Evaluate the expression

Answer:

a = 0.0040 m/s², v = 14.4 m/s.

Step-by-step explanation:

Given that,

The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m

Time, t = 1 hour = 3600 seconds

Let a is the acceleration of the bus. Using second equation of motion,

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

Where

u is the initial speed of the bus, u = 0

So,

[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]

Now using first equation of motion.

Final velocity, v = u +at

So,

v = 0+0.0040(3600)

v = 14.4 m/s

Hence, this is the required solution.

Answer:

65 minutes

Step-by-step explanation:

already 16 people in line

total is 81

81 - 16 equals 65

about 5 people every 5 minutes (basically 1 min per person)

so, answer probably 65

Answer:

Domain= {x:x £|R}

|R=any real number

Answer:

Heat flux boundary condition.

Step-by-step explanation:

Heat flux is boundary condition in positive x-direction. The specified temperature is constant and steady heat conduction. Temperature of exposed surface can be measured directly with the thermal condition expression.

Answer:

4

3

0

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x+3)

2y = -sqrt(x+3)

4y² = x + 3

x = 4y² - 3

now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :

f-1(x) = 4x² - 3

basically, just by itself, this function would be defined for all possible real values of x.

but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x

x<=0

Answer:

42%

Step-by-step explanation:

to find percentages, you move the decimal point twice to the right

Answer:

The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Step-by-step explanation:

Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:

1125/15 = X

75 = X

80 x 10 + 60 x 5 = 800 + 300 = 1100

85 x 10 + 55 x 5 = 850 + 275 = 1125

Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Answer:

Hence the correct option is 3rd option. 40

Step-by-step explanation:

If two figures are similar, then the ratio of the corresponding sides is proportional.

[tex]\frac{15}{30} =\frac{20}{n} \\\\n=\frac{30 \times 20}{15} \\\\n= 40.[/tex]

Answer:

E and C

Step-by-step explanation:

Answer:

44 seats in each row

Problem:

A rectangular auditorium seats 1144 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.

Step-by-step explanation:

Let n be the number of rows.

If the number of seats exceed the number of rows by 18, then the number ot seats can be represented by n+18.

So we have a n by n+18 rectangle whose number of seats in all is 1144.

So we need to solve n(n+18)=1144

Distribute: n^2+18n=1144

Subtract 1144 on both sides" n^2+18n-1144=0

What two numbers multiply to be -1144 but also add to be 18?

Hmmm.. let's break -1144 down a little into smaller factors.

-1144=2(-572)=4(-286)=8(-143)=-8(13)(11)=-26(44)

We found a pair of factors that will work? -26 and 44.

So the factorization of our quadratic equation is (n-26)(n+44)=0.

This implies either n-26=0 or n+44=0 .

n=26 by adding 26 on both sides for first equation.

n=-44 by subtracting 44 on both sides for second equation.

n=26 is the only one that works.

This means there are 26 rows and 26+18 seats in each row.

26 rows

44 seats in each row

That product does equal 1144 seats in all.

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Answer:

7.5 dm

Step-by-step explanation:

Plus mo baka tama ako

Step-by-step explanation:

3x-2x=5+10 [taking variables on one side and constant on other]

x=15

soln:

3x-5= 2x+10

3x -5+5=2x+10+5 [ adding 5 on both side]

3x=2x+15

3x-2x=2x+15-2x [subtracting 2x on both side]

x=15

Ans=15

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

[tex]3x - 5 = 10 + 2x[/tex]

[tex]3x - 2x = 10 + 5[/tex]

[tex]1x = 15[/tex]

[tex]x = 15[/tex]

Answer:

69.6

Step-by-step explanation:

sin 55 = x / 85

0.8191520443 = x / 85

x = 69.6

9514 1404 393

Answer:

  29.4 m/s

Step-by-step explanation:

Speed is proportional to time, so we have ...

  speed / time = s/3 = 49/5

  s = 3/5(49) = 29.4

The speed of the object is 29.4 m/s after 3 seconds.

