Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 65.30 miles apart. If one travels 14 miles per hour slower than the other, what is the rate of the slower train? (Round your answer to the nearest integer)

Answer:

  d.  √34 ≈ 5.82

Step-by-step explanation:

Both of choices B and D are valid calculations and should have resulted in the same estimate. Choice B, however, is incorrectly rounded, leaving choice D as the better answer.

___

The other answer choices do not result in a number between 5 and 6, so are clearly incorrect.

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

dapends on what x is but i think the answer is A or D

Answer:

Step-by-step explanation:

Look at the picture.

The lines l and m are parallel, therefore alternate interior angles are congruent.

Therefore [tex]\beta=50^o[/tex]

Supplementary angles add up to 180°.

Therefore

[tex](5x-16)+\theta=180[/tex]          add 16 to both sides

[tex]5x+\theta=196[/tex]         subtract 5x from both sides

[tex]\theta=196-5x[/tex]

We know: the sum of the triangle angle measures is 180°.

Therefore we have the equation:

[tex]50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22[/tex]

Answer:

Step-by-step explanation:

Answer:

The question has a typo in it...so if you mean least: 2 groups......greatest: 12

Step-by-step explanation:

Least:

24, 60, and 36 are all even numbers, so they can divide by 2 so each group would have 12 Sopranos, 30 Altos, and 18 tenors.

Greatest:

24, 60, and 36 can all be divided by 12. So, each group would have 2 Sopranos, 5 altos, amd 4 tenors.

The greatest number of the group that can be formed is 12.

Based on the information given in the question, in order to solve the question, we'll have to find the factors of the numbers given and this will be:

24 = 1, 2, 3, 4, 6, 8, 12, and 24.

36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36

60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Therefore, from the numbers given above, we can see that the greatest number that's common to all is 12.

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Answer:

p= 0.555 ; E= 0.222; then we have 0.555 +/- 0.222

Step-by-step explanation:

The confidence interval goes from 0.333 to 0.777.

To find the p, we need to locate the median of that series of numbers.

The median is 0.555 as is the middle value of that interval.

Now the E corresponds to the deviation or the Error that we can measure.

And since we know that our variance ranges between 0.333 and 0.777, we can sustract 0.333 to p and we can get 0.222. We can also check if we add 0.222 to p, and we can get 0.777.

Answer:

The value of a+b is 4.

Step-by-step explanation:

The given function is

[tex]\[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\][/tex]

It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.

For x≤3,

[tex]f(x)=9-2x[/tex]

For x>3,

[tex]f(x)=ax+b[/tex]

At x=0,

[tex]f(0)=9-2(0)=9[/tex]

[tex]f(f(0))=f(9)\Rightarrow a(9)+b=9a+b[/tex]

Using property f(f(x))=x,

[tex]f(f(0))=0[/tex]

[tex]9a+b=0[/tex]                     .... (1)

At x=1,

[tex]f(1)=9-2(1)=7[/tex]

[tex]f(f(1))=f(7)\Rightarrow a(7)+b=7a+b[/tex]

Using property f(f(x))=x,

[tex]f(f(1))=1[/tex]

[tex]7a+b=1[/tex]                     .... (2)

Subtract equation (2) from equation (1).

[tex]9a+b-(7a+b)=0-1[/tex]    

[tex]2a=-1[/tex]

Divide both sides by 2.

[tex]a=-\frac{1}{2}[/tex]

Substitute this value in equation (1).

[tex]9(-\frac{1}{2})+b=0[/tex]

[tex]b=\frac{9}{2}[/tex]

The value of a is [tex]-\frac{1}{2}[/tex] and value of b is [tex]\frac{9}{2}[/tex]. The value of a+b is

[tex]a+b=-\frac{1}{2}+\frac{9}{2}[/tex]

[tex]a+b=4[/tex]

Therefore the value of a+b is 4.

Answer:

12.83

Step-by-step explanation:

S = 12.091

N = 12

We must find the 12th point, X

The formula of S² (variance) as a function of µ (media) is as follows:

S² = (1/N Ʃ Xi²) - µ²

S² = 146.2

Multiplying both members by N,  

N S² = Ʃ Xi² – N µ²

On the other hand,

µ = (25 + 41 + 49 + 25 + 30 + 13 + 31 + 34 + 27 + 54 + 38 + X) / 12

µ = (367 + X) / 12

Replacing,

12 x 146.2 = 13607 + X² – 12 (367 + X)² / 144

1754.4 = 13607 + X² – 0.0833 (134689 + 734 X + X²)

1754.4 = 13607 + X² – 11219.5 – 61.14 X – 0.0833 X²

0.92 X² – 61.14 X + 633.1 = 0

This is solved by finding the two values of X that satisfy the equation.

