Question
A boat is travelling due south at a speed of 53 miles per hour. If the boat started off 29 miles directly west of the city
Johnstown, how fast (in radians per hour) is the angle opposite the southward path changing when the boat has travelled 23
miles? (Do not include units in your answer, and round to the nearest hundredth.)

Answer:

11/6

Step-by-step explanation:

2x/3 = 1/2

Cross multiply, get 4x = 3, x = 3/4

3y/4 = 3/2

Cross multiply, get 6y = 12, y = 2

x + y = 3/4 + 2 = 11/4

xy = 3/4 * 2 = 3/2

(x + y)/(xy) = (11/4)/(3/2) = 11/4 * 2/3 = 22/12 = 11/6

Answer:

5

Step-by-step explanation:

The square root of 29.16 is approximately 5.4. Therefore, the square root of √ 3⁶/²⁵ is approximately 5.4.

The square root of a number is a value that, when multiplied by itself, gives the original number.

To find the square root of √ 3⁶/²⁵, we can break it down into simpler steps.

Step 1: Simplify the expression inside the square root. √ 3⁶/²⁵ can be simplified as follows: √(3⁶ / 5²)

Step 2: Simplify the numerator and the denominator separately.

The numerator is 3 raised to the power of 6, which means multiplying 3 by itself six times:

[tex]3^6[/tex] = 3 × 3 × 3 × 3 × 3 × 3 = 729

The denominator is 5 raised to the power of 2, which means multiplying 5 by itself two times: [tex]5^2[/tex] = 5 × 5 = 25

So, the expression becomes: √(729 / 25)

Step 3: Simplify the expression inside the square root.

√(729 / 25) = √(29.16)

Step 4: Find the square root.

The square root of 29.16 is approximately 5.4. Therefore, the square root of √ 3⁶/²⁵ is approximately 5.4.

To know more about square root here

https://brainly.com/question/428672

#SPJ2

Answer:

The probability is [tex]P(X \le 0.60) = 0.000 [/tex]

Step-by-step explanation:

From the question we are told that

   The overall pass rate is  [tex]R  =  76\% =  0.76[/tex]

   The sample size is  n  =  400

   The percentage that passed is  [tex]k =  60\%  =  0.60[/tex]

Generally the standard error is mathematically represented as

     [tex]\sigma _{\= x } =  \sqrt{\frac{R (1 -R)}{n} }[/tex]    

  =>    [tex]\sigma _{\= x } =  \sqrt{\frac{0.76 (1 -0.76)}{400} }[/tex]

  =>    [tex]\sigma _{\= x } = 0.0214 [/tex]  

Generally the probability of a simple random sample of 400 having a pass rate of 60% or less is mathematically represented as

      [tex]P(X \le 0.60) = P(\frac{X - R}{ \sigma_{\= x}}  \le \frac{0.60 - 0.76}{0.0214} )[/tex]

=>   [tex]P(X \le 0.60) = P(Z \le -7.48 )[/tex]

Generally from the z-table  

      [tex]P(Z \le -7.48 ) =  0.000[/tex]

So

  [tex]P(X \le 0.60) = 0.000 [/tex]

Answer:

x=-10

Step-by-step explanation:

I explained the answer to your question in the photo

Answer:

74

Step-by-step explanation:

13x5+9=74

Answer:

27 feet

Step-by-step explanation:

We know that 3 feet = 1 yard.  So, multiply 9 by 3 and you get 27 feet.  Hope this helps!

Answer:

Step-by-step explanation:

1) Parallelogram ABCD, E is the midpoint of [tex]\overline{DC}[/tex], F is the midpoint of [tex]\overline{AB}[/tex] (given)

2) [tex]DE=\frac{1}{2}DC, BF=\frac{1}{2}AB[/tex] (When a segment is bisected, each part is half the length of the whole segment)

3) [tex]\overline{DC} \cong \overline{AB}[/tex] (opposite sides of a parallelogram are congruent)

4) [tex]DC=AB[/tex] (congruent segments have equal measure)

5) [tex]DE=BF[/tex] (substitution)

6) [tex]\overline{DE} \cong \overline{BF}[/tex] (segments with equal measure are congruent)

7) [tex]\angle D \cong \angle B[/tex] (opposite angles of a parallelogram are congruent)

8) [tex]\overline{AD} \cong \overline{BC}[/tex] (opposite sides of a parallelogram are congruent)

9) [tex]\triangle ADE \cong \triangle CBF[/tex] (SAS)

10) [tex]\overline{AE} \cong \overline{CF}[/tex] (CPCTC)

Answer:

x = 67; y = 121; z = 65

Step-by-step explanation:

x + 1 + 112 = 180

x + 113 = 180

x = 67

y - 9 = 112

y = 121

z + 3 + 112 = 180

z + 115 = 180

z = 65

Answer:

x=-1

Step-by-step explanation:

Answer:

36 degrees

Step-by-step explanation:

The whole shape is 90 degrees.

