A reconnaissance airplane P, flying at 19,000 feet above a point R on the surface of the water, spots a submarine S at an angle of depression of β = 21° and a tanker T at an angle of depression of α = 33°, as shown in the figure. In addition, ∠SPT is found to be γ = 119°. Approximate the distance between the submarine and the tanker.
The solution for the problem is:
Tan 33(degrees) = opposite/adjacent
Starting off with the submarine, find how far it is from
point R.
Tan 21 = 19,000/x
or
19,000/Tan 21= x
x = 49496.69 feet the submarine is from point R.
Now, find how far the tanker is from point R.
Tan 33= 19,000/x
or
19,000/Tan 33 = x
x = 29257.43 feet the tanker is from point R.
Now subtract and the difference would be the answer
= 49496.69 - 29257.43
The tanker and sub are 20239.26 feet away from each other.
rounding to estimate the difference of 18.14 - 9.88
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
Now it's just simple math. 18-10 = 8
Step-by-step explanation:
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
18-10=8.
find the next three terms in the geometric sequence: 400, 200, 100, 50
The next three terms in the geometric sequence are 25, 12.5 and 6.25.
The given geometric sequence is 400, 200, 100, and 50.
We need to find the next three terms in the geometric sequence.
What is the geometric sequence?A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term. i.e., To get the next term in the geometric sequence, we have to multiply with a fixed term (known as the common ratio), and to find the preceding term in the sequence, we just have to divide the term by the same common ratio.
In the given geometric sequence the common ratio is 1/2.
5th term=50/2=25
6th term=25/2=12.5
7th term=12.5/2=6.25
Therefore, the next three terms in the geometric sequence are 25, 12.5 and 6.25.
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how many pairs of feet are needed to have at least 76, toes
The packaging lists a model airplane’s length as 10.5 in. It also gives the scale as 1:83. What is the length of the actual airplane to the nearest foot?
a.87ft
b.104ft
c.127ft
d.73ft
A sea lion dove from the water's surface at sea level to an altitude of −216.12 meters in 2.4 minutes. What is the average change in the sea lion's altitude per minute? Enter the your answer in the box as a decimal.
Which equation is an identity?
7m – 5 = 8m + 7 – m
3w + 8 – w = 4w – 2(w – 4)
9 – (2v + 3) = –2v – 6
–3y + 3 = –3y – 6
Please explain your answer.
Answer:
The correct option is 2.
Step-by-step explanation:
The equations that are true for any value of the variable, no matter what value is plugged in for the variable, then they are called Identity equations.
The first equation is
[tex]7m-5=8m+7-m[/tex]
[tex]7m-5=7m+7[/tex]
Subtract 7m from both the sides.
[tex]-5=7[/tex]
This statement is false for any value of m. Therefore this is not an Identity equation.
The second equation is
[tex]3w+8-w=4w-2(w-4)[/tex]
Using distributive property,
[tex]2w+8=4w-2w+8[/tex]
[tex]2w+8=2w+8[/tex]
[tex]0=0[/tex]
This statement is true for any value of w. Therefore this is an Identity equation.
The third equation is
[tex]9-(2v+3)=-2v-6[/tex]
[tex]9-2v-3=-2v-6[/tex]
[tex]-2v+6=-2v-6[/tex]
[tex]6=-6[/tex]
This statement is false for any value of v. Therefore this is not an Identity equation.
The fourth equation is
[tex]-3y+3=-3y-6[/tex]
Add 3y on both the sides.
[tex]3=-6[/tex]
This statement is false for any value of y. Therefore this is not an Identity equation.
Hence the correct option is 2.
Sarah cut 6 yards of ribbon from a spool. How much did she cut in inches?
What does the y intercept represent in distance vs time squared?
A bar of soap weighs as much as 3/4 of an identical bar plus 3/4 of a pound. How much does the bar of soap weigh?
