Use variables to write an equation that represents the relationships between the time x and the distance y.
An eagle flies 40 miles per hour.
An equation that represents the relationships is y = ?

Answer:

[tex]\huge\boxed{B.\ \dfrac{12}{35}}[/tex]

Step-by-step explanation:

Look at the picture.

We know:

[tex]\sin\theta=\dfrac{a}{c}\\\\\tan\theta=\dfrac{a}{b}[/tex]

We have

[tex]\sin\theta=\dfrac{12}{37}\Rightarrow a=12,\ c=37[/tex]

Use the Pythagorean theorem.

[tex]a^2+b^2=c^2\\\\12^2+b^2=37^2\\\\144+b^2=1369\qquad|\text{subtract 144 from both sides}\\\\b^2=1225\to b=\sqrt{1225}\\\\b=35[/tex]

Calculate tangent:

[tex]\tan\theta=\dfrac{12}{35}[/tex]

Answer:

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

Step-by-step explanation:

Because of the slope, we would assume that it is 1/2 because when you use rise over run, the graph rises 1 unit up and shifts 2 units to the right.  The -2 is where the y-intercept is (0, -2) based on the picture seen above.  The slope is also positive where it is going up instead of going down.

The height of the pole, to the nearest tenth of a foot is given by: Option B: 6.7 feet

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Remember that we assume that pole is vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

Referring to the attached figure below, we get:

Using the tangent ratio, we get:

[tex]\sin(x) = \dfrac{\text{Length of perpendicular}}{\text{Length of hypotenuse}} = \dfrac{|AB|}{|AC|}\\\\|AB| = \sin(x) \times |AC|\\\\|AB| = \sin(57^\circ) \times 8 \approx 6.71 \approx 6.7\: \rm feet[/tex]

Thus, the length of the pole is approx 6.7 feet (option B).

Learn more about trigonometric ratios here:

https://brainly.com/question/22599614

Answer:YASSA POINTS

Step-by-step explanation:

40+32=72  

THE RESON IT IS SEVENTYTWO IS BECAUSE IT IS 72p^2

Factors of the given polynomial are 4p, (p + 1) and (p + 8).

   Given polynomial in the question,

Factorize the polynomial,

4p³ + 36p² + 32p = 4p(p² + 9p + 8)

                            = 4p(p² + 8p + p + 8)

                            = 4p[p(p + 8) + 1(p + 8)]

                            = 4p(p + 1)(p + 8)

    Therefore, 4p, (p + 1) and (p + 8) are the factors of the given polynomial.

Learn more,

https://brainly.com/question/15156417

Answer: you need 3/8 buckets of nuts to fill the barrel.

Step-by-step explanation:

I will find the equation and explain it with words at the same time, so it is easier to understand.

We know that:

1/4 buckets of nuts, fills 2/3 of the barrel.

Then we can write the equation:

(1/4) buckets of nuts = (2/3) of the barrel

We want to have a one in the right, which will mean that the barrel is complete, then we can multiply both sides by 3/2

(3/2)*(1/4) buckets of nuts = (3/2)*(2/3) of the barrel.

3/8 buckets of nuts = 1 of the barrel.

This means that you need 3/8 buckets of nuts to fill the barrel.

Answer:

11:10 am.

Step-by-step explanation:

The first thing I'm going to do is to add all the given time together

Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping

Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes

Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes

Total time = 5 hours + 35 minutes

The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping

Time = total time + time spent driving

Time = 5 hours 35 minutes + 35 minutes

Time = 6 hours and 10 minutes

Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer

Needed time = dinner time - time

Needed time = 5:10 pm - 6:10

Needed time = 17:10 - 6:10

Needed time = 11:10

This means that they ought to start their tour by 11:10 am, so that they can meet their dinner

Answer:

63 sq

Step-by-step explanation:

9*7

Answer:

1. y=3x

2. y=1x

3. y=7x

4. y=1x+7

5. y=3x-3

6. y=12x+2

Step-by-step explanation:

Hope this helps!

Answer:

30

Step-by-step explanation:

Perimeter of rectangle = 5y - 1 + 4y + 2 + 5y - 1 + 4y + 2

                                      = 18y + 2

18y + 2 = 128

18y = 128 - 2

     = 126

y = 126 ÷ 18

y = 7

Length of AD = 4y + 2

                      = 4(7) + 2

                      = 28 + 2

                      = 30

Answer:

2 is the number of dollars per seed.

6 is the number of lettuce seeds bought.

7 is the number of pea seeds bought.

Step-by-step explanation:

Two dollars multiplied by six plus seven packets of seeds.

Answer:

A

   The correct option is  C

B

  The  value of  z-test is  [tex]z = -2.267[/tex]

Step-by-step explanation:

From the question we are told that  

    The null hypothesis  [tex]H_o : p = 0.22[/tex]

    The alternative hypothesis  [tex]H_a : p \ne 0.22[/tex]

    The  level of significance is  [tex]\alpha = 0.01[/tex]

    The sample proportion is  [tex]\^ p = 0.15[/tex]

     The sample size is  n = 180

Generally from central limit theorem

if   np  and  nq  are  >  5  then  normal sampling distribution can be used

So  

     np =  180  * 0.22 =  39.6  >  5

and  

     nq =  180 * (1 -0.22) =  140.4 > 5

So normal sampling distribution can be used

Generally the z-test is mathematically represented as

      [tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1- p ) }{n } } }[/tex]

=>   [tex]z = \frac{ 0.15 - 0.22 }{ \sqrt{\frac{ 0.2(1- 0.22 ) }{ 180 } } }[/tex]

=>   [tex]z = -2.267[/tex]

Answer:

65 yd

Step-by-step explanation:

The image of this walking path of Cristal is missing, so i have attached it.

