In the diagram below, the man on the diving board is 6 ft. tall and the angle of elevation from the man in the water (angle 4) to the man on the diving board is 40. How far apart are the two men? Round your answer to the nearest tenth.
A picture of a swimming pool with a lifeguard sitting on an elevated chair on the right side of the pool. There is a person on a diving board on the left side of the pool who is lower than the lifeguard. The lifeguard is looking down at the person on the diving board and there is a solid line showing his line of sight. A dotted line is drawn from the lifeguard’s eyes horizontally. The angle between these two lines is labeled 1.
The distance between the two men is 7.2 ft. That is, they are 7.2 ft apart
Calculating DistanceFrom the question, we are to determine the distance between the two men
Let the distance between the men be x
From the given information,
The man of the diving board is 6 ft tall
and
The angle of elevation from the man in the water to the man on the diving board is 40°
Considering the triangle formed, we can write that
Opposite = 6 ft
Adjacent = x
Angle = 40°
From SOH CAH TOA, we have that
tan (angle) = opposite / adjacent
∴ tan 40° = 6 / x
x = 6 / tan 40°
x ≈ 7.2 ft
Thus,
The men are 7.2 ft apart
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Which graph Represents a function
The first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.
As per the question statement, we are provided with 4 distinct graphs attached hereby alongside.
We are required to determine, which of the above-mentioned graphs represent a function.
To solve this question, we need to know about the characteristics of a function, which we can match against our provided graphs and identify our required function.
A function is an operator, and hence, there will be a fixed pattern or sequence among it's outputs, which we can only find in the first graph from the right as shown in the reference image, since it is a straight line parallel to the Y-axis at (x = 1).
Therefore, the first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.
Function: In Mathematics, a function is an operator, which when provided with a certain input, performs a pre-determined set of operations on the input and then produces a fixed output.To learn more about Functions, click on the link below.
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Which statements would prove the lines are parallel?
The statements that would prove the lines are parallel are;
∠GHI ≅ ∠KJH
∠MJH + ∠NHJ = 180°
∠KJH + ∠IHJ = 180°
How to Identify Congruent Angles?
In congruency of angles formed in this type of scenario, we will make use of the following rules;
If two parallel lines are cut by a transversal, then, Alternate Interior Angles are congruent. If two parallel lines are cut by a transversal, then, Alternate Exterior Angles are congruent. If two parallel lines are cut by a transversal, then corresponding angles are congruent.Using the above congruency rules and applying them to our question, we can say that for lines HN and KM to be parallel to each other, then;
∠GHI ≅ ∠KJH because they are corresponding angles
∠MJH + ∠NHJ = 180° because they are supplementary angles
∠KJH + ∠IHJ = 180° because they are supplementary angles
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24 in the ratio 1:2:3
Answer:
4:8:12
Step-by-step explanation:
To find the ratio of 24 in 1:2:3,
first add the ratios = 6 then divide each ratio as a fraction of the total
[tex] \frac{1}{6} \times 24 \\ = 4[/tex][tex] \frac{2}{6} \times 24 \\ = 8[/tex][tex] \frac{3}{6} \times 24 \\ = 12[/tex]Therefore, 24 in ratio 1:2:3 is 4:8:12
two and one hundread eight thousandths in standard form
(5x10^2) x (8x10^4)
I NEED HELP PLEASE!!!!
Answer:
4 x 10^7 i.e. 40000000
Step-by-step explanation:
(4x10^7) is obtained by multiplying (5x10^2) by (8x10^4).
The equation can be solved by multiplying the coefficients (5 and 8) first, adding the exponents (2 and 4), and writing the result in scientific notation:
(5 x 8) x 10^(2 + 4) = 40 x 10^6 = 4 x 10^7.
Hope it helps! : )How many extra flowers did they order?
Answer:
B
Step-by-step explanation:
To find the number of extra flowers ordered, we can start by forming an equation based on the total amount paid by the customer.
Let the number of extra flowers be n.
Total paid
= cost of standard arrangement +(number of extra flowers)(cost per additional flower)
= $25 +n($1.25)
Given that the customer paid $45,
25 +1.25n= 45
Now that we have formed the equation, let's solve for n.
Subtract both sides by 25:
1.25n= 45 -25
1.25n= 20
Divide both sides by 1.25:
n= 20 ÷1.25
n= 16
Leah has an account balance of -150 dollars. Which of the following represents a debt greater than -150 dollars? - 175 dollars - 150 dollars -125 dollars 0 dollars
Owing 175 dollars is more than owing 150 dollars.