The solution requires solving the quadratic formula,

X12 = (-b ± √(b² - 4ac)) / 2a

The values are:

X1 = 12.83

X2 = 53.62

Since we know that the value is 25 or less, the answer is 12.83

The twelfth data point in the data set is x = 16.32

Let x be the value of the twelfth data point. We know that the sample standard deviation of the 12 points is 12.091. We can use the following formula to calculate the sample standard deviation:

s = √((Σ((xₙ - M)²) / (n - 1)))

where:

We can plug in the given values to get the following equation:

if x is the missing data point then:

M = (25 + 41 + 49 + 25 + 30 + 13+ 31 + 34 + 27 + 54 + 38 + x)/12

M = 30.6+ x/12

And we know that:

s = 12.091

n = 12

Replacing these values we get:

12.091 = √((Σ((xₙ - 30.6 - x/12)²) / (12 - 1)))

Apply the square in both sides:

146.19 = (Σ((xₙ - 30.6 - x/12)²) / (11)

Multiply both sides by 11:

146.19*11 = Σ((xₙ - 30.6 - x/12)²

1,608.12 = Σ((xₙ - 30.6 - x/12)²

Now we can solve the right side:

1,608.12 = (-5.6 -  x/12)² + (10.4 - x/12)² + (18.4-   x/12)² + (-5.6 -  x/12)² + (-0.6  -  x/12)² + (-17.6  -  x/12)² + (0.4  -  x/12)² + (3.4  -  x/12)² + (-3.6  -  x/12)² + (23.4  -  x/12)² + (7.4  -  x/12)² + ( x -    x/12)²

Now we can graph this, the positive solution is x = 16.32

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Answer:

dang im late but its 10=x

Step-by-step explanation:

The number of weeks it would take before the amount in each savings account is the same is 10 weeks.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Let the variable x represent the number of weeks.

Based on the information provided above, a linear equation that models the situation can be written in slope-intercept form as follows;

250 + 15x = 200 + 20x

20x - 15x = 250 - 200

5x = 50

x = 50/5

x = 10 weeks.

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Answer:

The demand equation is: D=-4p+23

Step-by-step explanation:

To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3

S=2(3)+5=11

Thus, when p=3 D=11 and, according to the problem  when p=1 D=19.

We already know two points on the demand curve. Great!

The demand equation is linear, so it has form D=bp+c.

The variable b is the slope of  the demand linear equation . It can be computed through the formula

[tex]b=\frac{y2-y1}{x2-x1}[/tex].  equation 1

Substituting the two points (3,11) and (1,19) on equation 1.

[tex]b=\frac{19-11}{1-3} =\frac{8}{-2}[/tex]

b=-4

Now we can find the value of  intercept of the demand equation c trough point-slope form y-y1=b(x-x1).

We can use any of the points. Let's take (3,11) and write in point-slope :

y-11=-4(x-3)

y=-4x+11+12

y=-4x+23

Rewrite the linear equation according our variables D and p

D=-4P+23

Finally we found the demand equation !

Answer:

Expected Value = -$42 (loss of 42 dollars)

Step-by-step explanation:

Complete Question Below:

"There is a 0.9986 probability that a randomly selected 33​-year-old male lives through the year. A life insurance company charges ​$182 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$110 comma 000 as a death benefit. If a 33-year-old male purchases the policy, what is his expected value?"

We can say P(survival) = 0.9986 and thus P(not survival) = 1 - P(survival) = 1-0.9986 = 0.0014

Also,

In case 33 year old doesn't live, the payment would be 100,000 - 182 = $99,818

And

In case 33 year old lives, the payment is

-$182

We know, the expected value is the sum of the product of each possibility with its probability.

[tex]ExpectedValue=\Sigma x*p(x)=(99818)(0.0014)+(-182)(0.9986)=-42[/tex]

This means a loss of $42 (or -$42)

Answer:

Step-by-step explanation:

The area formula is ...

  A = πr²

When r = 1/4 in, the area is ...

  A = π(1/4 in)² = π/16 in²

__

The circumference formula is ...

  C = πd

When the diameter is 3/4 in, the circumference is ...

  C = π(3/4 in) = (3/4)π in

Answer:

  x = -5, x = -6

Step-by-step explanation:

After canceling common terms from numerator and denominator, there are two factors remaining in the denominator that can become zero. The vertical asymptotes are at those values of x.

