1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mrac [35]
3 years ago
13

The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han

ds at 10 o'clock?
Mathematics
1 answer:
Allushta [10]3 years ago
4 0

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 -2abcosC

Where C is the angle between sides a and b

a =4 and b = 10  C = 60  and we are looking for side c

c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)


You might be interested in
Find the length of the side of rhoumbus whose diagonals are of length 6cm and 8cm.​
Artist 52 [7]

Answer:

In a rhombus, the diagonals bisect at right angles. That means half the diagonals form a right angle triangle then we can try the Pythagorean theorem. so -

one side of triangle =  6/2 =3 (half of the diagonal)

other side = 8/2 = 4

a^2 + b^2 = c2

3 ^2 + 4^2 = c^2

9+16 = c^2

c^2=25

c = \sqrt{25} = 5

the hypothenus forms one side of the rhombus and here the hypothenus is 5, so the lenght of a side is 5 !

6 0
3 years ago
7th grade math help lol
ELEN [110]

Step-by-step explanation:

F and C, I think those are the only ones

7 0
3 years ago
In a survey, 11 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped
pickupchik [31]

Answer:

The population standard deviation is not known.

90% Confidence interval by T₁₀-distribution: (38.3, 53.7).

Step-by-step explanation:

The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus 11 - 1 = 10.

Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,

  • The area to the left of the lower end of the interval shall be 1/2 \cdot (1 - 0.90)= 0.05.
  • The area to the left of the upper end of the interval shall be 0.05 + 0.90 = 0.95.

Look up the t-score of the upper end on an inverse t-table. Focus on the entry with

  • a degree of freedom of 10, and
  • a cumulative probability of 0.95.

t \approx 1.812.

This value can also be found with technology.

The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:

\displaystyle t \cdot \frac{s_{n-1}}{\sqrt{n}},

where

  • t is the t-score at the upper end of the interval,
  • s_{n-1} is the unbiased estimate for the standard deviation, and
  • n is the sample size.

For this confidence interval:

  • t \approx 1.812,
  • s_{n-1} = 14, and
  • n = 11.

Hence the width of the 90% confidence interval is

\displaystyle 1.812 \times \frac{14}{\sqrt{10}} \approx 7.65.

The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:

(38.3, 53.7).

5 0
3 years ago
Fidel has a rare coin worth $550. Each decade, the coin's value increases by %10
PIT_PIT [208]
Answer Answer Answer Answer

4 0
3 years ago
What is between 1/3 and 87/100 on a number line
Tanzania [10]
1/3 = 0.333333   87/100 = 0.87
3 0
3 years ago
Read 2 more answers
Other questions:
  • How do you solve for X ?4x-1=3x+3
    12·2 answers
  • Which of these graphs represents a function
    10·2 answers
  • How many solutions are there to the system of equations?
    6·2 answers
  • 7-4i divided by <br> 2+i <br> how to solve it?
    12·1 answer
  • Please help me please
    6·2 answers
  • Which equation of the solutions of x2 = -7x – 8
    5·2 answers
  • Given csc A= 37/12 and that angle A is in Quadrant I, find the exact value of sec A in
    8·1 answer
  • 11) A map of North Carolina is scaled so that 3 inches represents 93 miles. How far apart are Raleigh
    12·1 answer
  • Answer the question, don't mind the highlighted one
    13·1 answer
  • little melinda has nickels and quarters in her bank she has 8 fewer than nickels she has 5.60 in the bank how many coins of each
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!