Answer:
5624.22 feet
Step-by-step explanation:
You want to know the distance from a skyscraper 1465 ft tall to a point where the angle of elevation to its top is 14.6°.
TangentThe tangent relation tells you ...
Tan = Opposite/Adjacent
ApplicationThe distance between buildings is the side of the right triangle adjacent to the angle of elevation. The height of skyscraper B is the side opposite the angle of elevation. Using the tangent relationship, we can find the distance d between the buildings as ...
tan(14.6°) = 1465/d
c = 1465/tan(14.6°) ≈ 5624.22 . . . ft
The distance from A to B is about 5624.22 feet.
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please help with these 2 questions in math
The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.
When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).
Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.
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Please help i’ll give brainlist!!
Solve each proportion.
Answer: 12, 32/11
Step-by-step explanation:
3 12
4 32/11
Finding the area and perimeter
Answer:
Lion area: 60
Lion Perimeter: 34
Tiger Area: 60
Tiger perimeter: 64
Step-by-step explanation:
Select the correct answer. The product of two numbers is 21. If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21. The second number is 24. B. The equation that represents this situation is 3x = 21. The second number is 7. C. The equation that represents this situation is -3x = 21. The second number is -7. D. The equation that represents this situation is -3 + x = 21. The second number is 18.
Answer:
The product of two numbers is 21.
Step-by-step explanation:
If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.
Select the correct answer. Which function has an average rate of change of -4 over the interval [-2,2]?
A. x | -2 | -1 | 0 | 1 | 2
m(x) | -12 | -5 | -4 | -3 | 4
B.
C.
D.
Answer:
The correct answer is option B.
To find the function with an average rate of change of -4 over the interval [-2,2], we need to calculate the slope of the function between the two points -2 and 2.
Average rate of change = (f(2) - f(-2))/(2 - (-2)) = (-4)
Option B has the function qx with values {-4, 0, 0, -4, -12} at x values {-2, -1, 0, 1, 2}. The average rate of change of this function over the interval [-2,2] is indeed -4.
The circle below is divided into six equal pieces. If the area of the shaded region is 98pi what is the
circumference of the circle? Leave answer in terms of pi
Consequently, the circle's diameter is 28π√3.
What is its the circumference?The radius of a circular or other curved geometry form refers to its length. It is the border across any two-dimensional circle surface measured linearly in one dimension.
Since the circle is divided into six equal pieces, the shaded region represents one-sixth of the total area of the circle. Therefore, the total area of the circle can be found by multiplying the shaded area by 6:
Total area of circle = 6 × 98π = 588π
The formula for the area of a circle is A = πr², where r is the radius of the circle. Solving for r, we get:
r² = A / π = 588π / π = 588
r = √588 = 2√147 = 2√3 × √49 = 14√3
C = 2r is the method for calculating a circle's diameter. Plugging in the value of r, we get:
C = 2π(14√3) = 28π√3
Therefore, the circumference of the circle is 28π√3.
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Noel and alternative hypothesis for the study are (in the photo)
Please let me know which one of the answers in the photo is correct ! Thank you , 100 points!!
With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
What is a significance level?In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.
The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.
The correct option is A.
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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?
Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of
no difference between the triglyceride test levels.
Jason studied how quickly ants consume things. He counted the number of ants on a banana peel at the end of each minute for five minutes. His results formed the pattern below.
12, 19, 26, 33, 40
Let n represent the number of minutes since Jason began his study. Which expression could be used to predict the number of ants on the banana peel after n minutes?
5+7n
7+5n
12n
7n
The expression that could be used to predict the number of ants on the banana peel after n minutes is given as follows:
5 + 7n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In this problem, the difference between consecutive terms is of 7, meaning that it represents an arithmetic sequence with a common difference of 7.
The first term is of 12, hence we obtained the explicit formula as follows:
12 + 7(n - 1) = 12 + 7n - 7 = 5 + 7n.
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The diameter of a circle is 5 miles. What is the circumference?
Answer: Circumference, C = 15.71 miles
Step-by-step explanation:
The formula for the circumference of a circle is C = 2*pi*r, where C is the circumference and r is the radius. (Value of pi = 3.1415)
In this case, the diameter, d = 5 miles = 2*r, so we can substitute that into the formula:
C = pi*d = 3.1415*5
C = 15.7079 miles
Therefore, the circumference of the circle is approximately 15.71 miles, if we round to two decimal places.
