The angle of elevation from the base to the top of the mountain is 26.56°.
Given, The vertical height of a mountain = 1200 feet
The distance from the top of the mountain to the base = 2400 feet
Now, we need to find the angle of elevation from the base to the top of the mountain.
Hence, we can find the angle of elevation by using the formula
tanθ = Perpendicular/Base
Now, let's apply the formula,
tanθ = Perpendicular/Base 1200/2400= 0.5 tanθ = 0.5
Now, we need to find the value of θθ = tan⁻¹ 0.5θ = 26.56°
for such more question on angle of elevation
https://brainly.com/question/88158
#SPJ11
a crime reporter was told that on average, 3000 burglaries per month occurred in his city. the reporter examined past data, which were used to computed a 95% confidence interval for the number of burgalries per month. the confidence interval was from 2176 to 2784. at the 5% level of significance, do these data tend to support the alternative hypothesis, $h 1 \ne 3000$? calculate z test score
We need to calculate the z-test score. It is a statistical test for inference that tests the null hypothesis that the mean of a sample from a normal population equals a specified value, and it is a test of statistical significance. Z-score: Z = (x - μ) / (σ / √n)μ = 3000, x = (2176 + 2784) / 2 = 2480, σ is the standard error of the mean, and n is the number of data points.
Z = (2480 - 3000) / (3000 / √n). The standard error of the mean (SEM) is calculated as follows: SEM = σ / √nσ = (2784 - 2176) / (2 × 1.96) = 303.64. Therefore, SEM = σ / √n=303.64 / √n(303.64 / √n) = (3000 - 2176) / 1.96n = 141.56n = 142Z = (2480 - 3000) / (303.64 / √142)Z = -12.95.
Since Z is less than -1.96, the test is significant at the 5% level of significance. Therefore, we can refuse the null hypothesis, and the alternative hypothesis is accepted. Therefore, the data support the alternate hypothesis that the number of burglaries per month is not equal to 3000.
To know more about confidence intervals refer here:
https://brainly.com/question/24131141
#SPJ11
What is 5 1/2 x 5 = ?
Answer:27.5
Step-by-step explanation:
i did this with a calculator, but the answer is
27.5
how do you do this? I need helppppp
The constant of proportionality of the graph is k = 3/2.
How to get the constant of proportionality?A general proportional relation between two variables y and x can be written as:
y = k*x
Were k is the constant of proportionality.
To find the value of k, we need to identify a point of the form (x, y) on the given graph, and then replace the values in the equation above, for example, we can use the point (4, 6), replacing that we will get:
6 = k*4
6/4 = k
3/2 = k
That is the constant of proportionality.
Learn more about proportional relations at:
https://brainly.com/question/12242745
#SPJ1
To hire an accountant to prepare taxes costs a flat fee and an additional hourty rate. The amount the accountant costs can be modeled by the function A(X) = 140 +
25x, where x represents the number of hours the accountant works to prepare the taxes and 140 represents the flat fee. What is the value of A(215) and its
interpretation?
a A(215) = 3; If the accountant takes 215 hours to prepare the taxes, the cost wil be $2.
b A(215) = 3; If the account takes 3 hours to prepare the taxes, the cost wil be $215.
c A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost wil be $5,515.
d A(215) = 5515; If the accountant takes 5,515 hours to prepare the taxes, the cost will be $215.
Answer: The given function is:
A(x) = 140 + 25x
We need to find the value of A(215), which means we need to substitute x = 215 in the function and simplify:
A(215) = 140 + 25(215)
A(215) = 140 + 5375
A(215) = 5515
Therefore, the correct answer is (c) A(215) = 5515. The interpretation of this result is that if the accountant works for 215 hours to prepare the taxes, the cost will be $5,515, which includes the flat fee of $140 and an additional hourly rate of $25 for each hour worked.
Step-by-step explanation:
The value of A(215) and its interpretation are captured thus:
A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515
What does the function represents?The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for every hour the accountant works on the tax computation
A(x) = 140 + 25x
In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x
A(215) = 140+(25*215)
A(215) = 140+5375
A(215)=$5,515
Find out more about professional fees on: https://brainly.com/question/28447174
mike and alain play a game in which each player is equally likely to win. the first player to win three games becomes the champion, and no further games are played. if mike has won the first game, what is the probability that mike becomes the champion?
