cm. Therefore:

[tex]\displaystyle \large{t=\frac{72}{16}}\\\displaystyle \large{t=\frac{9}{2} \ \ \sf{s}}\\\displaystyle \large{t=4\frac{1}{2} \ \ \sf{s}}\\\displaystyle \large{t=4.5 \ \ \sf{s}}[/tex]

Therefore, time is 4.5 s

For the last question, we have to find distance. From the speed formula:

[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]

Multiply both sides by t.

[tex]\displaystyle \large{st=d}\\\displaystyle \large{d=st}[/tex]

Therefore, distance = speed * time

( 5 ) The question is given time be 4 hours and speed be 46 km/h. Therefore:

[tex]\displaystyle \large{d=46 \cdot 4}\\\displaystyle \large{ d=184 \ \ \sf{km}}[/tex]

Therefore, distance is 184 km.

Answer:

12.6 = c

Step-by-step explanation:

The Pythagorean therom is a^2 + b^2 = c^2

We already know 2 varibles (12 and 4) so we can just plug them in.

12^2 + 4^2 = c^2

144 + 16 = c^2

160 = c^2

[tex]\sqrt{160}[/tex] = [tex]\sqrt{c^2}[/tex]

12.6 = c

Hope this helps :)

Answer:

1. 220 minutes

2. $45.6

Step-by-step explanation:

Step-by-step explanation:

Step 1: Plot the points

L(1,2)

M(0,-1)

J(1,-2)

K(2,-1)

Step 2: Multiply each point by 5.

and record thise points so we have

L(5,10)

M(0,-5)

J(5,-10)

K(10,-5)

Step 3: Plot those points.

Answer:

Graph attached below.

Step-by-step explanation:

After dilation of 5, the new coordinates follow the rule :

Answer:

Step-by-step explanation:

red shirt: 10%

green shirt: 20%

not choosing white 10%

not chosing black 20%

where orange shirt???

[tex]\text{Area of rectangle} = \text{length} \times \text{width}\\\\~~~~~~~~~~~~~~~~~~~~~~~=4 ~\text{ft}~\times ~2 ~\text{ft}\\\\~~~~~~~~~~~~~~~~~~~~~~~=8~ \text{ft}^2\\\\~~~~~~~~~~~~~~~~~~~~~~~=1152~\text{in}^2[/tex]

Answer:

452.16 m³

Step-by-step explanation:

Given

Formula

Solving

The probability that a candidate chosen at random from among these two sets of candidates will have selected questions 1, 2 and 3 is 0.4179.

The probability that a candidate chosen at random from among these two sets of candidates will have selected questions 1, 2 and 3 will ba calculated thus:

= [(9C6 /12C9) × 1/2] + [(9C7)/12C10) × 1/2]

= 42/220 + 18/66

= 0.1909 + 0.2727

= 0.4179

In conclusion, the probability is 0.4179.

Learn more about probability on:

https://brainly.com/question/24756209

[tex]sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1-cos(30^o)}{2}}\implies \sqrt{\cfrac{1-\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2-\sqrt{3}}{2}~~}{2}}[/tex]

[tex]\sqrt{\cfrac{2-\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2-\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2-\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1+cos(30^o)}{2}}\implies \sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2+\sqrt{3}}{2}~~}{2}} \\\\\\ \sqrt{\cfrac{2+\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2+\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2+\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{~~ sin\left( \frac{30^o}{2} \right)~~}{cos\left( \frac{30^o}{2} \right)}\implies \cfrac{~~\frac{\sqrt{2-\sqrt{3}}}{2} ~~}{\frac{\sqrt{2+\sqrt{3}}}{2}}\implies \cfrac{\sqrt{2-\sqrt{3}}}{2}\cdot \cfrac{2}{\sqrt{2+\sqrt{3}}} \\\\\\ \cfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\implies \blacktriangleright \sqrt{\cfrac{2-\sqrt{3}}{2+\sqrt{3}}} \blacktriangleleft[/tex]

Answer:

-8.5

Step-by-step explanation:

no step involved just trace 2 out from y-axis

Answer:

find the common factor in the given algebraic expressions 4 (x-y) , 6(y-x)

Answer:

28/21

Step-by-step explanation:

28/21 is the equivalent to 4/3.

We know this is the fraction we are looking for because 28 + 21 = 49

Hope that helps!

The expenses for the duration of the four years that Kari will use in the university is $68600.

From the complete information, the expenses for the four years stay in the university will be calculated thus:

Tution = $8500

Room = $6700

Books = $1250

Miscellaneous expense = $700

Total = $17150

The expenses for the four years will be:

= $17150 × 4

= $68600

Learn more about expenses on:

https://brainly.com/question/14697297

Answer:

Since we want a positive number, x = 24.  y = 192/x = 8

Step-by-step explanation:

Let x and y be the two positive numbers.