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Martha made 2 2/3 pounds of pasta. she divided the pasta into fourths. how much pasta is in each portion?
Step-by-step explanation:
2 2/3 = 8/3
8/3 * 1/4 = 8/12 = 2/3 pound in each portion
if y is inversely proportional to the square root of x, and y is 16 when x is 0.25.find the value of y when x is 0.64
By inverse proportions, 6.4 is the value of y .
What are some examples of inverse proportions?
In the case of two quantities that are inversely proportional, one quantity falls as the other rises. The number of hours needed to construct a wall serves as an illustration of inverse proportion. The time required to build a wall decreases as more people work on the same project.
suppose that y =√kx
enter (0.25,16) to y =√kx
0.5k = 16
k = 5
y = 8√x
when x = 0.64
y = 8√0.64
y = 6.4
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Find the roots of the given complex number in trigonometric form:
square roots of 5 (cos(120°) + i sin(120°))
The two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).
The complex number in question is the square root of 5, written in trigonometric form as cos(120°) + i sin(120°). To calculate the two individual roots, we can use the identity for the square root of a complex number, which states that for any complex number, z, the square root of z is equal to (sqrt(|z|)) × (cos(θ/2) + i sin(θ/2)), where θ is the argument of z. In this case, we have |z| = 5 and θ = 120°. Therefore, the two individual roots are equal to (sqrt(5)) × (cos(60°) + i sin(60°)) and -(sqrt(5)) × (cos(60°) + i sin(60°)) = sqrt(5) × (cos(300°) + i sin(300°)).
In conclusion, the two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).
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The company Sea Esta has ten members on its board of directors. In how many different ways can it
elect a president, vice-president, secretary and treasurer?
Answer:
Step-by-step explanation:
The president, vice-president, secretary and treasurer are four different positions that need to be filled by ten individuals.
Therefore, the number of ways to elect the president is 10. After electing the president, the number of candidates available for the vice-president position reduces to 9. Similarly, after electing the president and the vice-president, the number of candidates available for the secretary position reduces to 8. Finally, after electing the president, vice-president, and secretary, the number of candidates available for the treasurer position reduces to 7.
Using the multiplication principle of counting, we can find the total number of possible combinations for all four positions by multiplying the number of candidates for each position:
Total number of ways to elect all four positions = (number of candidates for president) x (number of candidates for vice-president) x (number of candidates for secretary) x (number of candidates for treasurer)
= 10 x 9 x 8 x 7
= 5,040
Therefore, there are 5,040 different ways that Sea Esta can elect a president, vice-president, secretary, and treasurer from its board of directors.
Find the unknown dimension of a rectangle if its perimeter is 254 meters and one
dimension measures 6 meters. Use labeled sketches and equations to model and
solve this problem. Show your work. Label your answer with the correct units.
The perimeter does indeed equal 254 meters, which confirms that our answer is correct.
What in mathematics is the perimeter?Any two-dimensional closed shape's perimeter is defined as the entire distance encircling it. The perimeter of a rectangle, such as the following: Square perimeter equals the sum of its four edges. Rectangle perimeter equals the sum of its four edges.
Let's call the rectangle's unidentified size x.
P = 2l + 2w, where l is the length and w is the breadth, gives the perimeter of a rectangle.
So that we can create an equation:
254 = 2l + 2(6)
Simplifying the right side:
254 = 2l + 12
Subtracting 12 from both sides:
242 = 2l
Dividing both sides by 2:
121 = l
Consequently, the rectangle's undetermined measurement (length) is 121 metres.
We can compute the perimeter using both variables to confirm our conclusion:
P = 2(121) + 2(6) = 242 + 12 = 254
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I need to know the z score of 2,-2 and also the mean and standard deviation
Answer: two standard deviations below the average value.
Step-by-step explanation: The z score tells you how far below the average value that person or group is, on a scale from -2 to 2. The higher the z score, the more abnormal or anomalous the data being compared is. A z score of 1 indicates that the data is exactly average, while a z score of -2 indicates that the data is two standard deviations below the average value.
