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Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

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Answer:

y = 1/405 x² + 25

101 feet

Step-by-step explanation:

The vertex of the parabola is (0, 25).

The equation of the parabola is:

y − 25 = a (x − 0)²

y = ax² + 25

Two points on the parabola are (-225, 150) and (225, 150).

Plugging in one of those points:

150 = a (225)² + 25

125 = 50625 a

a = 1/405

The equation is therefore:

y = 1/405 x² + 25

50 feet from a tower is 175 feet from the center.

y = 1/405 (175)² + 25

y ≈ 101

Answer: 7.5 ounces of  7% acid solution is mixed with 12.5 ounces of 23% acid solution to obtain 20 oz of a 17% acid solution.

Step-by-step explanation:

Let x = Ounces of 7% acid solution

y=  Ounces of 23% acid solution

According to the question , we have two linear equations:

x+y=20    

i.e. y=20-x  ...(i)

0.07 x+ 0.23y =0.17 (20)

i.e.  0.07x+0.23y= 3.4 ...(ii)

Substitute value of y from (i) in (ii) , we get

0.07x+0.23(20-x)= 3.4

⇒ 0.07x+4.6-0.23x=3.4   [distributive property]

⇒ 0.07x-0.23x=3.4-4.6 [subtract 4.6 from both sides]

⇒ -0.16x=-1.2

⇒  x = 7.5    [divide both sides by-0.16]

put value of x in (i) , we get y= 20-7.5 =12.5

Hence, 7.5 ounces of  7% acid solution is mixed with 12.5 ounces of 23% acid solution to obtain 20 oz of a 17% acid solution.

Answer:

8.5cm

Step-by-step explanation:

convert 3.4metres to cm that is by multiplying by 100

3.4×100=340cm

1rep 40

?rep 340

that is 340/40

=8.5cm

Answer:

8.5 cm

Step-by-step explanation:

Scale = 1:40

Length of the room = 3.4 meters

3.4 meters =3.4 X 100 =340 cm

Since 1 unit on the diagram represents 40 units

The length of the diagram

[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]

The length of the room on the diagram is 8.5 cm.

Step-by-step explanation:

since you provided 1st and the last terms

the equation can be nth term

n/2 × ( a + l) = nth sum

n/2 × ( 1 + 121) = 671

n/2 × 122 = 671

61 n = 671

n = 11

a) so there are 11 terms

then,

so as 11th term is 121

let's find common diff

a + ( n-1) d = nth term

1 +( 11-1) d= 121

10d = 121 -1

10d = 120

common difference = 12

Answer:

3.6

Step-by-step explanation:

1/9+1/6

1/3^2+1/2x3=1/x

2+3/3^2x2=1/x

5/3^2x2=1/x

x.5=18

5x=18

5x/5= 18/5

x=18/5

x=3.6

To paint the room if they worked​ together in 4 hours 14 min.

To find time if they work together.

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.An arithmetic sequence is a sequence where the difference between each successive pair of terms is the same. The explicit rule to write the formula for any arithmetic sequence is this:

an = a1 + d (n - 1).

Given that:

(1 room/Sally's time) + (1 room/Steve's time) = (1 room)/(time working together)

1/9+1/6+=+1/x

Multiply both sides by 54x

6x+9x=54

15x=54

x=3.6hours

Working together, they can paint the room in 3 hours 6 min.

So, to paint the room if they worked​ together in 3 hours 6 min.

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Answer:

D

Step-by-step explanation:

a function is a relation of two sets that associates to every number of the first set only one number of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.

Answer:

D. the quadratic equation

Step-by-step explanation:

This is because in a function, there can not be multiple solutions for one x value. Each of the graphs display points in which the answer to x is multiple values of y, which is not a characteristic of a function.

You can see this by doing a vertical line test. Place and guide your pencil or any straight edge along the beginning of a graph to the end. If the line crosses x at two or more points, the graph is not a function. The quadratic equation is the only one that is a function because as your pencil moves along, you will see that each point has its own x value and nothing overlaps.

Answer:

1/4

Step-by-step explanation:

There are 80 students.

25 are girls and 55 are boys.

10 are foreigners and 70 are Nepalese.

62.5% are Nepalese boys.

This means that the number of Nepalese boys is:

62.5/100 * 80 = 50

There are 50 nepalese boys and so there are 20 nepalese girls.

The probability of selecting a Nepalese girl is therefore:

20 / 80 = 1/4

Hey there! I'm happy to help!

Let's set this up a system of equations where x represents the number of 10 dollar bills and y represents the number of 20 dollar bills.

10x+20y=440

x=y+2

We see that x has a value of y+2, so we can replace the x in the first equation with y+2 so we can solve for y.

10(y+2)+20y=440

We use distributive property to undo the parentheses.

10y+20+20y=440

We combine like terms.

