Chapter 4
Solve.
1. Two trains leave a station at the same time, heading in opposite directions.
One train is traveling at 80 km/h, the other at 90 km/h. How long will it
take for the trains to be 425 km apart?​

Answer:

the answer is a

Step-by-step explanation:

Answer: F

Step-by-step explanation: Amy lynn's kitchen offers a variety of breakfast specials, there are four choices for customers to choose from, but each choice has a combination. Which makes it 8 combinations Amy Lynn' serves

Answer:

True

12+7>9(2-3)-8

19> (-9)-8

19>-17

Step-by-step explanation:

Answer:

12+7=19 and 9(2-3)-8=-17

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

2 sin²(x) + 3 sin(x) + 1 = 0

(2 sin(x) + 1) (sin(x) + 1) = 0

2 sin(x) + 1 = 0   OR   sin(x) + 1 = 0

sin(x) = -1/2   OR   sin(x) = -1

The first equation gives two solution sets,

x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ

x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ

(where n is any integer), while the second equation gives

x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ

2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0

2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0

(2 sec(x) + 1) (cot(x) + 1) = 0

2 sec(x) + 1 = 0   OR   cot(x) + 1 = 0

sec(x) = -1/2   OR   cot(x) = -1

cos(x) = -2   OR   tan(x) = -1

The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives

x = tan⁻¹(-1) + nπ = -π/4 + nπ

sin(x) cos²(x) = sin(x)

sin(x) cos²(x) - sin(x) = 0

sin(x) (cos²(x) - 1) = 0

sin(x) (-sin²(x)) = 0

sin³(x) = 0

sin(x) = 0

x = sin⁻¹(0) + 2nπ = 2nπ

2 cos²(x) + 2 sin(x) - 12 = 0

2 (1 - sin²(x)) + 2 sin(x) - 12 = 0

-2 sin²(x) + 2 sin(x) - 10 = 0

sin²(x) - sin(x) + 5 = 0

Using the quadratic formula, we get

sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(x) + cot²(x) - 3 = 0

2 (cot²(x) + 1) + cot²(x) - 3 = 0

3 cot²(x) - 1 = 0

cot²(x) = 1/3

tan²(x) = 3

tan(x) = ± √3

x = tan⁻¹(√3) + nπ  OR   x = tan⁻¹(-√3) + nπ

x = π/3 + nπ   OR   x = -π/3 + nπ

Answer:

Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.

Step-by-step explanation:

this is correct...

trust me :)

The sign is positive because it represents a quantity of something, in this case, months.

Callie has 4 months to pay off the bill.

The rational number is +4.

A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

The sign is positive because it represents a quantity of something, in this case, months.

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Answer:

1. n ≥ 4

2. N ≥ nlog(2)÷log3

Step-by-step explanation:

1

1 byte = 8 bits

each byte = 8 trits

a 6 bit number = [tex]2^{6} = 64[/tex]

3n ≥ 64

divide through by3

n ≥ 64/3

we take the logarithm

n ≥ [tex]\frac{log64}{log3}[/tex]

n ≥ 1.8062 ÷ 0.4771

n≥3.785

when approximated, n ≥ 4. So the number of trits needed in the storage of 6 bit is atleast 4

2.

to hold n bits, we can do something similar.

3N ≥ 2n

we take log of both sides

such that;

N ≥ [tex]\frac{nlog(2)}{log(3)}[/tex]

Answer:

20.8%

Step-by-step explanation:

The number of the pieces of mail handled by the U.S postal service decreased from 212,000,000,000 to 168,000,000

Therefore the percentage decrease can be calculated as follows

= 212,000,000,000-168,000,000,000

= 44,000,000,000/212,000,000,000 × 100

= 0.2075 × 100

= 20.8 %

Hence the percentage decrease is 20.8%

Answer:

A. From hour 0 to hour 5

Step-by-step explanation:

For all Plato users

Interval of the temperature decreasing is from hour 0 to hour 5.

an interval is defined as a group of numbers which includes all numbers between the beginning and the end.

According to given data is showing that the temperature decreasing zero hour to 1 hour , then 1 to 2 hour, then 2 to 3 hour, then 3 to 4 hour, then 4 to 5 hour.