The probability that Mike becomes the champion given that he has won the first game is 7/12.
To find the probability that Alain wins the championship given that Mike won the first game, we can repeat the same reasoning as before, but with Alain as the starting player.
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game)
This leads to:
P(Alain wins championship | Alain won first game) = 5/8
Therefore, we can conclude that:
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game) = 1 - 5/8 = 3/8 + 1/8 = 4/8 = 1/2
Thus, The probability that Mike becomes the champion given that he has won the first game is 7/12.
Learn more about Probability:
https://brainly.com/question/24756209
#SPJ4
Kevin bought snacks for his team's practice. He bought a bag of popcorn for $1.60 and a 8-pack of juice bottles. The total cost before tax was $16.80. How much was each bottle of juice?
Answer:
$1.90
Step-by-step explanation:
16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.
1) Set up and equation equated to 15.20.
8x = 15.20
x = 15.20/8
x = 1.90
Therefore, each bottle of juice costs $1.90.
Please help! Im a struggling depressed student that needs to desperately catch up.
Answer:
25%
Step-by-step explanation:
30/120 = 1/4
1/4 = 25%
Sasha had 30 minutes to do a three-problem quiz. She spent 8 3/4
minutes on questions A and 5 1/2
minutes on question B. How much time did she have left for question C?
SOLVE WITH EXPLANATION GIVING BRAINLIEST IF YOU SOLVE IT CORRECTLY WITH EXPLANATION IF YOU DONT YOU GET REPORTED :/
Answer:
6.
[tex]2x - 1 = x + 3[/tex]
[tex]x = 4[/tex]
[tex] y = 4 + 3 = 7[/tex]
So the solution is (4, 7).
7. Substituting 4x into the second equation:
[tex]4x + x = 5[/tex]
[tex]5x = 5[/tex]
[tex]x = 1[/tex]
[tex]y = 4(1) = 4[/tex]
So the solution is (1, 4).
what is x−10=4 pls help me
Answer:
Step-by-step explanation: 14 = x
Answer:
The answer to your question would be 14
Step-by-step explanation:
Simple equation
14 - 10 = 4
I hope this helps and have a wonderful day!
A line passes through the points
Answer:
5x+2y = -24
Step-by-step explanation:
We have the point (-4,-2) and a slope of -5/2.
Using the point-slope form of a line:
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line.
y- -2 = -5/2(x- -4)
y+2 = -5/2 (x+4)
Multiply each side by 2.
2(y+2) = -5(x+4)
2y+4 = -5x-20
Add 5x to each side.
5x+2y +4 = -20
Subtract 4 from each side.
5x+2y = -24
A water tank is being drained for cleaning. The volume of water in the tank is given by V (t) = 15(40 − t)2 liters, where t is
the number of minutes after the draining began. (Remember to include UNITS in your answers, when appropriate. )
1) a) (4 points) How much water was in the tank when draining began?
VALUE :
b) (4 points) How much water was in the tank 10 minutes after the draining began?
VALUE :
c) (6 points) What was the average rate of change of the volume of water during the first 10 minutes?
VALUE :
d) (6 points) What was the rate of change of the volume of water 10 minutes after the draining began?
VALUE :
e) (8 points) Is the rate at which the volume is changing increasing or decreasing during the draining? EXPLAIN
a) There were 24,000 liters of water in the tank when draining began.
b) There were 9,000 liters of water in the tank 10 minutes after draining began.
c) the average rate of change of the volume of water during the first 10 minutes was -1,500 liters/minute.
d) The rate of change of the volume of water 10 minutes after draining began was -900 liters/minute.
e) The rate of water draining from the tank is slowing down as time goes on.
a) The volume of water in the tank when draining began can be found by setting t = 0 in the equation [tex]V(t) = 15(40-t)^2[/tex]:
[tex]V(0) = 15(40-0)^2 = 24,000[/tex] liters.
Therefore, there were 24,000 liters of water in the tank when draining began.
b) The volume of water in the tank 10 minutes after draining began can be found by setting t = 10 in the equation [tex]V(t) = 15(40-t)^2[/tex]:
[tex]V(10) = 15(40-10)^2 = 9,000[/tex] liters.