30y+20=440

We subtract 20 from both sides.

30y=420

y=14

Since there are 2 more $10 bills, there would be 16 of those.

Therefore, there are 16 $10 bills and 14 $20 bills.

Have a wonderful day! :D

Answer:

The relation PriceVSDemand usually is an inverse relationship.

This means that, as the price of the object increases, the demand will decrease.

An inverse relationship is:

D = k/P

Where D is the demand, P is the price and K is a constant that depends on the situation.

Of course this relationship also can be something like:

D = k/P^n

With n ≥ 1.

If n = 1 we have the same as above, and if n > 1, the demand decreases faster as the price increases.

If

Answer:

The probability that a randomly selected student is female or a physics major is 0.65.

Step-by-step explanation:

Note: This question is not complete. A complete is therefore provided before answering the question as follows:

A physics class has 40 students. Of these, 14 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is_______.

The Step-by-step explanation is therefore provided now as follows:

The probability that a randomly selected student is female or a physics major can be calculated using the following formula:

P(PM or F) = P(PM) + P(F) - P(PMF)

Where;

P(PM or F) = Probability of student selected is Physics Major or Female = ?

P(PM) = Probability of student selected is Physics Major = Number of Physics Major / Total number of students in the Physics class = 14 / 40 = 0.35

P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45

P(PMF) = Probability of student selected is Physics Major and Female = Number Physics Major that female in the Physics class / Total number students in the Physics class = 6 / 40 = 0.15

Substituting the values into equation (1), we have:

P(PM or F) = 0.35 + 0.45 - 0.15 = 0.65

Therefore, the probability that a randomly selected student is female or a physics major is 0.65.

Answer:

what is the physics question

Step-by-step explanation:

Answer:

The confidence level that will yield the interval that we are most confident in containing the actual value of the population parameter is (d) 99.9%

Step-by-step explanation:

the confidence level can be explained simply as a range of values that are well defined and  that  they contain a specified probability that the value of a parameter lies within the confidence level.

for example when we compare a 99.2% confidence level and 99.9% confidence level, when we have a narrow confidence interval 99.2 (say) this implies that there is a smaller chance of obtaining an observation within that interval, so therefore, our accuracy is higher. Also a 99.2% confidence interval is narrower than a 99.9% confidence interval which is wider. The 99.9% confidence interval is more accurate than the 99.2%.

so that is why we concluded that the most confidence level is 99.9%.

Answer:

Which confidence interval is most likely to contain the population parameter?

✔ between 7.0 and 9.0 hours of sleep

Step-by-step explanation:

Answer:

Step-by-step explanation:

The claim: "Less than 40% of college students graduate with student loan debt."

The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%

If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.

A type I error occurs when the research rejects the null when it is actually true.

Answer:

it's option b that is the right answer

Answer:

2/7

Step-by-step explanation:

Joseph bought a cheese and cut it into 7 equal pieces, so the denominator is 7.

Saved 5 pieces for cooking.

Gave 2 pieces to Omar.

Hope this helps :) ❤❤❤

Answer:

Step-by-step explanation:

if he gives to Omar 2 pieces of 7

2/7 = 28.57% for Omar rest of is for himself

Answer:

0.287

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 = ₇C₄ (0.53)⁴ (0.47)³

P ≈ 0.287

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)

Hey there! I'm happy to help!

When you divide fractions, you are technically multiplying by the reciprocal, which is the numerator and denominator flipped. This means that 22/33 divided by 6/9 is equal to 22/33 multiplied by 9/6.

If we multiply these together, we get an answer of 1.

I hope that this helps! Have a wonderful day!

The calculated division of the numbers 22/33 divided by 6/9 is 1

From the question, we have the following parameters that can be used in our computation:

22/33 divided by 6/9

When represented as an equation, we have

22/33 divided by 6/9 = 22/33 ÷ 6/9

Represent as a product expression

So, we have

22/33 divided by 6/9 = 22/33 * 9/6

So, we have the following result

22/33 divided by 6/9 = 1

Using the above as a guide, we have the following:

the result is 1

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Answer:

Area = 0.019 m²

Step-by-step explanation:

stess = applied Force over Area

since stress = 0.987 MPa

and the force = 1.87 Kn

then Area = h * t

Q = F / (h * t)

0.987 mPa = 1.87 kN / (h* t)

since h * t = Area then 1.87 / 0.987  

Area = 1.89 x 0.01 =

Area = 0.019 m²

Answer:

it takes approximately 3 hours

Step-by-step explanation:

Answer:

B. Square both sides of the equation.

Step-by-step explanation:

You cannot do anything to the equation unless you square both sides to eliminate the square root on the left (squaring each individual term of the equation does not help; you need to square the entire square root to eliminate it).

Hope this helps!