-  Their product is 192: x*y = 192

-  the sum of the first plus 3 times the second is a minimum:  x + 3y

From the first equation, y = 192/x.  Substitute that into the second equation:

x + 3y = x + 3(192/x) = x + 576/x

Now take the first derivative, set it to zero, and solve for x:

d(x + 576/x)/dx = 1 - 576/x2

0 = 1 - 576/x2

0 = x2 - 576                         [Multiplied both sides by x2]

576 = x2

√576 = √x2

±24 = x

Since we want a positive number, x = 24.  y = 192/x = 8

As a check, the factors of 192 are 192*1, 96*2, 48*4, 24*8, 16*12

192 + 3*1 = 195

96 + 3*2 = 102

48 + 3*4 = 60

24 + 3*8 = 48

16 + 3*12 = 52

24 + 3*8 is indeed the minimum

Answer:

B

Step-by-step explanation:

Group like them

such that the coefficient stands alone

by subtracting both sides by 9.5

Answer:

what are the objectives of census class 7

Question 3

Let the number of times an odd number was chosen be x. Then, the number of times an even number was chosen is x+4.

[tex]x+x+4=50\\\\2x+4=50\\\\2x=46\\\\x=23[/tex]

So, the answer is 23 times.

Question 4

If 8 ordered pizza, 4 did not order pizza.

[tex]\frac{4}{12}=\frac{1}{3}[/tex]

So, the answer is 1 out of 3.

Here we would be using distance formula to calculate the distance between those two points.

Points are,

★ Distance Formula :

We have :

Substituting the values :

Centroid of a triangle :-

Midpoint of two points:-

Answer:

I cannot change what is the truth

Step-by-step explanation:

attempt to change the truth would resulted in dinaur catastrophe

Answer:

Alright, so, the ratio is 2:5

In total, there are 7

So, 56/7=8

8x2=16

8x5=40

So after moving 2 students,

14 on the van, 42 on the bus

(you can use the true/false now)

Answer:

1. False

2. True

3. True

4. False

Step-by-step explanation:

Going to the museum:

Total: 56 students

van:bus = 2:5

2x + 5x = 56

7x = 56

x = 8

2x = 16

5x = 40

16 students go by van

40 students go by bus

40 - 16 = 24

Going back to school:

14 students go by van

42 students go by bus

van:bus = 14/42 = 1:3

42 - 14 = 28

Questions:

1. False

2. True

3. True

4. False

Answer:

I guess it is 9 cm²

Step-by-step explanation:

Hope it helps.....

Answer:

1728 ft³

Step-by-step explanation:

Lower part:

volume = 19 ft × 12 ft × 6 ft = 1368 ft³

Upper part:

volume = 10 ft × 12 ft × 3 ft = 360 ft³

Total Volume = 1728 ft³

Using the normal approximation to the binomial, it is found that there is a 0.119 = 11.9% probability that at least 60 will return next month.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that:

Thus, the mean and the standard error for the approximation are given as follows:

Using continuity correction, the probability that at least 60 will return next month is P(X > 60 - 0.5) = P(X > 59.5), which is 1 subtracted by the p-value of Z when X = 59.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{59.5 - 54}{4.6476}[/tex]

Z = 1.18

Z = 1.18 has a p-value of 0.881.

1 - 0.881 = 0.119.

0.119 = 11.9% probability that at least 60 will return next month.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

the function has vertical asymptotes when x = 0 and x = 4

Step-by-step explanation:

Answer:

[tex]y = -\frac{1}{3} x + 6[/tex]

Step-by-step explanation:

Slope-intercept form: [tex]y = mx + b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

The formula to find the slope of a line is [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex].

1) Plug the coordinates into this [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex].

[tex]m = \frac{9 -6 }{-9 - 0 }[/tex]

2) Solve it. Simplify it if possible.

[tex]m = \frac{3 }{-9}[/tex]

Simplified: [tex]m = \frac{1 }{-3 }[/tex]

3) Plug the result into [tex]y = mx + b[/tex].

[tex]y = \frac{1}{-3} x + b[/tex]

4) Plug one of the points ([tex]x_{1}, y_{1}[/tex] or [tex]x_{2}, y_{2}[/tex]) into [tex]y = \frac{1}{-3} x + b[/tex] to find [tex]b[/tex].

[tex]6 = \frac{1}{-3}(0) + b[/tex]

[tex]6 = 0 + b[/tex]

[tex]6 - 0 = b[/tex]

[tex]6 = b[/tex]

5) Plug the result of [tex]b[/tex] into [tex]y = \frac{1}{-3} x + b[/tex].

[tex]y = \frac{1}{-3} x + 6[/tex]

The negative situated in the denominator can be genaralised to the fraction.

Therefore, [tex]y = -\frac{1}{3} x + 6[/tex].

Answer:

254,000

Step-by-step explanation:

What is 25.4 x 10 to the 4th power?

Translate:

25.4 * 10⁴

25.4 * 10,000

Here, we will be moving the decimal four times to the right:

25.4 * 10,000

254,000

Note: if you're not sure, you can always use a calculator to double check :)

Hope this helps!

Answer:

The expression is division.

Step-by-step explanation:

2/5 ÷3/4=0.075

Answer:

[tex]\frac{2}{5} \times\frac{4}{3}[/tex]

Step-by-step explanation:
To find the answer we use KCF (Keep, Change, Flip).

[tex]\frac{2}{5} \div\frac{3}{4}[/tex]
[tex]\frac{2}{5} =\frac{2}{5}[/tex]
[tex]\div=\times[/tex]
[tex]\frac{3}{4} =\frac{4}{3}[/tex]
[tex]\frac{2}{5} \times\frac{4}{3}[/tex]

Which means the expression used to find the answer would be "2/5 × 4/3."

Hope this helps.