Therefore, there were 9,000 liters of water in the tank 10 minutes after draining began.
c) The average rate of change of the volume of water during the first 10 minutes can be found using the formula:
average rate of change = [tex]\frac{(V_{10} - V_0)}{10}[/tex]
Where [tex]V_{10}[/tex] and [tex]V_0[/tex] are the volumes of water in the tank 10 minutes and 0 minutes after draining began, respectively.
Substituting the values we found in parts (a) and (b), we get:
average rate of change [tex]= \frac{(9,000 - 24,000)}{10} = -1,500[/tex] liters/minute.
Therefore, the average rate of change of the volume of water during the first 10 minutes was -1,500 liters/minute.
d) The rate of change of the volume of water 10 minutes after draining began can be found by taking the derivative of V(t) with respect to t and evaluating it at t = 10:
[tex]V'(t) = -30(40-t)[/tex]
[tex]V'(10) = -30(40-10) = -900[/tex] liters/minute.
Therefore, the rate of change of the volume of water 10 minutes after draining began was -900 liters/minute.
e) To determine whether the rate at which the volume is changing is increasing or decreasing during the draining, we need to look at the sign of the second derivative of V(t) with respect to t. The second derivative is:
[tex]V''(t) = -30[/tex]
Since V''(t) is negative for all values of t, we conclude that the rate at which the volume is changing is decreasing during the draining. In other words, the rate of water draining from the tank is slowing down as time goes on.
To know more about the derivative
brainly.com/question/30408231
#SPJ4
question 1(multiple choice worth 3 points) (05.05 lc) according to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise. the numbers for each year are, roughly, 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3. what is the mean of these statistics? 24 2.18 24.18 2
The mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18. (option 2).
To find the mean of a set of numbers, we add up all the numbers in the set and then divide by the total number of items in the set. In this case, we have the following numbers: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, and we want to find the mean.
To do so, we first add up all the numbers:
2 + 1 + 2 + 2 + 1 + 2 + 2 + 3 + 3 + 3 = 21
Then we divide by the total number of items in the set, which is 10:
21 / 10 = 2.1
Therefore, the mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18.
Learn more about Statistics:
https://brainly.com/question/15525560
#SPJ4
The ordered pairs (−4, 7) and (2, −2) are points on a graph of a linear equation. Which other points are also on the same line?
Select ALL that apply.
(−2, −6)
(−2, −5)
(4, −6)
(4, −5)
(0, −5)
(0, 1)
We can find the equation of the line passing through the given two points (-4, 7) and (2, -2) using the slope-intercept form of a linear equation:
slope (m) = (change in y) / (change in x) = [tex](-2 - 7) / (2 - (-4)) = -9/6 = -3/2[/tex]
Using point-slope form with the first given point (-4, 7), we get:
[tex]y - 7 = (-3/2)(x - (-4))\\y - 7 = (-3/2)x - 6\\y = (-3/2)x + 1[/tex]
Now we can plug in the x-coordinates of the other points given and check if they satisfy the equation.
[tex](−2, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(-2) + 1\\-6 = 3 + 1\\-6 ≠ 4 (not on the line)[/tex]
[tex](−2, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(-2) + 1\\-5 = 3 + 1\\-5 ≠ 4 (not on the line)(4, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(4) + 1\\-6 = -6 + 1\\-6 ≠ -5 (not on the line)(4, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(4) + 1\\-5 = -6 + 1\\-5 = -5 (on the line)[/tex]
To learn more about the equation of the line visit:
brainly.com/question/18831322
#SPJ1
10 ft
20 ft
15 ft
Find the area.
A = [?] ft²
Round to the nearest
hundredth.
The total area of the composite figure is 114.25 square feet.
How to find the area of the shape?The area of a circle of diameter D is:
A = 3.14*(D/2)²
And the area of a triangle of base B and height H is:
A = B*H/2
We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:
A = 10ft*15ft/2 = 75ft²
And half of a circle of diameter of 10ft, whose area is:
A = 0.5*3.14*(10ft/2)² = 39.25 ft²
Then the total area of the figure is:
area = 75ft² + 39.25 ft² = 114.25 ft²
Learn more about area at:
https://brainly.com/question/24487155
#SPJ1
What is the area of this figure?
Enter your answer in the box.
Answer:
Step-by-step explanation:
wios,wal
Winston is baking a pie. The diameter of the pie is 12 inches. What is the area of the pie? Use 3. 14 for pi and round your answer to the nearest tenth
If the diameter of the pie is 12 inches, then the area of pie is 113.04 in² and 113 in² after rounding to the nearest tenth.