Thereby, the correct answer is A) -175 dollars
Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)
A. LN is a segment bisector
B. LN is an angle bisector
C. L is the vertex of a pair of congruent angles in the diagram
D. N is the vertex of a pair of congruent angles in the diagram
E. L is the vertex of a right angle
F. N is the vertex of a right angle
Answer: A
Step-by-step explanation:
A. True by the definition of a bisector.
B. False, this is an assumption based on appearances.
C. False, this is an assumption based on B.
D. False, this is an assumption that LN and JK are perpendicular.
E. False, assumption based on appeareances
F. False, assumption based on D.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. The product of 7 and the square of a number.
Answer:
[tex]7 * x^2[/tex]
distance in space is often written using a lightyear. A lightyear is the distance light travels in one year. It is equal to 6,000,000,000,000 miles. Write this measurement in scientific notation. PLS HELP ME ASAP!!!!!!!!!!!!!!!!!!!!!!!! >_
Answer:
Step-by-step explanation:
C
You bike 14 1/4
miles from your house to a state park. You travel 1/3
of that
distance in the woods. You bike along the bank of a stream for the last 1/2
of
the woods. On how many miles of your trip do you bike along the bank of
the stream?
By taking some products between fractions and mixed numbers, we will see that your trip along the bank has a length of (2 and 9/24) miles.
How many miles do you travel along the bank of the stream?Here we know that the total distance of the travel is (14 + 1/4) miles.
In this case, we know that 1/3 of that distance is traveled in the woods, so the total distance traveled in the woods is given by the product:
D = (1/3)* (14 + 1/4) mi = (14/3 + 1/12) mi
Now we know that 1/2 of the distance traveled in the woods is traveled along the bank of a strem, then the distance that we are looking for is given by the product:
D' = (1/2)*(14/3 + 1/12) mi = (7/3 + 1/24)mi
Now we can simplify that mixed number as:
(7/3 + 1/24)mi = (6/3 + 1/3 + 1/24) mi = (2 + 8/24 + 1/24)mi = (2 + 9/24) mi
Your trip along the bank of the stream has a length of (2 + 9/24) miles.
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Find the length of the segment indicated round your answer to the nearest tenth if necessary
The length of the segment indicated to the nearest tenth are as follows:
x = 7x = 8How to find the length of a segment?The length of the segment can be found as follows:
Therefore, the segment indicated in question 5 is the radius of the circle.
The radius of a circle is the distance from the centre of the circle to any point on it's circumference.
The radius is half of diameter.
The radius from the second to one end of the circumference is given as 7. Therefore, the radius from the centre to another end of the circumference will be as follows:
x = 7The second circle, the line from the centre bisect the chord into equal halves. Since the other half is 8, that means the second half will be as follows:
x = 8Therefore, the length of the segment indicated are 7 and 8 respectively.
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help !!!!!!!!!!! please
Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
As given,
Given measures of the triangle ABC are
Angle A=(18 +18)°
=36°
Consider side opposite to ∠A=a ,∠B=b ,∠C=c
Given side length
AC=b
=20
AB=c
=12
BC=c
=x+12
Using cosine law
cos A= (b²+c²-a²)/2bc
⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)
⇒(1+√5)/4=(544-x²-24x-144)/480
⇒x²+24x-280+120√5=0
⇒x²+24x-11.7=0
Now, x = [-24±√24²-4(1)(-11.7)]/2(1)
= (-24±24.955)/2
≈ (-24 ±25)/2
Hence, x = (-24+25) /2
= 1/2
or x = -24.5 side length cannot be negative.
Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
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Estimate 0.049127568 to the nearest hundredth. Express your answer as a single digit times a power of ten.
Please I need help
What is the expression after applying the distributive property?
−3.6(−2+(−7))
Enter your answer by filling in the boxes.
(-3.6) ( ) + ( ) ( )
The expression after applying the distributive property is: (-3.6)(-2) + (-3.6)(-7).
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is the distribution property?The distributive property states that when the sum of two (2) or more addends are multiplied by a specific number, the same output would be produced as when each addend is multiplied respectively by the number, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
x(y + z) = xy + xz.
By applying the distributive property of multiplication to the given expression, we have the following expression:
-3.6(-2 + (-7)) = (-3.6)(-2) + (-3.6)(-7).
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Using only the values given in the table for the function,
f(x), what is the interval of x-values over which the
function is increasing?
(-6-3)
(-3,-1)
(-3.0)
(-6-5)
The interval of x-values over which the function is increasing is (-3 , -1)
What is function ?A law that connects two variables—the dependent and the independent variables—is known as a function.
A function's range and domain are always specified.
The x and y values are:
-6 -34
-5 3
-4 -10
-3 -11
-2 -6
-1 -1
0 -2
1 -15
It is necessary to identify the range of x-values across which the function increases.
The function is not rising in this interval, hence the first option is (-6, -3).
