A building casts a shadow of 40 feet on the ground. A wooden figure of a man is placed on the building and casts a shadow an additional 10 feet beyond the building's shadow. What is the height of the man?\
The height of the man from the given question is; 37.5 ft
How to solve trigonometric ratios?This question will form a triangle where;
Height of building = 30 ft
Height of man = h ft
Initial height of shadow = 40 ft
Additional height of shadow = 10 ft
Using similarity theorem, we have;
h/30 = (40 + 10)/40
h/30 = 5/4
h = (30 * 5)/4
h = 37.5 ft
Read more about Trigonometric Ratios at; https://brainly.com/question/13276558
#SPJ1
Work out the bearing of D from C.
(Hint: bearings are written with three digits.)
Answer:
050°
Step-by-step explanation:
The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.
From the diagram, the angle is 050°
Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
the measure of line AD is 8
Step-by-step explanation:
lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8
Suppose a population parameter is 0.8, and many large samples are taken
from the population. If the sample proportions are normally distributed, with
95% of the sample proportions falling between 0.684 and 0.916, what is the
standard deviation of the sample proportions?
Using the Empirical Rule, it is found that standard deviation of the sample proportions is of 0.058.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.0.684 and 0.916 is within 2 standard deviations of the mean(below and above), hence there are 4 standard deviations between these measures, so:
4s = (0.916 - 0.684)
s = (0.916 - 0.684)/4
s = 0.058.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
Attached is a document that I need help on, please help!!!
The ratio of the median weekly earnings is 3 : 5
The ratio of the median weekly earningsFrom the graph, we have the median weekly earnings to be:
High school diploma = $750Bachelor's degree = $1250So, the ratio is:
Ratio = $750 : $1250
Simplify
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph A?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
Both rectangles have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Simplify
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph B?In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume of the red cube to the blue cube in graph C?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width.
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graph
The most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
Read more about bar charts at:
https://brainly.com/question/24741444
#SPJ1
Use the interactive to make a line that passes through the points 3'2 and -1'-1 slope
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
Equation of a lineThe standard equation of a line is expressed as y= mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points on a line (3, 2) and (-1, -1)
Slope = -1-2/-1-3
Slope = 3/4
Determine the y-intercept
2 = 3/4(3) + b
2 = 9/4 + b
b = 2 - 9/4
b = -1/4
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
Learn more on equation of a line here: https://brainly.com/question/18831322
#SPJ1
Discrete Math please help
Considering the given operations, the discrete sets are given as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.What is operation A - B?It is the operation of elements that are in set A but not in set B, hence, since A - B = {1, 5, 7, 8}, we have that:
A = {1,5,7,8}
What is operation B - A?It is the operation of elements that are in set B but not in set A, hence, since B - A = {2,10}, we have that:
B = {2,10}
What is the intersection operation?It contains the elements that are in both sets, hence, since [tex](A \cap B) = \{3,6,9\}[/tex], we have that the sets are completed as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.More can be learned about discrete math at https://brainly.com/question/13309484
#SPJ1
Please help me
14.7 ÷ 4.2
Answer:
how many times does 4.2 go into 14.7
1. 4.2
2. 8.4
3. 12.6
14.7-12.6=2.1 or one half of 4.2
3.5
Hope This Helps!!!
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. Running Play Outcomes Play 1 –3 yards Play 2 2 yards Play 3 –1 yard Play 4 –2 yards Play 5 –3 yards Play 6 1 yard What is the average change in field position per running play? –6 yards per play –1 yard per play 0 yards per play 1 yard per play Mark this and return
Answer:
Step-by-step explanation:
-3 +2 +-1 +-2 +-3 +1 = -6 yards total
-6 / 6 = -1 yard per play average
Alejandro kicks a football. The graph below shows the height of the football hh in meters after tt seconds. What is the football’s greatest height?
Answer:
The answer will be 30.625 m
What is the volume of a regular pyramid having a base area of 24 inches and height of 6 inches
Answer:
V= 48 in^2
Step-by-step explanation:
Formula
Since the base has a known area, we do not need the full volume formula. This formula is
V = B * h / 3
B is the area of the base and h is the height measured from the top of the pyramid to the base meeting the base at right angles.
Givens
B = 24 in^2
h = 6 in
Solution
V = B * h / 3
V = 24 * 6/3
V= 48 in^2
Carmen drew this figure to represent the dividend of a division expression.
A number line going from negative 4 to positive 12. An arrow goes from 0 to 9.
What number is represented by the arrow?
The number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a number line shown in the picture.
As we can see each unit is represented by 1.
So after 2 there will be 3 and after 4 there will be 5 and so on.
So after 8, there will be 9 which is represented by the arrow.
Thus, the number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.
Learn more about the number line here:
brainly.com/question/13189025
#SPJ1
Answer: 9
Step-by-step explanation:
The number line going from - 4 to + 12 represents the range of possible values for the dividend of the division expression. The arrow going from 0 to 9 indicates the actual value of the dividend. Therefore, the number represented by the arrow is 9.
Find the minimum sample size n needed to estimate u for the given values of c, o, and e. C=.95, O=6.4, E= 2
If 6^(2x)=4 find 36^(6x-2) could anyone help me please?
Answer:
3.160
Step-by-step explanation:
You can solve for x using logarithm.