The formula for the area of a circle is: A = π × r²
where A is the area, pi is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given the diameter of the pie, which is 12 inches. To find the radius, we need to divide the diameter by 2:
r = 12 / 2
= 6 inches
Now we can use the formula for the area of a circle to find the area of the pie:
A = π × r²
A = 3.14 × 6²
A = 113.04 square inches
Rounding to the nearest tenth gives:
A ≈ 113.0 square inches
Therefore, the area of the pie is approximately 113.0 square inches.
To learn more about area of a circle click here
brainly.com/question/28642423
#SPJ4
Can someone please
Help me on this? I’ll give 20 points for this
Answer:
a) 6x10^-6 b) 0.000006 c) I would not be concerned
Step-by-step explanation:
a)
50% is just half and more just means added onto.
Half of 4x10^-6 is 2x10^-6
If you add that onto the original value, you will have:
6x10^-6 (standard form)
b)
0.000006 (ordinary number)
c)
I would not be concerned about the increase in probability of a side effect while using the new medicine. The probability to begin with is extremely low, almost insignificant. While the 50% increase may sound intimidating, it is just a 50% increase on a number that is already very very small. Honestly, it makes almost no difference.
Triangle WXY, with a vertex X at (3, 0), is rotated clockwise 270° about the origin.
Which of the following rotations is equivalent 270° clockwise rotation about the origin?
clockwise 270°
counterclockwise 90°
counterclockwise 360°
clockwise 90°
Answer: A rotation of 270° clockwise is equivalent to a rotation of 90° counterclockwise, because a full rotation is 360° and 270° clockwise is the same as 90° counterclockwise in terms of direction.
Therefore, the answer is: counterclockwise 90°.
Step-by-step explanation:
how many ways can you select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer?
There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.
In this case, n = 15 and r = 3.
Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To know more about combination formula refer here:
https://brainly.com/question/22436873#
#SPJ11
7 2/9 - 5 5/7 = ?
rlly stuck on this math assignment currently
Answer:
95/63 or 1 32/63
Step-by-step explanation:
turn the fraction into a mixed number/improper fraction
65/9-40/7
find a common denominator which in this case is 63
so, the first fraction you will multiply the numerator and denominator by 7 to get
455/63
then the second fraction multiply the numerator and the denominator by 9
360/63
then you would subtract the two numerators KEEP THE DENOMINATOR THE SAME
455/63-360/63=95/63
If f(x) =3x+2 what is f(5)?
In the function f(x) = 3x + 2, f(5) = 17
What is a function?A function is a mathematical equation which shows the relationship between two variables.
Since we have the function f(x) = 3x + 2 and we want to find f(5), we proceed as follows.
To find f(5) in f(x) = 3x + 2, we note that f(5) is the value of f(x) when x = 5. So, we substitute x = 5 into the equation.
So, f(x) = 3x + 2
Substituting x = 5 into the equation, we have
f(5) = 3(5) + 2
= 15 + 2
= 17
So, f(5) = 17
Learn more about functions here:
https://brainly.com/question/24779057
#SPJ1
A sphere has a radius 2. 7 centimeters what is its surface area to the nearest sqaure centimeters
The surface area of the sphere with a radius of 2.7 centimeters is approximately 91.68 square centimeters.
To calculate the surface area of a sphere, we use the formula:
A = 4πr²
where A is the surface area and r is the radius.
Plugging in the value of the radius (2.7 cm), we get:
A = 4π(2.7 cm)² = 4π(7.29 cm²) ≈ 91.68 cm²
Rounding to the nearest square centimeter, we get the final answer of approximately 91.68 square centimeters.
Learn more about Surface Area:
https://brainly.com/question/16519513
#SPJ4
pleaseeee help!!!!!!!!!
The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is: [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.
What number of records will increase by a factor?o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".
To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:
New number of records = N x F
For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:
New number of records [tex]= 100 x 3 = 300[/tex]
So, the new number of records would be 300.
The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:
[tex]12,000 x (1.02)^48[/tex]
Simplifying this expression, we get:
[tex]12,00x0 1.02^48[/tex]
Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48
Learn more about factor here:
https://brainly.com/question/14452738
#SPJ1
Which picture should be next in the sequence?
