QUESTION 2
First Street and Second Street run parallel to each other and both are one-way streets. First Street runs West, Second Street runs East. The city is planning to build a new road, also one way, that runs NE and cuts through both First Street and Second Street at an angle. Traffic turning off of Second Street will have to make a 53° turn onto the new road (see angle f). What angle would traffic turning off of First Street have to make turning onto the new road(See angle a)? Provide your answer and the step-by-step process you used to find it!

This is equivalent to 3/2 as an improper fraction and 1 & 1/2 as a mixed number.

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Explanation:

x = total distance in miles

The train and monorail take 1/3 and 1/2 of the total distance respectively

Add up those fractions to get

1/3 + 1/2 = 2/6 + 3/6 = 5/6

Remember that you can only add fractions when the denominators are the same.

5/6 of the total distance consists of the train and monorail.

That means the walking portion must be 1 - 5/6 = 6/6 - 5/6 = 1/6 of the total distance.

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

In short, we found that 1/6 of the total distance consists of walking.

(1/6)x = 1/4 mile

x/6 = 1/4

4x = 6*1

4x = 6

x = 6/4

x = 3/2

x = 1.5 miles is the total distance

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Check:

1/6 of x = 1/6 of 3/2 = (1/6)*(3/2) = 3/12 = 1/4 mile walking

1/3 of x = (1/3)*(3/2) = 3/6 = 1/2 mile on the train

1/2 of x = (1/2)*(3/2) = 3/4 of a mile on the monorail

1/4 + 1/2 + 3/4 = 1/4 + 2/4 + 3/4 = 6/4 = 3/2 = 1.5 miles total

This confirms our answer.

Answer:

AC=KM

AB=KL

BC=LM

Step-by-step explanation:

Answer:

AC=MK

AB=KL

BC=LM

This are corresponding sides

Answer:

10.9 feet

Step-by-step explanation:

its Pythagoras but reversed. So instead of a squared plus b squared equals c squared its (c squared)-(a squared) equals (b squared)

so (12x12) - (5x5) = 119

square root of 119 is 10.9

sorry im replying on phone i cant do exponents and stuff

Answer:

its still missing

Step-by-step explanation:

U changed it for yourself, not other peoples

Answer: it will say “assigned” but it wouldn’t come up like that for your teacher. I’ve tried it before and it doesn’t work

Step-by-step explanation:

Answer: A

Step-by-step explanation:

A (71x28) x (0.01x0.1) = 0.71 x 2.8

B (71 x 28) x (0.1 x 0.1) = 7.1 x 2.8

C (0.71 x 2.8) x (0.01 × 0.1) = 0.0071 x 0.28

D (71 x 28) x (100 × 10) = 7100 x 280

Answer:

The answer is 18^4

Step-by-step explanation:

Its the answer

Answer: [tex]\frac{1}{-2}[/tex]

Step-by-step explanation:

Slope =

       [tex]\frac{Y2-Y1}{X2-X1}[/tex]

[tex]\frac{10-9}{4-6}[/tex]

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

Answer:

Step-by-step explanation:

Total number of gifts = Sum of all gifts given to each guest

                                    = (Number of guests) * (Number of gifts per guest)

By making the number of gifts per guest the subject of the formula:

Number of gifts per guest = Total number of gifts/Number of guest

But:

Total number of gifts = 32

Number of guests = 8

Number of gifts per guest = Total number of gifts/Number of guest

                                              =32/8

Answer:

see explanation

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c (a ≠ 0 )

• if a > o then curve opens up

• if a < 0 then curve opens down

for y = - 2x² + 4x ← in standard form with a = - 2, b = 4 and c = 0

here a = - 2 < 0 so curve opens down

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

the axis of symmetry is a vertical line passing through the vertex

the x- coordinate of the vertex, which is also the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1

equation of axis of symmetry is x = 1

substitute x = 1 into the equation for y- coordinate of vertex

y = - 2(1)² + 4(1) = - 2 + 4 = 2

vertex = (1, 2 )

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to find the zeros let y = o , that is

- 2x² + 4x = 0 ← factor out - 2x from each term

- 2x(x - 2) = 0

equate each factor to zero and solve for x

- 2x = 0 ⇒ x = 0

x - 2 = 0 ⇒ x = 2

the zeros are x = 0 and x = 2

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

since the graph opens down then it has a maximum value

this is the y- coordinate of the vertex

thus maximum at y = 2

The plane left Bristol airport at 16:55.