[tex]\displaystyle F(x)=\frac{x\frac{2x}{2}}{x(x+5)(x+6)}=\frac{x}{(x+5)(x+6)}[/tex]

The denominator will be zero when ...

  x + 5 = 0 . . . . at x = -5

  x + 6 = 0 . . . . at x = -6

A plane traveling at a speed of 4000 miles per hour would take approximately 6.25 hours to travel around a planet with a circumference of 25,000 miles.

To solve this question, we will use the concept of time, speed, and distance. We know that the plane travels at a speed of 4000 miles per hour and the Earth's circumference is 25000 miles. Thus to compute the time it would take for the plane to travel around the planet, we can use the relation 'Time = Distance / Speed'.

The distance in this case is the circumference of the Earth, which is 25000 miles and the speed is the plane's speed, which is 4000 miles/hour. So, we simply divide 25000 miles by 4000 miles/hour:

Time = 25000 / 4000 = 6.25 hours

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Answer:

The greatest distance we can be from the base camp at the end of the third displacement is 6.69 km

Step-by-step explanation:

We can think of each displacement as a vector, with a given magnitude and direction.

A vector can be written using its x and y coordinates like this

[tex]\vec{t}=(x, y)[/tex]

So, for the displacements a and c their vector coordinates would be:

[tex]\vec{a}=(2, 0)[/tex]

[tex]\vec{c}=(-1, 0)[/tex]

As the b displacement has an angle of 30° toward the north from due east, we can find its x and y coordinates using the following formulas:

[tex]x=(magnitude)*cos(angle)[/tex]

[tex]y=(magnitude)*sin(angle)[/tex]

Note: the angle in the formula is the one formed with the east measured counterclockwise.

So, the x and y coordinates for the b displacement will be:

[tex]\vec{b}=(2*cos(30), 2*sin(30))[/tex]

As the vector additon is commutative, the order won't affect the final position. Nevertheless, any change in the direction of any displacement will change the final position. So, in order to find the combination greatest distance we should calculate the following additions and find the one with the greatest magnitude:

[tex]\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}[/tex]

[tex]\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}[/tex]

[tex]\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}[/tex]

[tex]\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}[/tex]

Each resultant vector can be found adding each component. Afterwards, the magnitude can be found using the following formula:

[tex]|\vec{R}|=\sqrt[ ]{(R_{x})^2 +{(R_{y})^2}}[/tex]

Now, let's calculate!

[tex]\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}[/tex]

[tex]R_{1_x}} =2+2*cos(30)-1=2.73[/tex]

[tex]R_{1_y}} =0+2*sin(30)+0=1[/tex]

[tex]\vec{R_{1}}=(2.73,1)[/tex]

[tex]|\vec{R_{1}}|=\sqrt[ ]{(2.73)^2 +{(1)^2}}=3.86[/tex]

[tex]\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}[/tex]

[tex]R_{2_x}} =2-2*cos(30)-1=0.73[/tex]

[tex]R_{2_y}} =0-2*sin(30)+0=-1[/tex]

[tex]\vec{R_{2}}=(-0.73,-1)[/tex]}

[tex]|\vec{R_{2}}|=\sqrt[ ]{(-0.73)^2 +{(-1)^2}}=1.03[/tex]

[tex]\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}[/tex]

[tex]R_{3_x}} =2+2*cos(30)+1=4.73[/tex]

[tex]R_{3_y}} =0+2*sin(30)-0=1[/tex]

[tex]\vec{R_{3}}=(4.73,1)[/tex]

[tex]|\vec{R_{3}}|=\sqrt[ ]{(4.73)^2 +{(1)^2}}=6.69[/tex]

[tex]\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}[/tex]

[tex]R_{4_x}} =2-2*cos(30)+1=1.26[/tex]

[tex]R_{4_y}} =0-2*sin(30)-0=1[/tex]

[tex]\vec{R_{4}}=(1.26,-1)[/tex]

[tex]|\vec{R_{4}}|=\sqrt[ ]{(1.26)^2 +{(-1)^2}}=1.79[/tex]

So, after all the calculation, we can know for sure that the vector [tex]\vec{R_{3}}[/tex] has the biggest magnitude. Then, the greatest distance we can be from the base camp at the end of the third displacement is 6.69 km

Final answer:

To maximize your distance from base camp, move 2.0 km east, then 2.0 km 30° north of east, and finally 1.0 km west. The total distance achievable is around 3.732 km. The order of displacements does not affect the maximum distance reached.