Rewrite in logarithm form
[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]
find 2^x=4x, find x
Whatever... I'll try to solve the first two problems.
[tex]2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}[/tex]
1.
[tex]x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4[/tex]
One solution is [tex]x=4[/tex], and [tex]4\in D[/tex], therefore[tex]\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4[/tex].
We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.
Simplify this equation 10 ^-8
Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing? State your answer as a reduced fraction. Find an equation of a line in the form y = mx + b that describes the amount of gas in your tank.
The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank.The rate of gas will be calculated as:-
Suppose the hours are represented by x and the gallons are represented by y.
The rate of the gas will be the slope so the slope will be calculated as:-
[tex]m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \dfrac{2-20}{3-0}[/tex]
[tex]m =\dfrac{-18}{3}[/tex]
m = -6
The equation will be given as:-
y = mx + c
y = -6x + 20
Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
Please answer all four of the questions I would really appreciate it <3
Answer:
1)A because 3 < 3.9 < 4
2)C because 8.2<8.23<8.3
3) D because 6.1>5.9
4)B because 3.6<3.625<3.7
Hope it helps!
The graphs below have the same shapes. What is the equation for the red graph? g(x)= A g(x) = 2^x + 5 B 2^x - 5 C. g{x} = 2^x+5 D G(x) = 2^x-5
its about efficiency in systems
.......................
which number is the
same distance away from -12 as 2?
Answer:
-26
Step-by-step explanation:
2 is 14 away from -12. The other number that is 14 away from -12 is -26.
-12 + x = 2
x = 14
-12 - 14 = -26
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is a 9 oz box of rice $1.25. (option d)
What is the best buy?In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.
Unit cost = total cost / total oz
$0.90 / 6 = $0.15
$1.93 / 12 = $0.16
$2.42 / 16 = 0.151
$1.25 / 9 = 0.14
To learn more about division, please check: https://brainly.com/question/13281206
#SPJ1
About 10% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. Round your answer to two decimal places.
Answer:
The standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.
Step-by-step explanation:
Standard deviation: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
The given parameters are:
Proportion, p = 10%
Sample size, n = 1000
The standard deviation is calculated as:
σ=[tex]\sqrt{np(1-p}[/tex]
So, we have:
σ=[tex]\sqrt{1000*10%*(1-10%)}[/tex]*(1-10%)
Evaluate:
σ= 9.49
Hence, the standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.
Read more about standard deviation at:
https://brainly.com/question/475676
#SPJ10
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Using translation concepts, the sequence that is used to obtain the translated image is:
Reflection over the y-axis.Shift right of one unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For all the vertices, the transformations follow the given pattern:
(x,y) -> (-x,y) -> (-x + 1, y).In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) -> (-x + 1, y), the function is shifted right one unit.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Which property is not used to simplify the following expression?
(x + 5) - 2+ 7 = 2(x + 5) + 7.
= (2x + 10)+7
= 2x + (10 + 7)
= 2x + 17
O distributive property
O associative property of addition
O commutative property of multiplication
O commutative property of
addition
Answer:
Seitokachou-sama uhuuuyy7 is
Translate to an equation then solve the equation. Seven times the difference of some number and 2 amounts to the quotient of 196 and 14. (Type the question using x as the variable. Do not simplify.) x= ____
Answer:
x = 4
Step-by-step explanation:
7 * ( x-2) = 196/14
7x -14 = 14
7x = 28
x = 4
There were 582 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed.
Answer:
let the no. of students who failed the examination be X
therefore, no. of students passed = 5x
total no. of students = 582
5x + X = 582
6x = 582
x = 97
no. of students failed the examination = 97
no. of students passed = 97*5 = 485
Consider the function shown on the graph.
Answer:
C.) y = 3(x - 3)(x - 7)
For the function:
x intercept: (3, 0), (7, 0)vertex point: (5, -12)point: (8, 15)Writing equation:
y = a(x - h)² + k
15 = a(8 - 5)² - 12
15 = 9a - 12
9a = 15 + 12
9a = 27
a = 3
So the equation is:
y = 3(x - 5)² - 12
y = 3(x² - 10x + 25) - 12
y = 3x² - 30x + 63
y = 3(x - 3)(x - 7)
What is the length of CD? In this diagram, AABC~ AEDC.
The length of CD will be option C. 3
From given diagram, triangle ABC and EDC meet at a common vertex C.
So, triangle ABC and EDC both are congruent to each other.
Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.
Therefore,
AB/ED = AC/EC = BC/CD
AC/EC = BC/CD
18/6 = (12 - x)/x
Simplifying the expression,
We get
18x = 6(12 - x)
Multiplicating the terms in right hand side,
18x = 72 - 6x
Solving 6x on both sides,
we get
18x + 6x = 72 - 6x + 6x
24x = 72
Dividing both the sides by 24, we get
24x/24 = 72/24
x = 3
Hence, the length of CD is 3.
Learn more about congruent triangle here:
https://brainly.com/question/2938476
#SPJ10
Transform each graph as specified below.
(a) The graph of y= f(x) is shown. Draw the graph of y=1/2f(x).
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
Answer:
x f(x)
0 0
-2 -4
4 -2
You need to draw y = 2 f (x-1)
So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values
New function
x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.
y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)
Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)