This is a problem from time and distance. We can solve this problem by following a few steps.

We have to know the relation between time, speed, and distance. The relation is denoted as,

t = s/v; t is denoted as time interval, v is denoted as velocity or speed in this case and s is denoted as displacement or distance.

We have to find the time. Here velocity is 162 mph and the total distance between  Bristol airport to Leeds Bradford airport is 216 miles.

t = 216 miles/ 162 mph = 1.33 hour = 80 minutes.

Therefore the plane left Bristol airport is, ( 18 hours 15 minutes - 80 minutes) = 16 hour 55 minutes = 16:55

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Answer: 20

Step-by-step explanation:

130+60= 190

60 ÷ 3 = 20

Answer:

37.0seconds

Step-by-step explanation:

when you round you take the second number (8) and find out if it is higher or lower than 5. When it is higher you round up.

But, since the next number is 9 you have to continue to round up the next number which is 6.

Hope this is helpful!

Carmen invested her saving in fund B as $11,000.

For the given question;

Let 'x' be the amount invested by Carmen in fund B.

The, the amount invested in fund A is x - 5000.

The profit on fund A is 2% = 2%(x - 5000).

the profit on fund B is 5% = 5%(x).

Then, the total profit is $670.

The equation will be .

2%(x - 5000) +  5%(x) = 670

2(x - 5000)/100 +  5(x)/100 = 670

2x - 10,000 + 5x = 67,000.

Further simplifying.

7x = 67,000 + 10,000

7x = 77,0000

x = 11,000

Thus, amount invested in fund B is $11,000.

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The initial number of bacteria in a culture is found as 200.

Using the model P = P₀e^(kt),

Where:

P(t) = the amount of bacteria at time t = 2000.

P₀ = initial amount at time t = 0

r = growth rate

t = time (number of periods)

k is the growth constant.

For t = 3 hours.

400 =P₀e^(k*3)    ......eq 1

2000 = P₀e^(k*10)   ......eq 2

Re writing eq 1.

400 = P₀e^(k*3)

as (400/P₀) = [e^k]^3,

Solve for e^k,

∛(400/P₀) = e^k

For eq 2.

2000 = P₀e^(k*10)

Rewrite it as;

(2000/P) = [e^k]^10.  

Substituting ∛(400/P₀) for e^k, we obtain:              

(2000/P₀) =  (400/P₀ )^(10/3)

Solved for P.  

Raise sides by the power of 3, we get:

(2000/P₀)^3 = (400/P₀)^10.

Therefore,

2000^3/  P₀^3  =  400^10/P₀^10

Solve,

2000^3/ 1 =  400^10/P₀^7

Taking reciprocal.

Solving

P₀^7 = 400^10/2000^3

P₀^7 = 1.31 x 10¹⁶

Take the 7th root of both sides;

P₀ = 200.67

Thus, the initial number of bacteria in a culture is found as 200.

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Answer:

its 16

Step-by-step explanation:

Answer:

FG = 16

Step-by-step explanation:

the angle between EF ( y- axis) and EH (x- axis) is right

thus the 4 angles in EFGH are right angles meaning the figure is a square.

the sides of a square are congruent , so

GH = FG , that is

3x + 1 = x + 11 ( subtract x from both sides )

2x + 1 = 11 ( subtract 1 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Then

FG = x + 11 = 5 + 11 = 16

Answer:

Not a function

Step-by-step explanation:

It is not a function because it doesn't pass the vertical line test.