11) m/EFG=132°, m/CFG=x+111,
and m/EFC=x+23. Find mLEFC.
Applying the angle addition postulate, the value of x in the image given is calculated as: 49.
What is the Angle Addition Postulate?The Angle Addition Postulate states that for any angle, the sum of its adjacent angles is equal to the angle formed by combining them.
Therefore, we have:
x + 11 + x + 23 = 132
Combine like terms to find the value of x:
2x + 34 = 132
2x = 132 - 34
2x = 98
2x/2 = 98/2
x = 49
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13 Convert 20 to a percentage.
The Revenue and Cost equations for a company are known to be polynomials of order 1 and 2 respectively. It is also known that the graphs of the two equations meet at points A(1,1) and B(5,9) while the third point of the cost function is C(2,0), obtain the following:
a) The Revenue equation and the cost equation
b) What do the common solutions to the two equations signify?
Answer: a) We know that the Revenue equation is a polynomial of order 1, so we can write it in the form:
R(x) = ax + b
where a and b are constants to be determined. We also know that R(1) = 1 and R(5) = 9, so we have two equations:
a(1) + b = 1
a(5) + b = 9
Solving these equations simultaneously, we get:
a = 2, b = -1
Therefore, the Revenue equation is:
R(x) = 2x - 1
Similarly, the Cost equation is a polynomial of order 2, so we can write it in the form:
C(x) = ax^2 + bx + c
where a, b, and c are constants to be determined. We know that C(1) = R(1) = 1 and C(5) = R(5) = 9, so we have two equations:
a(1)^2 + b(1) + c = 1
a(5)^2 + b(5) + c = 9
We also know that C(2) = 0, so we have a third equation:
a(2)^2 + b(2) + c = 0
Solving these equations simultaneously, we get:
a = 1, b = -4, c = 4
Therefore, the Cost equation is:
C(x) = x^2 - 4x + 4
b) The common solutions to the Revenue and Cost equations represent the production level(s) at which the company makes a profit, since the Revenue equation represents the amount of money the company earns and the Cost equation represents the amount of money the company spends. In other words, the common solutions are the values of x for which R(x) - C(x) > 0. At these production levels, the company's revenue is greater than its cost, resulting in a profit. At production levels where R(x) - C(x) < 0, the company is making a loss. At production levels where R(x) - C(x) = 0, the company is breaking even. Therefore, the common solutions to the two equations signify the production levels at which the company makes a profit or breaks even.
Step-by-step explanation:
Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it
The resulting number is 12/5
What are arithmetical operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it
So, performing the operations,
15/16+15/16×3/5
= 15/16(1+3/5)
= 15/16(8/5)
= 120/80
= 3/2
Now,
3/2+3/2×3/5
= 3/2(1+3/5)
= 3/2(8/5)
= 24/10
= 12/5
Hence, the resulting number is 12/5
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Find the value of x.
13)
O
(2x+8)
62°
20 22 Kuta Software LLC.
14)
A
(x-4) (2x+1)
All rights reserve d-1-Made with Infinite Geometry.
Answer:
Without additional information or context, it is not possible to find the value of x for the given diagrams. Please provide more information or the full problem statement.
2. Evaluate the logarithmic expression using properties of logs and the change of base formula
Expression
a. log5.625
b. log6.4 +log6.12
c. log3.9^4
(i put a period after a imaginary number)
The expressions can be written as :a. log5.625 ≈ 0.75.
b. log6.4 + log6.12 ≈ 1.67.
c. log3.9^{4} ≈ 2.47.
What is logarithm function?
A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.
a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:
log5.625 = log(5625/1000)
Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:
log5.625 = log(5625) - log(1000)
Using the change of base formula, we can convert the logs to a common base, such as 2 or e:
log5.625 = log(5625)/log(10) - log(1000)/log(10)
Evaluating the logs using a calculator or by simplifying, we get:
log5.625 ≈ 0.75
Therefore, log5.625 ≈ 0.75.
b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:
log6.4 + log6.12 = log(6.4 × 6.12)
Using the change of base formula, we can convert this to a common base:
log6.4 + log6.12 = log(6.4 × 6.12)/log(10)
Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:
log6.4 + log6.12 ≈ 1.67
Therefore, log6.4 + log6.12 ≈ 1.67.
c. Using the property log(a^{n}) = n log(a), we can simplify the expression:
log3.9^{4} = 4 log3.9
Using the change of base formula, we can convert this to a common base:
log3.9^{4} = 4 log(3.9)/log(10)
Evaluating the log using a calculator or by simplifying, we get:
log3.9^{4} ≈ 2.47
Therefore, log3.9^{4} ≈ 2.47.