So the interval of the temperature decreasing is from hour 0 to hour 5.

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Answer:

Multiply y = 0 by -1

Step-by-step explanation:

Given

y = 0 (1)

x + y = 40 (2)

What should you multiply the equation y=0 by so that when added to x + y = 40, the variable y will cancel out ?

Multiply (1) by -1

y = 0 × -1

-y = 0 (1b)

Add (1b) and (2)

-y = 0

x + y = 40

(0 + x) + (-y + y) = 0 + 40

x + (0) = 40

x = 40

You should multiply the equation y = 0 by -1 so that when added to x + y = 40 the variable y will cancel out

Answer:

The hypothesis test is right tailed because of claim made by SEO account manager that a web page on average has more than 10 keywords.

Step-by-step explanation:

The given hypothesis test is right tailed due to the claim made by SEO account manager. The tail of hypothesis test decided by looking at alternative hypothesis. The claim stated as " a web on average has more than 10 keywords" and this leads to alternative hypothesis as

Ha:μ>10.

The alternative hypothesis shows the greater than area or also known as right tailed area. Thus, given hypothesis test is right tailed.

Answer:

Step-by-step explanation:

First solve the inequality by writing it.

-4s < 6s + 1

Now subtract -1 on both sides.

-4s - 1 < 6s

Now add 4s on both sides to combine like terms.

-1 < 10s

Now divide 10 on both sides.

-0.1 < s

Now flip it over properly.

s > -0.1

Hope this helped! <3

Answer:

11.a) is 15+5.50+3 maybe

11.b) is $3.50 because 15-12=3 3+5.50=8.50 8.50+3=11.50 11.50-8=3.50

Answer:

The simplest form is 6m+91.

Step-by-step explanation:

Consider the given information.

[tex]-10(-3m-10)-3(-8m+3)[/tex]

First, remove the parenthesis by multiplying -10 and -3 inside the parenthesis.

[tex]30m+100-24m-9[/tex]

Now, rearrange the like terms.

[tex]30m-24m+100-9[/tex]

Combine the like terms.

[tex]6m+91[/tex]

Hence, the simplest form is 6m+91.

Answer:

x = 2y

Step-by-step explanation:

Simplifying

3x + -6y = 0

Solving

3x + -6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6y' to each side of the equation.

3x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0

3x + 0 = 0 + 6y

3x = 0 + 6y

Remove the zero:

3x = 6y

Divide each side by '3'.

x = 2y

Simplifying

x = 2y

Answer:

Marina's design uses more cardboard.

in Kristen's design, it uses:

3*4/2*2+10*5+3*10+4*10=132 sq inches.

in Marina's design, it uses:

6*3*2+3*7*2+7*6*2=162 sq inches.

132<162

Therefore Marina's design uses more cardboard.

The difference between 2 designs are:

162-132

=30 sq inches

Answer:

We reject H₀, we find that the  current level of mercury uptake in the Everglades has decrease

Step-by-step explanation:

We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)

Test Hypothesis:

Null hypothesis             H₀          μ   =  μ₀

Alternative hypothesis Hₐ          μ   <  μ₀

Sample size 25             then n < 30 we will use t-student table

Population mean : μ₀ = 15 ppm

sample mean :  μ  = 14,6 ppm

sample standard deviation:   s = 1 ppm

Sample size n :  25

degrees of freedom   df = n - 1         df = 24

We will develop the test for CI 90%  then  α = 10%      α = 0,1   α/2 = 0,05

For that values in t student table we find:

t(c) = 1,711    by symmetry t(c) = - 1,711

To compute ts

t(s) =  ( μ - μ₀ ) / s/√n

t(s) = 14,6 - 15 / 1 /√25

t(s) = - 0,4*5 / 1

t(s) = - 2

Comparing t(c)and t(s)

|t(s)| > |t(c) |      and t(s) < t(c)         -2 < -1,711

Therefore t(s) in in the rejection region, we reject H₀  

Answer:

10% of $50.00 is $5.00 SO ORGINAL PRICE IS $55.00

Step-by-step explanation:

50÷10=5

5 00+50.00= $55.00

Answer:

Step-by-step explanation:

10 (10+2)

Answer:

Step-by-step explanation:

The question says "Create a matrix to display the data".