The weight of the bar of soap can be found by setting up the equation [tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex] and solving for 'w', which results in the soap weighing 3 pounds.
To find the weight of the bar of soap, we can set up an equation based on the given information. Let's define the weight of the soap as 'w'. According to the problem, the weight of the soap is equal to [tex]\frac{3}{4}[/tex] of itself plus [tex]\frac{3}{4}[/tex] of a pound, which can be written as:
[tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex]
Now, to solve for 'w', we need to isolate it on one side of the equation. We can do this by subtracting [tex]\(\frac{3}{4}w\)[/tex] from both sides:
[tex]w - \(\frac{3}{4}w\) = \(\frac{3}{4}\)[/tex]
This simplifies to [tex]\(\frac{1}{4}w\) = \(\frac{3}{4}\)[/tex], so when we multiply both sides by 4 to solve for 'w', we get:
w = 3 pounds
Therefore, the bar of soap weighs 3 pounds.
How many integers between 100 and 999 have all distinct digits (i.e., no two digits the same)?
Final answer:
To determine how many integers between 100 and 999 have distinct digits, we calculate the possibilities for each position, giving us 9 options for the first digit, 9 for the second, and 8 for the third, resulting in a total of 648 integers.
Explanation:
The question is about finding the number of integers between 100 and 999 with distinct digits. To find this, we calculate the possibilities for each digit separately. The first digit can be anything from 1 to 9 (excluding 0 because the number cannot be less than 100), so there are 9 possibilities for the first digit. For the second digit, since it cannot be the same as the first, there are 9 possibilities (0 can now be included). Finally, for the third digit, we subtract the choices we've already used, so there are 8 possible digits left.
Calculating the total, we multiply the possibilities for each digit: 9 (first digit) × 9 (second digit) × 8 (third digit) = 648. Therefore, there are 648 integers between 100 and 999 that have all distinct digits.
stacey has 18 bracelets after she organizes the bracelets by color she has 3 equal groups how many bracelets are in each group
Determine which numbers could not be used to represent the probability of an event. select all that apply.
a. minus−1.5, because probability values cannot be less than 0.
b. 0.0002, because probability values must be rounded to two decimal places.
c. startfraction 64 over 25 endfraction 64 25, because probability values cannot be greater than 1.
d. 33.3%, this is because probability values cannot be greater than 1.
e. startfraction 320 over 1058 endfraction 320 1058, because probability values cannot be in fraction form. f. 0, because probability values must be greater than 0.
Two similar right triangles have areas of 6 square inches and 150 square inches. The length of the hypotenuse of the smaller triangle is 5 inches. What is the sum of the lengths of the legs of the larger triangle?
To solve for the sum of the lengths of the legs of the larger triangle, we need to know the sum of the legs of the smaller triangle and multiply it by the scaling factor, which is 5. However, we can't find this sum with the given information because we don't have individual leg lengths of the smaller triangle.
Explanation:To find the sum of the lengths of the legs of the larger triangle, we first need to establish the scale factor between the two similar triangles based on their areas. The area of a triangle scales with the square of the length of its sides. Given that one triangle has an area of 6 square inches and the other has an area of 150 square inches, the scale factor in area is given by the square root of the ratio of the larger area to the smaller area, which is √(150/6), which simplifies to 5. Therefore, if the hypotenuse of the smaller triangle is 5 inches, the hypotenuse of the larger triangle will be 5 times larger, that is 5 * 5 = 25 inches.
Given that the triangles are similar, all corresponding lengths scale by the factor of 5. If we denote the length of the legs of the smaller triangle as a and b, and the legs of the larger triangle as A and B, then A = 5a and B = 5b. Although we don't know the exact lengths of a and b, we can use the Pythagorean Theorem which states that the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b). For the smaller triangle, we have c² = a² + b². But since we only know c (which is 5 inches for the smaller triangle), we cannot directly find the individual lengths of a and b.