Answer:

11/12 cups

Step-by-step explanation:

2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12

Hello,

3x+9+8x-25=28

11x-16=28

x=44/11

x=4

So, GE=3x+9=3*11+9=42

Answer:

12

Step-by-step explanation:

10 - 1/2 x = 12-4/3x

60 - 3x = 72-2x

-12 = - x

Answer:

(5) we have multiple the powers

Answer:

[tex]T =56.3[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Measure of T

This is calculated as:

[tex]\cos T = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos T = \frac{5}{9}[/tex]

Take arccos

[tex]T = \cos^{-1}{(5/9)}[/tex]

[tex]T =56.3[/tex]

Answer:   6.1% decrease

Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.

=========================================================

Explanation:

The salary decreased by 51500-48355 = 3145

Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.

This converts to the percentage 6.11% and that rounds to 6.1%

----------------

As an alternative, you can use the formula method below

A = old value = 51500

B = new value = 48355

C = percent change when going from A to B

C = [ (B-A)/A ] * 100%

C = [ (48355-51500)/51500 ] * 100%

C = (-3145/51500)*100%

C = -0.0611*100%

C = -6.11%

C = -6.1%

The negative C value indicates a percent decrease.

Answer:

0.7246 radians

Step-by-step explanation:

According to the Question,

Given that, a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches

d = √{ (12)² +(15)² }  = √(144+225) = √369inches

 Tan∅ = 17/√369

Taking the [tex]Tan^{-1}[/tex] , we have

∅ = [tex]Tan^{-1}[/tex](17/√369) ≈ 0.7246 radians

Answer:

Step-by-step explanation:

[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]

= -5x² + 25xy + xy - 5y²

= 5x(-x + 5y) - y(-x +5y)

= (-x + 5y)(5x - y)

Answer:r=v^2/A

Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:

A*r=v^2     so to isolate r, divide by A and get:

r=v^2/A.

Answer:

[tex]P(X = 0) = 0.03125[/tex]

[tex]P(X = 1) = 0.15625[/tex]

[tex]P(X = 2) = 0.3125[/tex]

[tex]P(X = 3) = 0.3125[/tex]

[tex]P(X = 4) = 0.15625[/tex]

[tex]P(X = 5) = 0.03125[/tex]

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

5 tosses:

This means that [tex]n = 5[/tex]

Probability distribution:

Probability of each outcome, so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Answer:

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.

The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 120 ounces and a standard deviation of 20 ounces.

This means that [tex]\mu = 120, \sigma = 20[/tex]

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is

p-value of Z when X = 140 subtracted by the p-value of Z when X = 100.

X = 140

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

[tex]Z = \frac{140 - 120}{20}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84

X = 100

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

[tex]Z = \frac{100 - 120}{20}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

0.84 - 0.16 = 0.68

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.

The probability that a randomly selected infant has a birth weight between 110 and 130

This is the p-value of Z when X = 130 subtracted by the p-value of Z when X = 110.

X = 130

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

[tex]Z = \frac{130 - 120}{20}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.69

X = 110

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

[tex]Z = \frac{110 - 120}{20}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.31

0.69 - 0.31 = 0.38 = 38%.

The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.

Answer:

x2 - 4x - 5 factored form is (x - 5)(x + 1)

Answer:

(x − 5)(x + 1)

Step-by-step explanation:

The answer above is correct.

Step-by-step explanation:

Hey there!

Here;

f(x) = 5x + 1

g(x) = (√x)

Now;

fog(X) = f(g(x))

= f(√x)

= 5√x + 1

Therefore, fog(X) = 5√x + 1.

Hope it helps!

Answer:

To solve for x, you must multiply by the reciprocal.

In this case, multiply both sides by [tex]\frac{3}{2}[/tex] .

When doing this the result will be x = 3