The are 3 products:

- McBurger   - Mini McBurger   - ChocoLatte Shake

The figures represent monthly sales for each product, in a given year. This means 12 figures for each product - represent the 12 months of the year.

These figures will appear on the matrix, with the horizontal arrangement representing each month of the year and the vertical arrangement representing each product's sales.

In that light, you'll have a 12 by 3 matrix.

[tex]\left[\begin{array}{ccc}46&23&88\\63&41&46\\58&35&39\\77&44&52\\81&62&67\\102&88&99\\183&95&189\\197&99&238\\125&108&188\\111&111&97\\83&98&51\\218&63&12\end{array}\right] 12 by 3 matrix[/tex]The first row represents sales in January, the second row represents sales in February, the third row represents sales in March, the fourth row represents sales in April, etcetera.

The first column represents sale of McBurger, the second column represents sale of Mini McBurger, the third column represents sale of Choco-Latte Shake.

Answer:

D.) x²-10x+25 sq. units

Step-by-step explanation:

The question is not properly written. The question should have been:

If each side of a square is (x-5) units, which expression can be used to represent the area of the square.

Area of a square = L² where:

L is the length of the square

Given

L = x-5

Required

Area of the square

Substitute the given function into the formula to get the required as shown:

Area of the square = (x-5)²

Expand

A(x) = (x-5)(x-5)

A(x) = x(x)-5x-5x-5(-5)

A(x) = x²-10x-25

Hence the area of the square is (x²-10x+25)sq. units. Option D is correct.

Answer:

Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]

Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]

Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]

Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]

Step-by-step explanation:

Let [tex]x[/tex] denotes cost of each item bought by Spongebob.

Number of items bought by Spongebob = 3

So,

Cost of items bought by Spongebob = [tex]3x[/tex]

Cost of each item bought by Patrick = [tex]x-1.50[/tex]

Number of items bought by Patrick = 5

Cost of items bought by Patrick = [tex]5(x-1.50)[/tex]

Both Spongebob and Patrick paid the same amount of money.

So,

[tex]3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75[/tex]

So,

Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]

Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]

Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]

Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]

Answer:

0.348

Step-by-step explanation:

Answer:

.348

Step-by-step explanation:

Hope this helped

Answer:

[tex]\frac{1}{524160} or 1.910^{-6}[/tex]

Step-by-step explanation:

In order to solve this, you would need to multiply the probability of you choosing the one that goes first, so 1 in 16 discs, then the next one so 1 in 15, and so on untill the fifth disc.

So you would have to do this:

[tex](\frac{1}{16})(\frac{1}{15})(\frac{1}{14})(\frac{1}{13})(\frac{1}{12})\\\frac{1}{524160}[/tex]

That is the probability that the rack ends up in alphabetical order, if you pull discs randomly, 1 in 524160 chances.

Probabilities are used to determine the chances of an event.

The probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]

The given parameters are:

[tex]\mathbf{CD = 16}[/tex]

[tex]\mathbf{r = 5}[/tex] -- CDs to arrange

So, the total number of arrangements of 5 CDs from the 16, is:

[tex]\mathbf{Total = ^{16}P_5}[/tex]

Apply permutation formula

[tex]\mathbf{Total = \frac{16!}{(16 - 5)!}}[/tex]

This gives

[tex]\mathbf{Total = \frac{16!}{11!}}[/tex]

Expand

[tex]\mathbf{Total = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11!}{11!}}[/tex]

[tex]\mathbf{Total = 16 \times 15 \times 14 \times 13 \times 12 }[/tex]

[tex]\mathbf{Total = 524160}[/tex]

There is only one possibility of the CDs being in alphabetical order.

So, the probability is:

[tex]\mathbf{Pr = \frac{1}{524160}}[/tex]

Hence, the probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]

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Answer:

can you give a chart or something?

Answer:

What I think, Is that it... It might be, It can take 3 seconds