Since the question asks for the sum of the legs of the larger triangle (A+B), we only need to find the sum of the legs of the smaller triangle (a+b) and scale it up by the same factor. If a and b were known, we would do (a+b)*5 to get the sum for the larger triangle. However, without those individual lengths, we cannot find the sum based on the given information. To solve this problem, additional information about the lengths of the legs of the smaller triangle would be needed.
there are 24 students in science class. mr james will give each pair of students 3 magnets . so far ,mr James has given 9 pairs of students their magnets . how many magnets doses mr james need sp that each pair of students has exactly 3 magnes?
24/2 = 12 pairs of students
if he gave 9 pairs of students magnets there are 12-9 = 3 pairs left
3 magnets per pair
3*3 = 9 more magnets are needed
Answer:
the answer is d
Step-by-step explanation:
If there were to be 9 boys and 6 girls at a party and the host wanted each to be given the same number of candies that could be bought in packages containing 12 candies, what is the fewest number of packages that could be bought? I got 36. But i'm not sure.
Using the least common factor of 15 and 12, it is found that the fewest number of packages that could be bought is of 5.
How to find the least common factor of two amounts?To find the lcm(least common multiple), we factor the numbers by prime factors, and then multiply these factors.
In this problem, packages of 12 candies will be used to give candies for 9 + 6 = 15 people, hence the least number of candies is lcm(12,15).
Then:
12 - 15|2
6 - 15|2
3 - 15|3
1 - 5|5
1 - 1
Hence lcm(12,15) = 2 x 2 x 3 x 5 = 60.
Since 60 candies are needed, and each package has 12 candies, the number of packages is given by:
n = 60/12 = 5.
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List the sample space in the experiment "roll two dice - a red die and a white die." (hint: use a table)
Sasha donated 9/100 of her class’s entire can collection for the food drive. What decimal is equivalent to 9/100?
select the function that represents a geometric sequence?
Answer:
The correct option is A.
Step-by-step explanation:
A geometric sequence is defined as
[tex]A(n)=ar^{n-1}[/tex]
Where, a is the first term of the sequence, r is the common ratio and n is number of term. So, n can not be negative or zero.
In option A, the given sequence is
[tex]A(n)=P(1+i)^{n-1}[/tex]
Where, n is positive integers.
Here the first term is P and (1+i) is the common ratio. So, this sequence is geometric sequence.
Therefore the correct option is A.
Answer:
A is correct just took the test
Step-by-step explanation:
Table tennis the path of a table-tennis ball after being hit and hitting the surface of the table can be modeled by the function h=-4.9t(t-0.42) where h is the height in meters above the table and t is the time in seconds. how long does it take the ball to hit the table?
A sign in an elevator says the elevator can lift up to 450 kg. John has 10 boxes that weigh 13.75 kg each, and a number of additional boxes that weigh 15.5 kgs each. If he puts the 10 boxes on the elevator, how many of the additional boxes can be lifted in the same load?
A student is calculating how many additional boxes can be added to an elevator that already has 10 boxes of a certain weight. By using the weight capacity of the elevator and the weights of the boxes, the student determines the number of extra boxes that can be accommodated in the elevator's load.
To solve this problem, we need to first calculate the total weight of the 10 boxes:
Weight of 10 boxes = 10 boxes x 13.75 kg/box = 137.5 kgSubtract this weight from the maximum capacity of the elevator: 450 kg - 137.5 kg = 312.5 kgDivide the remaining weight by the weight of each additional box to find out how many more boxes can be lifted: 312.5 kg ÷ 15.5 kg/box ≈ 20 boxesHow far will a cyclist travel in 1/4hour if he cycles at 18km per hour?
Alexandra has 78 emails in her inbox. She deletes 47 emails. How many emails are left in her inbox? Draw jumps and label the number line to show your thinking. —————————————78
This problem can be solved directly by subtraction.
We are given that there are initially 78 emails in her inbox.