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Help please I got 5.76 I don’t know if that’s right
Answer:
trust yourself cuh
Step-by-step explanation:
Question 2
(03.01 LC)
Which of the following is not created when a plane slices through a cone?
O Point
O Line
O Circle
O Square
A square is not created when a plane slices through a cone.
What is square?
A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.
What is cone?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.
According to given information:When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.
If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.
If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.
Therefore, a square is not created when a plane slices through a cone.
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For a 99% confidence interval with a sample size of 10 What is the critical t-value?
how do i solve this problem?
Option A correctly describes the area of the graph of the function.
How is an area of the graph calculated?
The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.
It is the integration of the function polynomial of the possible values of x that the function curve lies in.
Here the function equation is : [tex]f(x) = ( 25 - x^{2} )[/tex]
From the figure, we can see that the value of x varies from -5 to 5.
Initial x-value of integration = minimum value of x
= -5
Final x-value of integration = maximum value of x
= 5
Thus, the area of the graph can be correctly calculated as. :
[tex]Area = \int\limits^{maxX}_ {minX} \, f(x)dx[/tex]
[tex]Area = \int\limits^5_ {-5} \, (25-x^{2} )dx[/tex]
Hence, Option A correctly calculates the area of the graph given.
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For this linear inequality, describe how to represent the solutions on a graph:
y< 2x+5
O check all solutions to see if they make true statements
O shade to the left of the boundary
shade below the boundary line
O shade above the boundary
Answer / Step-by-step explanation:
To represent the solutions of the linear inequality y < 2x + 5 on a graph, we can follow these steps:
First, we draw the boundary line y = 2x + 5, which is a straight line with a slope of 2 and a y-intercept of 5.
Since the inequality is y < 2x + 5, we need to shade the region that is below the boundary line. This is because any point below the line will have a y-coordinate that is less than 2x + 5, which satisfies the inequality.
We can also use a dashed line to represent the boundary line, since the inequality is strict (y < 2x + 5, not y ≤ 2x + 5).
Finally, we can check the solutions to the inequality by picking any point in the shaded region and plugging its coordinates into the inequality. If the resulting statement is true, then that point is a valid solution to the inequality. If the statement is false, then the point is not a solution.
Therefore, to represent the solutions of the inequality y < 2x + 5 on a graph, we would shade below the dashed line y = 2x + 5.
which is more 7,000 milliliters or 7 liters?
Answer:
It’s the same
Step-by-step explanation:
There equal
7 liters = 7000 milliliters
The diameter of the base of a cone is shown on the grid. Each square unit on the grid has a side length of 1 foot. The volume of the cone is approximately 200.96 cubic feet. Determine the height of the cone, and construct it vertically on the grid with respect to the center of the cone's base.
Use 3.14 for .
Answer:
First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).
Next, we can use the formula for the volume of a cone to find the height:
V = (1/3)πr^2h
Substituting the given volume and radius, and using 3.14 for π, we get:
200.96 = (1/3) x 3.14 x 4^2 x h
Simplifying and solving for h, we get:
h = 200.96 / (1/3 x 3.14 x 4^2)
h = 200.96 / 53.02
h ≈ 3.79 feet (rounded to two decimal places)
To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.
Parts of similar triangles
Find x
In the triangle, x has a value of 18.
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The two arms of a right angle are made up of height and base.
We know that the respective sides of the two triangles in the diagram are proportional since they resemble one another. Namely, we have
AB / AE = BC / CD
Inputting the values provided yields:
x / 12 = 9 / 6
Finding x and simplifying results in:
x = 12 * (9/6) = 18
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19 less than a number is 28
Answer: 47
Step-by-step explanation:
28+19=47
47-19=28