The next picture in the sequence of pictures is a picture that has 16 cells
Identifying the next picture in the sequenceA pattern is a recurring design, shape, or arrangement that has a regular or logical repetition.
From the figure, we can see that teh pattern is
Picture = 2^n
Where n is the position
For the next picture, we have
n = 4
This means that
Picture = 2^4
So, we have
Picture = 16
Hence, the next picture would have 16 cells
Read more about sequence at
https://brainly.com/question/31096593
#SPJ1
how can you use a fuormula to find the sum of the measures of the interior angles of a regular polygon?
The formula to find the sum of the measures of the interior angles of a regular polygon is: S = (n - 2) * 180 where S is the sum of the interior angles, and n is the number of sides of the polygon.
This formula can be derived using the fact that the sum of the interior angles of any polygon is equal to (n - 2) * 180 degrees, where n is the number of sides.
For a regular polygon, all interior angles are equal, so we can divide the sum of the interior angles by the number of sides to find the measure of each angle. Let's call this measure x. Then we have:
S = nx
Solving for x, we get:
x = S/n
Substituting S = (n - 2) * 180, we get:
x = ((n - 2) * 180)/n
This formula gives us the measure of each interior angle of a regular polygon in terms of its number of sides. To find the sum of the measures of the interior angles, we can simply multiply the measure of each angle by the number of sides and then sum them up. Alternatively, we can use the formula S = (n - 2) * 180 directly to find the sum of the interior angles without finding the measure of each angle first.
To know more about interior angles of a regular polygon click here:
brainly.com/question/29774899
#SPJ4
1. What is the diameter of the circle above?
2.
What is the radius of the circle above?
Answer:
diameter = 34 radius = 17
Step-by-step explanation:
Look at the line in the middle of the circle that is the diameter, diameter is a straight line passing from side to side through the center of a circle.
radius is the distance from the center of the circle to any point on its circumference.
Tristan was out at a restaurant for dinner when the bill came. His dinner came to $22. He wanted to leave a 16% tip. How much do was his meal plus the tip, before tax, in dollars and cents
Answer: 25 dollars and 52 cents
Step-by-step explanation:
Bill = $22
Tip = 16/100 X 22 = $3.52
Total = 22 + 3.52 = $25.52
Answer:
$25.52
Step-by-step explanation:
16% × 22= $3.52
3.52 + 22= $25.52
a 17 ft ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 2ft/s, how fast will the top of the ladder be coming down the wall when the top is 8 ft above the ground
The top of the ladder is coming down the wall at a rate of 15.39 ft/s
Let's assume that the ladder makes a right angle with the wall and the ground. Let's call the distance between the bottom of the ladder and the wall "x" and the height of the ladder at a given time t "y". We want to find the rate of change of "y" with respect to time "t", or dy/dt, when y = 8 ft.
We can use the Pythagorean theorem to relate "x" and "y":
x^2 + y^2 = 17^2
Taking the derivative of both sides with respect to time "t", we get
2x(dx/dt) + 2y(dy/dt) = 0
We want to find dy/dt when y = 8 ft and dx/dt = 2 ft/s. We can solve for dy/dt
2x(dx/dt) + 2y(dy/dt) = 0
2y(dy/dt) = -2x(dx/dt)
dy/dt = -x/y(dx/dt)
Substituting x = sqrt(17^2 - y^2) and dx/dt = 2 ft/s, we get:
dy/dt = -(17^2 - y^2)/y
When y = 8 ft, we get
dy/dt = -(17^2 - 8^2)/8 = -15.39 ft/s
Learn more about Pythagorean theorem here
brainly.com/question/29253365
#SPJ4
Use the drop-down menus to complete the sentence. the transformation is because the preserved.
A transformation is said to be not rigid because the segments is preserved.
A transformation is a function that maps one set of points to another set of points. There are different types of transformations, including translation, rotation, reflection, dilation, and combinations of these. Each type of transformation preserves certain properties of the shape or object.
The properties that are preserved during a transformation depend on the type of transformation
Similarly, a rotation is a transformation that rotates a shape or an object around a fixed point. During a rotation, the distance between any two points on the shape or object is preserved, but the direction may change. A reflection is a transformation that flips a shape or an object across a line. During a reflection, the distance between any two points on the shape or object is preserved, but the orientation may change.
To know more about transformation here
https://brainly.com/question/11709244
#SPJ4
1. nonrigid
2. segment lengths are not