We take out or delete 47 emails therefore we subtract 47 from 78, hence:
78 – 47 = 31
So there are 31 emails left in her inbox.
1.Parallelogram ACFD is split in two parts so that ABED and FEBC are congruent isosceles trapezoids. What are the measures of all the angles of trapezoid FEBC if angle D is 48°?
I know that Angle C is 48 degrees
I know that Angle F is 132 degrees
What is < CBE equal to and why?
What is < FEB equal to and why?
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
How are the variables on the graph related?
Answer choices:
A. As speed decreases, height stays constant.
B. As speed decreases, height increases.
C. As speed increases, height decreases.
D. As speed increases, height increases.
The graph demonstrates a uniform relationship between speed and height, indicating that as speed increases, height also increases. Therefore, the correct answer is:
D. As speed increases, height increases.
The Graph indicates a uniform relationship between speed and height. To interpret this in the context of the answer choices:
D. As speed increases, height increases.
This is the most appropriate choice based on the information provided. In a uniform relationship, as speed increases, the corresponding height also increases. Therefore, Option D accurately captures the relationship depicted on the graph.
How many radians are in one degree, accurate to three decimal places?
One radian is approximately 0.0175 degrees. To convert from radians to degrees, multiply the radians value by 57.3°. This conversion is commonly used in mathematics and physics.
Explanation:One radian is equal to approximately 0.0175 degrees. To convert from radians to degrees, you can use the conversion factor of 1 radian = 57.3°. So, to convert an angle from degrees to radians, you can multiply the degrees value by 0.0175. This conversion can be used when working with angular measurements in mathematics and physics.
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The standard deviation of the sampling distribution of x overbarx, denoted sigma subscript x overbarσx, is called the
This is called as the standard error of the mean. Standard error is a numerical term that calculates the accurateness with which a sampling embodies a populace or population. In statistics, a sample mean moves away from the real mean of a population; this deviancy is the standard error.
given : 100cm= 1 m .01 = 1cm
Final answer:
The equation 100 cm = 1 m is used to create a conversion factor that allows for conversion between centimeters and meters. This conversion factor is essential when measuring lengths and is part of the metric system, which also includes units like kilometers, millimeters, micrometers, and nanometers.
Explanation:
Understanding Conversion Factors
When considering the statement that 100 cm is equivalent to 1 m, we can create a conversion factor to help us switch from one unit of measurement to another. A conversion factor is a ratio of equivalent measurements used to convert a quantity from one unit to another. In this case, 100 cm/1 m is our conversion factor, and it is equal to 1 because both numerator and denominator represent the same length but in different units.
If we were to divide both sides of the equation by 1 meter, we would get 1 m/1 m on one side and 100 cm/1 m on the other, simplifying to just 1 because any fraction with the same number in the numerator and denominator equals 1. Hence, utilizing this conversion factor allows any given number in meters to be converted into centimeters, and vice versa, without changing the measure's value.
Furthermore, knowing other unit conversions like 1 meter equals 0.001 kilometers, 1.094 yards, or 39.37 inches can be very useful in different contexts. Similarly, we can break down meters into smaller units such as centimeters, millimeters, micrometers, and nanometers, with each having its place in the metric system.
write the fraction in simplest form 8/10
The simplest form of 8/10 is 4/5.
Given,
8/10
We need to write it in the simplest form.
What is the simplest form of a given fraction?It means that there is no common factor between the numerator and the denominator other than 1.
Example:
4/8
4 = Numerator
8 = Denominator
4 = 4 x 1
8 = 4 x 2
= 4 x 1 / 4 x 2
Cancel the common factor 4.
= 1/2 is the simplest form of 4/8
Find the simplest form of 8/10.
= 8/10
Look for a common factor.
= 2 x 4 / 2 x 5
Cancel the common factor 2.
= 4 / 5
Now we do not see any common factor.
= 4/5
Thus the simplest form of 8/10 is 4/5.
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