Answer:

21

Step-by-step explanation:

The absolute value of an expression is its distance from 0.

For example, take the number -5:

<-------|------------------|------------->

        -5                   0

It is 5 units to the left of zero, so its absolute value is 5, NOT -5 because distance is always positive, no matter the direction.

To evaluate the given expression, first find each absolute value:

[tex]|-15| = 15, \, \, \, \, \, \, |-6| = 6[/tex]

Then, simplify:

[tex]|-15| + |-6| \\ =15 + 6 \\= 21[/tex]

So, the evaluated expression is 21.

Answer:

1- 1/9

Step-by-step explanation:

[tex]p(5 then 10) = \frac{4}{9} \times \frac{2}{8} [/tex]

[tex]p(5 then 10) = \frac{1}{9} [/tex]

Assuming without replacement

The expected value and the standard error of the sample mean derived from a random sample of 2 pizzas is 0.57

The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample.

The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.

given

Size of the pizzas 16- inch

normal distribution mean is 16 inch

standard deviation= 0.8

μ=16

σ=0.8

n=2

The standard error of the sample mean derived from a random sample of 2 pizzas is:

σₓ= σ / [tex]\sqrt{n}[/tex]

σₓ = 0.8 /[tex]\sqrt{2}[/tex]

σₓ=0.57

The standard error of the sample mean derived from a random sample of 2 pizzas is 0.57

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Answer:

x ≈ 3.9810717

Step-by-step explanation:

The number (3×100)+(1×110)+(4×11,000) in standard form will be 4.4410 × 10⁴

It should be noted that standard form simply means a way of presenting numbers as a mathematical expression.

The number given is illustrated as:

= (3×100)+(1×110)+(4×11,000)

= 300 + 110 + 44000

= 44410

This will be expressed in standard form as:

= 4410

= 4.4410 × 10⁴

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The solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35 which is the correct answer would be option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have to determine the solution of three-fifths times v plus 3 equals two-fifths times v minus 4.

Translate the phrase into an algebraic expression:

⇒ (3/5)v + 3 = (2/5)v - 4

Rearrange the likewise terms and apply arithmetic operations,

⇒ (3/5)v - (2/5)v  = - 3 - 4

⇒ (1/5)v = - 7

⇒ v =  - 7 × 5

⇒ v = - 35

Therefore, the solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35.

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Bette needs 8 jumbo cans of frosting to frost 280 cupcakes.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes which are given in the question.

Let x jumbo cans of frosting would she need to frost 280 cupcakes

As per the given question, we can write the ratio as

3 jumbo cans of frosting : 105 cupcakes = x jumbo cans of frosting : 280 cupcakes

⇒ 3/105 = x/280

⇒ x = ( 280 × 3 )/ 105

⇒ x = 8

Therefore, she needs 8 jumbo cans of frosting to frost 280 cupcakes.

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This is an invalid statement. The law of syllogism is what was used to draw the conclusion in the statement here.

This is the law that is used in logic in the form of

The law of Syllogism can be interpreted as if a person is at least at the age of 25 then they rae able to rent a car. Now given that Anna has fulfilled this condition because she is at the age of 28, then she would be able to rent a car.

Therefore the second option ios correct

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Answer:

The population after x years will be P = 29000 + 700x

Let the population after the years be represented by P

Population of the town in 2003 = 29000

Annual increase in growth = 700

Then, the population after x years will be:

P = 29000 + 700(x)

P = 29000 + 700x

Therefore, the population will be P = 29000 + 700x.

Answer: 1.one cup

2. 2 cups of each

Step-by-step explanation:

We will have the following:

We will have that the value at the end will be $180 000.

The number of periods will be 15*12 = 180.

The interest per month is 0.05/12 = 0.0042

Now:

Here "A" is the value at the end, "P" will be the monthly payments, "i" the monthly interest rate and "n" the number of periods. So:

So, they will need to deposit approximately $671.2 each month.