90 - 54 = 36

36 degrees

Answer:

36*

Step-by-step explanation:

a right angle is 90* and so you do

90-54=36

meaning your missing angle is 36*

Answer:

The width of pen A is 7 feet,

The Length of Pen A is  11 feet,

The width of Pen B is 6 feet,

The Length of Pen B is 12 feet

Step-by-step explanation:

The width of pen A is 7 feet,

The Length of Pen A is 7 + 4 = 11 feet,

The width of Pen B is 7+4-5 = 6 feet,

The Length of Pen B is 2*(7+4-5) = 12 feet

[tex]w+w+w+w+4+4=(w+4-5)+(w+4-5) +2*(w+4-5)+2*(w+4-5)\\4w+8=6w-6\\14=2w\\w=7\\[/tex]

Answer:

The guinea pig is 210 millimeters longer than the fish.

Step-by-step explanation:

Using the normal approximation to the binomial, the probabilities are given by:

a) 0.8485 = 84.85%.

b) 0.0244 = 2.44%.

In a normal distribution 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]

In this problem, we have that:

The mean and the standard deviation of the approximation are given, respectively, by:

[tex]\mu = np = 600(0.05) = 30[/tex]

[tex]\sigma = \sqrt{np(1-p)} = \sqrt{600(0.05)(0.95)} = 5.3385[/tex]

Item a:

Using continuity correction, the probability is P(X > 24.5), which is one subtracted by the p-value of Z when X = 24.5, hence:

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

[tex]Z = \frac{24.5 - 30}{5.3385}[/tex]

[tex]Z = -1.03[/tex]

[tex]Z = -1.03[/tex] has a p-value of 0.1515.

1 - 0.1515 = 0.8485.

0.8485 = 84.85% probability.

Item b:

This probability is P(X < 19.5), which is the p-value of Z when X = 19.5, hence:

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

[tex]Z = \frac{19.5 - 30}{5.3385}[/tex]

[tex]Z = -1.97[/tex]

[tex]Z = -1.97[/tex] has a p-value of 0.0244.

The probability is of 0.0244 = 2.44%.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

C

Step-by-step explanation:

The term range is used when looking for y.

This automatically eliminates the possibility of B and D.

Since y applies only to the vertical aspect of the graph, we can ignore all of the horizontal information (time minutes)

Looking at distance, the bug's lowest point was at 100cm and at its highest point at 400cm

This means the minimum is 100 and maximum is 400

In other words:

100 <= y <= 400

Answer:

C) 100 ≤ y ≤ 400

When we are talking about range, we are talking about y values, so B is disqualified.

When determining range you want the lowest & highest y values.

On this graph the lowest value of y is 100 (seen between 5 and 6 seconds).

The highest value of y is 400 (seen at 8 seconds).

Therefore, 100 ≤ y ≤ 400.

I believe it is 35!

I hope this helps you, and don't forget to give this answer brainliest if it really helped!

Answer:

Use Desmos.com. It is a site that can graph basically anything you want.

Step-by-step explanation:

Answer:

  n² -10 = 6

Step-by-step explanation:

If n represents a positive number, then "the square of a positive number" is represented by n². When that value is decreased by 10, it becomes ...

  n² -10

and if that value is 6, the math expression is ...

  n² -10 = 6

__

Additional comment

Increasing the value by 10 gives ...

  n² = 16

and taking the positive square root gives us the value of the number:

  n = √16 = 4

in this question we have to multiply 4 with 4 then we have to minus 16 with 10 we get the answer 6

= 4 × 4 = 16

= 16 - 10

= 6

Answer:

9m⁸

Step-by-step explanation:

3^2=9

(m⁴)² = m⁸

9*m⁸

Answer:

answer is 0.025

Step-by-step explanation:

answer is 0.025

Answer:

2,870 and 30

Step-by-step explanation:

m    dm    cm    mm

                0        8

8 mm = 0,8 cm

Step-by-step explanation:

48 cm

Remember that i = √(-1), so that

• i ² = -1,

• i ³ = i x i ² = i x (-1) = -i

• i ⁴ = i x i ³ = i x (-i) = -i ² = -(-1) = 1

Multiplying by i again gives i ⁵ = i and the cycle starts over.

The main observation to make here is that raising i to any multiple of 4 returns 1. So,

i ⁴⁸ = (i ⁴)¹² = 1¹² = 1

i ²²³ = i ²²⁰⁺³ = i ²²⁰ x i ³ = (i ⁴)⁵⁵ x i ³ = 1⁵⁵ x (-i) = -i

i ¹¹³ = i ¹¹²⁺¹ = i ¹¹² x i = (i ⁴)²⁸ x i = 1²⁸ x i = i

i ⁸² = i ⁸⁰⁺² = i ⁸⁰ x i ² = (i ⁴)²⁰ x i ² = 1²⁰ x (-1) = -1

i^48 = 1

i^223 = -i

i^113 = i

i^82 = -1

one shirt is for $25 so multiple that by 3 and get $75

70

(

mi

hr

)

=

70

(

mi

hr

)

y

=

70

(

mi

hr

)

x

hr

=

70

(

mi

hr

)

Answer:

18x + 9

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

(8) fx=x2-2x-2

8(2)-2(8)-2

16-16-2

-2