From the image attached, we can see that the path "x" is the hypotenuse path a the triangle.

Thus, we can use pythagoras theorem to find the area. Thus;

x² = 16² + 63²

x = √(16² + 63²)

x = √4225

x = 65 yd

Answer:A=4 Years B=6 years

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

5x+6=10+10=8x-15

Step-by-step explanation:

Answer:mrs robinson would need total of four buses

Step-by-step explanation:

this is because if you have 135 and you divide it by 42 it gets you 3.2 and you cant have .2 of a bus so you must round up to the nearest whole number which would be 4

Answer:

a}[tex]P_1= 0.3[/tex]

b)[tex]P_2 =0.45[/tex]

c) NOT INDEPENDENT

Step-by-step explanation:

From the question we are told that

Sample space

Math majors are 3

computer science majors are 3

Generally the sample space is

Mathematically the sample space required on Monday is given as  [tex]S_m= 3c_1 * 3C_2[/tex]

where [tex]S_m[/tex] =sample space on Monday

Therefore,

[tex]P_1[/tex] = [tex]\frac{3C_1 *3C_2}{6C_3}[/tex]

[tex]P_1=\frac{3*3}{20}[/tex]

[tex]P_1=\frac{6}{20}[/tex]

b)

Generally the the equation is given as

[tex]P_2 =P(\frac{x \cap y}{y})[/tex]

where

x  is  selecting two math major and 1 computer science major on Monday

y is at leas one math major selected

[tex]P_2 =\frac{^3C_1*^3C_2}{^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}[/tex]

[tex]P_2 =\frac{3*3}{3*3 + 3*3 +^1*1}[/tex]

c)

Generally in representing independent events

[tex]P_3=p(x \cap y)[/tex]

=>[tex]p(x) * p(y)[/tex]

Mathematically

[tex]n(x)= ^3C_1 *^3C_2[/tex]

[tex]n(y)={^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}[/tex]

therefore

[tex]n(x \cap y) =^3C_1 *^3C_2[/tex]

This does not satisfy the two equations stated above therefore NOT INDEPENDENT

Answer:

$ 50,340.97

Step-by-step explanation:

From the above question, we can deduce that we are to find the Initial amount invested which is also called the Principal.

The formula to find Principal in a compound interest question is:

P = A / (1 + r/n)^nt

Where:

A = Total Amount obtained after invested = $80,000

r = Interest rate = 3.1% = 0.031

n = number of times interest in compounded = Quarterly = 4

t = time in years = 15

P = $80,000/(1 + 0.031/4)^4 × 15

P = $80,000/(1 +0.00775)^60

P = $ 50,340.97

Hence, James would have to invest $50,340.97 today to have $80,000 in 15 years.

Answer:

4.659

Step-by-step explanation:

4.58

+0.079

4.659

Answer:

do u know the answer ik it's five units up but that it

Answer: a vertical stretch with a scale factor of 2. and a translation of 5 units up.

Step-by-step explanation:

Answer:

Uhhhh what?

Step-by-step explanation:

I am confused...

Step-by-step explanation:

When dividing or multiplying by a negative number, remember to flip the inequality sign.

-3x < 15

x > -5 (divide -3 on both sides, flip the inequality sign)

The correct options are 2 and 9. (D and E)

Answer:

D. 2

E. 9

Step-by-step explanation:

[tex] - 3x < 15 \\ \\ x > \frac{15}{ - 3} \\ \\ x > - 5 \\ \\ [/tex]

Since x > - 5,

Therefore possible values of x would be 2 and 9 out of the given ones.

Answer:

21.759

Step-by-step explanation:

Given that :

Mean (m) = 25

Standard deviation (s) = 12.5

Sample size (n) = 40

α = 90%

The confidence interval is obtained using the relation:

Mean ± Zcritical * s/sqrt(n)

Zcritical at 90% confidence interval = 1.64

25 ± 1.64 * (12.5/sqrt(40))

Lower boundary : 25 - 1.64(1.9764235) = 21.75866546

Upper boundary : 25 + 1.64(1.9764235) = 28.24133454

(21.759, 28.241)

Hence, lower bound of confidence interval is : 21.759

Answer:

<M = 32 and <Y = 103

Step-by-step explanation:

1. Since triangle BCM is congruent to triangle ZYR, we know the corresponding parts of the triangles are congruent. Therefore, <Z = <B = 45. The sum of a triangle’s angles is 180, so <M = 180 - <B - <C = 180 - 45 - 103 = 32

2. This is the exact same diagram, so we can use the information we have collected in #1. Since corresponding parts of congruent triangles are congruent, <Y must be congruent to <C, which equals 103. Therefore, <Y = 103.

I hope this helps! :)

Answer:

4x – 5

4 (x – 5)

4 ( x + 5)

5 less than the sum of 4 and a number

5 less than the product of 4 and a number

the product of 4 and the difference of a number and 5

4 more than the sum of a number and 5

5 more than the product of 4 and a number

the product of 4 and the sum of a number and 5

4 more than 5 less than a number