Answer:

7.2 qt

Step-by-step explanation:

1. Determine how much blue paint is needed in comparison to white paint

9 ÷ 5 = 1.8

For every 1 part of white paint, 1.8 times that amount of blue paint is needed.

2. Multiply the 4 qt of white paint by 1.8

4 · 1.8 = 7.2

The number of blue paints Mitch will need given the proportion of white and blue paints is 7.2qt

Given:

Blue paints = 9

White paints = 5

Ratio of blue paints to white paints = 9 : 5

Ratio of blue paints to white paints = x : 4

9 : 5 = x : 4

9/5 = x/4

cross product

9 × 4 = 5 × x

36 = 5x

x = 36/5

x = 7.2 qt

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Answer:

Total Area = [tex]104+16\,\sqrt{13}[/tex]

Step-by-step explanation:

If T.A. stands for Total Area, then we need to add the area of two equal right angle triangles of base 6' and height 4', which give : 2 * (6' * 4'/2) = 24 square feet. tothe area of three rectangles (the lateral faces of this triangular base prism):

[tex](8')*(4')+(8')*(6')+(8')*(\sqrt{6^2+4^2})= 32+48+8\,\sqrt{52} =80+8\,*\,2\,\sqrt{13}=80+16\,\sqrt{13}[/tex]

Therefore the total area of the prism is:

[tex]24+80+16\,\sqrt{13} =104+16\,\sqrt{13}[/tex]

Answer:

8 units

Step-by-step explanation:

We need to rewrite an equation in the standard for  a circle form.

r is radius.

(x−h)²+(y−k)²= r²

x² + y² – 2x + 8y – 47= 0

x² - 2x + y² + 8y - 47 = 0

x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0

(x - 1)² + (y + 4)² - 1 - 16 -47 =0

(x - 1)² + (y + 4)² - 64=0

(x - 1)² + (y + 4)² = 8²

Radius is 8.

The radius of the circle is 8 units

The radius of a circle is a line drawn from the center to the circumference of the circle

The equation of the circle is given as;

[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]

Rewrite the equation as:

[tex]x^2 - 2x + y^2 + 8y = 47[/tex]

Next, we rewrite the equation in the standard form

So, we have:

x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47

Evaluate the exponents

x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47

Rewrite the equation as follows:

x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16

Express as perfect squares

(x - 1)² + (y + 4)² = 64

(x - 1)² + (y + 4)² = 8^2

The radius of the circle is calculated as:

r^2 = 8^2

By comparison, we have:

r = 8

Hence, the radius of the circle is 8 units

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Answer:

26 and 11

Step-by-step explanation:

When your add them you get 37, and when you multiply 26 by two you get 52. 52-11 is 41.

Answer:

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Step-by-step explanation:

From the given information:

the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.

If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex]  probability  that this is their last visit.

If zero employee was admitted ;

Then:

Probability = (0.80)⁵

Probability = 0.3277

If one employee is admitted once;

Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]

Probability = 0.2731

If one employee is admitted twice

Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]

Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]

Probability = 0.1820

If two employees are admitted once

Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = 0.0910

∴

the probability that the company's total hospital costs in a year are less than 50,000  = 0.3277 + 0.2731 + 0.1820

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Answer:

4d/k or [tex]\frac{4d}{k}[/tex]

Step-by-step explanation:

first multiply both sides by four

you will have 4d=fk

then divide by k

4d/k=f

Answer:

1/200

Step-by-step explanation:

There are 24 - 0 + 1 = 25 integers from 0 - 24 (inclusive) and 7 - 0 + 1 = 8 integers from 0 - 7 (inclusive) so there are 25 * 8 = 200 possible outcomes from selecting a random integer from each interval. Of these outcomes, there is only one where you select a 5 both times, so the probability is 1/200.

The probability of selecting a 5 both​ times is 0.005

Given:

integer from 0 to 24 ​

integer from 0 to 7

Now let determine the probability of selecting a 5 both​ times

P(getting  5 both​ times)=?

P(1st time 5)=1/25

P(2nd time 5)=1/8

Hence:

P(getting  5 both​ times) =(1/25)(×1/8)

P(getting  5 both​ times)=0.04×0.125

P(getting  5 both​ times)=0.005

Inconclusion The probability of selecting a 5 both​ times is 0.005

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Answer:

Nominal level of measurement

Step-by-step explanation:

The level of measurements used in this study is the nominal level of measurements. The nominal level of measurements involves the use of numbers to help classify the categories in an experiment.

In this case study, values were gotten for each categories which are brown hair, blonde hair, black hair and other hair colors. Thus, the level of measurements used is the nominal level of measurement.

There is something wrong with the calculation because data was gotten for a total of 600 respondents while the mean that was calculated involved only 503 omitting about 97 respondents.

Answer:

16

Step-by-step explanation:

6*2 = 12

12 + 4 = 16