Explanation:

The greatest distance you can be from base camp at the end of the third displacement is achieved when you move 2.0 km due east, then 2.0 km 30° north of east, and finally 1.0 km due west in any order.

This results in a total distance of approximately 3.732 km from base camp.

Regardless of the order in which you take the displacements, the resultant greatest distance achieved remains the same.

Answer:

Step-by-step explanation:

The magnitude of a fraction of a fraction (their product) is always smaller than the magnitudes of either fraction. So, if both decimals are positive, the result is less than either factor.

___

Negative numbers are less than 1, so there can be several cases of interest when one or both numbers are negative.

Both numbers negative

The product will be positive, so will be greater than either negative factor.

__

One number negative, the other number positive

The product will be negative, so will be less than the positive factor and greater than the negative factor. (Multiplying a negative number by a positive fraction moves it closer to zero on the number line, hence to a value that is greater than the negative factor.)

Answer:

Step-by-step explanation:

An  way  to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

Step-by-step explanation:

There are 5 green marbles among the 10 in the bag, so the probability of drawing one at random is 5/10 = 0.50.

The odds in favor of drawing a green marble will be the ratio of the number of green marbles to the number that are not green: 5 : 5. Usually, the odds are expressed using integers with no common factors, so they would be written as 1 : 1.

Answer:

75 = 32 + 6 + x

Answer:

I believe it would be the first option on edge

Step-by-step explanation:

X + 6 + 32 = 75

Answer:

The answer is true.

Step-by-step explanation:

An ad valorem tax is based on the assessed value of a property. These include property taxes on real estate, sales tax on consumer goods etc,

When you are earning rent from a property, then you have to pay some tax for it, that will surely affect the amount of ad valorem property taxes levied on the properties.

Therefore, the answer is true.

Answer:

  129°

Step-by-step explanation:

If CE is between CD and CF, then angle DCF is the sum of the given angles:

  75° +54° = 129°

Answer:

129

Step-by-step explanation:

bc it just is right

Answer:

(a) He must travel 5.25 km

(b) 17.7° south of west

Step-by-step explanation:

(Please see attached file)

1. He was supposed to travel 5.3 km due north to return to base camp

(vector S)

S = (Sx, Sy)

Sx= 0

Sy= 5.3

2. He discovers that he actually traveled 8.5 km at 54° north of due east (vector D)

D= (Dx, Dy)

Dx= Dcos Ф = 8.5cos54° = 5.0

Dy= Dsen Ф = 8.5sen54° = 6.9

3. He now needs to reach the base camp. Then, we need to find vector R.

From vectors addition/subtraction:

S = D + R

R = S - D

R= (Rx, Ry)

Rx = Dx - Sx = 0 - 5.0 = -5.0

Ry = Dy - Sy = 5.3 - 6.9 = -1.6

Magnitude of R = [tex]\sqrt{Rx^{2}+Ry^{2} }[/tex]

Magnitude of R = [tex]\sqrt{(-5.0)^{2}+(-1.6)^{2} }[/tex]

Magnitude of R = 5.25 km

Direction:

tanβ = [tex]\frac{Ry}{Rx}[/tex]

tanβ = [tex]\frac{1.6}{5.0}[/tex]

tanβ = 0.32

β = tan-1 (0.32)

β= 17.7° south of west

Answer:

D

Step-by-step explanation:

((p^4*q)/p^8)^2.

p^4/p^8=p^(4-8)=p^-4=1/p^4

(q/p^4)^2=(q^2/p^8)

To simplify an algebraic expression, eliminate denominators, distribute factors, rearrange and combine like terms, and isolate the variable. Checking the reasonableness of the answer is also important after simplification.

To simplify an algebraic expression or equation involving variables, you should first look at what needs to be solved for and then work the problem out using only variables. This helps in minimizing calculation time and reducing the chance of errors. Here are some steps to simplify algebraic expressions:

Additionally, by variable rescaling and setting some limits for the error margin, you can further simplify the algebra by eliminating as many parameters as possible. Always check your final answer to ensure it's reasonable.

Answer:

8 1/3

Step-by-step explanation:

The question is asking how many TOTAL (meaning it is increased so it could either be multiplication or addition) miles Loney walked in FIVE days. She walk 1 2/3 A DAY. This can be solved in two ways: multiplication AND addition. Addition: you just have tot turn the mixed fraction into improper fraction and then add the answer five times. But...wouldn’t multiplication be faster and easier..? Sure.