The function is rising in this range, hence the second alternative is (-3, -1).
The function is not rising in this interval, hence the third alternative is (-3, 0).
The function is not rising in this period, hence the fourth alternative is (-6, -5).
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PLSS heLP on my math
16. A snack mix contains toasted oat cereal,
pretzels, and nuts in a ratio of 2:2:1 by
mass. What mass of each ingredient is
needed to make the following amounts of
snack mix?
a) 330 g
b) 210 g
c) 500 g
d) 750 g
The mass of ingredient is given by 66g, 45g, 100g, 150g.
What is mass?
Mass is a parameter of measurement that calculates how much matter is contained in a body.
Mass is a physical quantity. Mass is measured in terms of the weight of a body. Gram, kilogram, and pounds are some standard mass units to measure it. The SI unit of mass is the kilogram; however, smaller objects are measured in grams.
Given, the ratio of the ingredients by mass as 2:2:1.
Let x be the mass of the ingredients.
A) total mass is given by 330g
therefore, 2x+2x+1x = 330
5x = 330
x = 330/5
x = 66
Hence the mass of oat = 2(66) = 132g
mass of cereal = 2(66) = 132 g
mass of nuts = 66g
B) 2x+2x+1x = 210
5x = 210
x = 210/5
x = 42g
Hence, the mass of oat = 2(42) = 84g
mass of cereal = 2(42) = 84 g
mass of nuts = 84
C) 2x+2x+1 = 500
5x = 500
x = 100
hence, the mass of oat = 2(100) = 200g
mass of cereal = 2(100) = 200 g
mass of nuts = 100g
D) 2x+2x+1 = 750g
5x = 750
x = 750/5
x = 150
Hence, the mass of oat = 2(150) = 300g
mass of cereal = 2(150) = 300 g
mass of nuts = 150g
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A scientist is experimenting on a newly discovered virus. The ideal
temperature for this new virus to thrive is 20°C. The temperature can
vary by 15°C and the virus can still survive.
Write an absolute value linear inequality that represents the
acceptable temperatures for this virus to survive. Use t as your
variable.
The required absolute value linear inequality is 15 ≤ t ≤ 20.
What is absolute value linear inequality?
A variable enclosed by the absolute value sign of an inequality is known as an absolute value inequality.
Given highest temperature as 20°C and lowest temperature as 15°C
Given variable is t.
From the first condition we get t ≤ 20 ...........(1)
From the second condition we get 15 ≤ t .....(2)
From the inequalities (1) and (2), we get
15 ≤ t ≤ 20
Therefore, the required absolute value linear inequality is 15 ≤ t ≤ 20.
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Tell whether x and y are proportional x: 4,6,12,16 y: 6,8,16,20
Check the picture below.
What is the length of segment BC? (4 points) A coordinate plane is shown. Point B is located at negative 3, negative 2, and point C is located at 0, 2. The points are connected by a line segment. a 4 b 5 c 6 d 7
By means of vector sum and Pythagorean theorem, the line segment BC has a length of 5 units.
What is the length of the line segment?
We find a line segment whose endpoints are known and set on Cartesian plane, the length of the line segment must be found by means of vector sum and Pythagorean theorem. First, determine the vector associated to the line segment:
[tex]\overrightarrow {BC}[/tex] = C(x, y) - B(x, y) = (0, 2) - (- 3, - 2) = (3, 4)
Second, determine the magnitude of the vector derived in the previous step:
BC = √(3² + 4²)
BC = 5
The length of the line segment BC is equal to 5 units.
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factorise the expression (a+b)^2=4
The factored expression of the expression given as (a + b)^2 = 4 is (a + b + 2)(a + b - 2) = 0
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to factor the expression?The expression is given as
(a + b)^2 = 4
Express 4 as 2^2
So, we have
(a + b)^2 = 2^2
Rewrite as
(a + b)^2 - 2^2 = 0
Apply the difference of two squares
So, we have
(a + b + 2)(a + b - 2) = 0
Hence, the equivalent expression of the expression given as (a + b)^2 = 4 when it is factored is (a + b + 2)(a + b - 2) = 0
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The points A, B and C are 3 corners of a rectangle. What are the coordinates of D, the 4th corner?
PLEASE HELP URGENTLY WILL MSRK BRAINLIEST! :D
Answer:
(5,7)
Step-by-step explanation:
Answer:
(5,7)
Step-by-step explanation:
Abscissa of D will be the abscissa of A. A(5,9)
Abscissa of D = 5
Ordinate of D will the ordinate of C. C(8,7).
Ordinate of D = 7
So, D(5,7)
PLEASE I NEED HELPNSMKSJSBW
Check the picture below.
[tex]\stackrel{\measuredangle U}{(3x-4)}~~ + ~~\stackrel{\measuredangle V}{(x+20)}~~ + ~~\stackrel{\measuredangle W}{(6x+6)}~~ = ~~180 \\\\\\ 10x+22=180\implies 10x=158\implies x=\cfrac{158}{10}\implies {\Large \begin{array}{llll} x=\cfrac{79}{5} \end{array}}[/tex]
The function A(t) (70 6t)2 gives the area of the oil slick (in
square meters) t hours after Lindsay first spots it.
a. Find the rate at which the area is growing exactly one hour after
Lindsay first saw it.
b. Express your answer as a derivative.
Answer: Heres your answer! I hope we can be friends!
Step-by-step explanation: The answer for A is the specified rate fro 70+66, which would be 126x2 is 166. B as derivative would be your preference! I hope this helped have a good day!
K-
Assume that random guesses are made for 8 multiple-choice questions on a test with 5 choices for each question, so
that there are n = 8 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct
answers.
Click on the icon to view the binomial probability table.
The probability of no correct answers is
(Round to three decimal places as needed.)
www.
Using the binomial distribution, it is found that:
The probability of no correct answers is 0.1678 = 16.78%.
For each question, there are only two possible outcomes, either it is answered correctly, or it is not. The answer of a question is independent of any other question, thus the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.In the context of this problem, considering the number of questions and the probability of each being answered correctly, the parameters are given as follows:
n = 8, p = 0.2.
The probability of no correct answers is P(X = 0), hence:
P(X = 0) = (0.8)^8 = 0.1678.
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need help y’all pls ♀️
In this Triangle, ΔUVW, UW is extended through point w to point x
∠ WUV = (3x - 4)°
∠ VWX = (6x + 6)°
∠ UVW = (x + 20)°,
the value of x is 5
According to the question, given that
∠ WUV = (3x - 4)°
∠ VWX = (6x + 6)°
∠ UVW = (x + 20)°
because ∠ VWX = ∠ WUV + ∠ UVW
⇒ (6x + 6) = (3x - 4) + (x + 20)
⇒ (6x + 6) = 4x + 16
⇒ 2x = 10
⇒ x = 5
{The sum of triangle's interior angles is 100°}
{The sum of supplementary angles is 180°}
Therefore, In ΔUVW, UW is extended through point w to point x, then the value of x is 5.
The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.
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Please help me Please help me please
Answer:
1. given
2. corresponding angle theorem
3. vertical angle theorem
4. transitive
Step-by-step explanation:
1. it is given because the question supplies the fact at the top above the diagram called "Given:"
2. corresponding angle theorem: "when a line intersects 2 parallel lines, then the corresponding angles in the 2 regions of intersection are congruent" (also look at correspond_screenshot, the first image)
3. vertical angle theorem: "when two straight lines intersect, they form two sets of linear pairs with congruent angles" (also look at vertical_screenshot, the second image)
4. transitive: since we now know <2 ~= <1 ~= <3, we can say <2 ~= <3
("If any segments or angles are congruent to the same angle, then they are congruent to each other")
The expression models the final price of a television set with an instant rebate in a state that charges a sales tax. what is the expression that represents the price of the television set after the instant rebate is applied and before the tax is applied? question 4 options: x - 300 0.07x x 0.07x (x - 300)
C x -300 is the expression that represents the price of the television set after the instant rebate is applied and before the tax is applied
We are given that an expression models the final price of television set with an instant rebate in a state that charges a sales tax.
0.07x+(x-300)
The sale tax in on the original price .
We have to find an expression that represents the price of the television set after the instant rebate is applied but before the tax is applied.
Let x be the original price of television.
Instant rebate is subtracted from original price x.
Then , the cost of the television set=x-300
In the given expression 0.07 x is sales tax. where tax is 7 % on the original price x.
Sales tax is added to the price of television set.
Hence, option C is true and answer is C x -300
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Isabelle's family raises honey bees and sells the honey at the farmers' market. To get ready for market day, Isabelle fills 24 equal sized jars with honey. She brings a total of 16 cups of honey to sell at the farmers' market. Use an equation to find the amount of honey each jar holds. To write a fraction, use a slash ( / ) to separate the numerator and denominator. cups
Answer:
2/3
Step-by-step explanation:
The amount of honey each jar holds is 2/3 cups.
Fraction
The fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 5/8 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
Given that:-
Number of equal sized jars filled by Isabelle = 24 jars
Total amount of honey brought by Isabelle to the sell at the farmer's market = 16 cups
We have to find the amount of honey each jar holds.
From the data given in the question, we can write,
24 jars = 16 cups
Hence, using the equation, we can write the fraction,
1 jar = (16/24) cups
1 jar = 2/3 cups
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