Step 1: Turn mixed fraction into improper.

1 2/3 as an improper fraction is 5/3. How? well multiply and denominator and the whole number and then add the numerator!

Step 2. Make an equation.

The equation should look like 5/3 x 5/1 (1 under 5 because remember there is ALWAYS an imaginary 1 under whole number while multiplying with fractions!)

Step 3. Multiply across

5x5=25

3x1=3 so it’s 25/3. There isn’t any LCM between 25 and 3 so we can only turn it into mixed number (you DEFINITELY can’t leave it like that! You MUST reduce to lowest terms for the correct answer!)

Step 4. Turn back into a mixed number.

there are several ways to do this.

1. Divided 25 by 3 and put the quotient as a whole number, remainder as a numerator and keep the same denominator.

OR

2. More faster way (if you know multiplication tables!)

How many times does 3 (denominato) goes into 25(numerator)? Well, read out the multiplication tables of 3!

3 times 8 equals 24! 3x9 will make it 27 so it doesn’t match with our numerator. So the answer is times 8! It becomes our whole number and it’s still 24 and our numerator is 25 so we have 1. Therefore, 1 is our numerator and we keep the same denominator :)

Hence, the answer is 8 1/3! Hope it helped! :D

The number of miles that Laney walked in total will be 25/3 miles.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Laney walks one and two-thirds of a mile to school from her house and rides the bus home. If she walked five days last week.

Then the number of miles that Laney walked in total will be given by the product of the 1  2/3 and 5.

Number of miles = (1  2/3) x 5

Number of miles = (5/3) x 5

Number of miles = 25 / 3 miles

The number of miles that Laney walked in total will be 25/3 miles.

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Answer:   b)  [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Sample space for the arrangement of red bushes :

[rrww , rwwr , wwrr , wrwr, rwrw , wrrw]

i.e. Total possible outcomes = 6

If the two rosebushes middle of the row are red , then the first and the last rosebushes must be white (wrrw).

i.e. the number of favorable outcomes for middle of the row are red =1

Now, the probability that the 2 rosebushes in the middle of the row will be the red rosebushes :

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{6}[/tex]

Hence, the correct answer is option (b).

Answer:

Museum is at 7 blocks south and 5 blocks east to the Hotel

Step-by-step explanation:

                    | - - H

                    |

                    |_ _ _ _ _ _ _  

                                          |

                                          |

                                          |

                                          |

                                    Museum

Therefore, Museum is at 7 blocks south and 5 blocks east to the Hotel.

Amelia drive 8 kilometers per liter.

13.875 liters needs to drive 111 kilometers.

Amelia used 6 liters for gasoline to drive 48 kilometers.

Here we have to find how many km she drive per liter.

Amelia used 6 liters to drive 48 kilometers

Amelia used 1 liter to drive 48/6 kilometers = 8 kilometers

Therefore, Amelia drive 8 kilometers per liter.

Now, to travel 8 kilometers, she needs 1 liter gasoline

To travel 1 kilometer, she needs 1/8 liter gasoline

To travel 111 kilometers, she needs 111/8 liters gasoline = 13.875 liters

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The standard quantity of metal per​ ring is 0.57 kilograms.

Step-by-step explanation:

Each ring requires 0.52 kilograms of a special metal.

The allowance for waste is 0.03 kilograms per​ ring, while the allowance for rejects is 0.02 kilograms per ring.

So, the standard quantity of metal per​ ring = 0.52 kg of metal required + 0.03 kg of allowance for waste + 0.02 kg of allowance for rejects)

= [tex]0.52+0.03+0.02=0.57[/tex] kilograms.

Hence,  the standard quantity of metal per​ ring is 0.57 kilograms.

Answer:

  an apparent solution that does not satisfy the original equation

Step-by-step explanation:

Usually, an extraneous solution is introduced by the solution process. Sometimes it takes the form of multiplying an equation by 0, often the result of eliminating the denominators of rational functions.

Other times, it takes the form of adding branches to a function that are unintended or undefined. (Squaring a square root will often introduce "solutions" that require the square root to be a negative value.) The attached graph shows that x=4 is an extraneous solution to ...

  √x = x-6

It shows up when the equation is squared:

  x = x² -12x +36   ⇒   (x -9)(x -4) = 0

The "solution" x=4 is extraneous because it does not satisfy the original equation.

As in this graphed example, using graphical methods to find solutions can often avoid extraneous solutions.

Answer:

 an apparent solution that does not satisfy the original equation

Step-by-step explanation: