Answer:
4/8
Step-by-step explanation:
15 1/8 - 1/2(4/8) = 14 5/8
Horizontal stadia sights. Determine the error in distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight
The error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
Tan(θ) = Perpendicular/Base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given the uppermost portion of a that is 3.0m long stadia rod is inclined 14 cm toward the observer, therefore, the angle of inclination, θ can be written as
tan(θ)=0.14/3
θ = 2.672°
Also, the rod intercept is 1.75m, therefore, t the error in distance in the distance is,
tanθ=x/1.75
x = 1.75 tan(θ)
x = 1.75 × tan(2.672°)
x = 0.08167 m = 8.167 cm
Hence, the error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
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55. a rubber ball is dropped from a height of 60 feet. if it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.
The required total distance the ball travels, approximately, is 180 feet.
Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).
The first fall distance (a) is 60 feet.
The first rebound distance (r) is (2/3) * 60 feet.
The total distance covered during the first fall and rebound cycle is:
60 + (2/3) * 60 = 60 + 40 = 100 feet.
Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:
Second fall distance = r * a
= (2/3) * 60
= 40 feet.
Second rebound distance = r*(2/3) * 60
= (2/3) * 40
= 80/3 feet.
The total distance covered during the second fall and rebound cycle is:
40 + (80/3) ≈ 66.67 feet.
The pattern will continue for the subsequent cycles.
To represent this as an infinite geometric series, we can write:
Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]
Where:
a = 60 feet (height of the first fall)
r = 2/3 (rebound factor)
Using the formula for the sum of an infinite geometric series:
Total distance = a / (1 - r)
Total distance = 60 / (1 - 2/3)
Total distance = 60 / (1/3)
Total distance = 60 * 3
Total distance = 180 feet.
Therefore, the total distance the ball travels, approximately, is 180 feet.
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solution for -2 1/3 divided by 4 2/3
Answer:
-0.5
Step-by-step explanation:
: The proliferation of the Internet has given rise to a new method of advertising, called spamming, that essentially is a more cost-effective method of the telephone solicitation method known as cold calling. If a company buys three mailing lists with 2,500, 3,500, and 4,000 email addresses respectively and spams them with promotional material, how many potential customers has it reached?
The number of potential customers that the company has reached is 10,000 e--mail addresses.
What is a word problem in mathematics?A word problem is a real-life problem and it can be approached with the use of a mathematical model, interpretation into variables, and arithmetic operations usage.
Given that:
A company buys three mailing lists with 2500, 3500, and 4000 addresses respectively.The number of potential customers that the company has reached is:
= 2500 3500 + 4000 e--mail addresses.
= 10,000 e--mail addresses.
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The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
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Ms. Stewart teaches three science classes. Her students are freshmen and
sophomores. Her student data are shown in the relative frequency table.
Which statement is false?
The statement that is false is 15% of her students are in biology, the correct option is A.
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n
List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of X_i and Y_j (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
We are given that;
The relative frequency table
Now,
This is because the relative frequency table shows that 0.15 of her students are freshmen in biology and 0.2 of her students are sophomores in biology. Therefore, the total percentage of her students in biology is 0.15 + 0.2 = 0.35, which is 35%, not 15%.
The other statements are true based on the relative frequency table.
Therefore, by the two-way table the answer will be 15% of her students are in biology.
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Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!
WILL MARK BRAINLIEST FOR WHOEVER ANSWERS THIS !!! :DD
Answer:
0.25m or 1/4m
Step-by-step explanation:
Given Height of Dorsal Fin = 1/6 of Length of whale Sculpture,
and given length of whale sculpture = 1.5m or [tex]1\frac{1}{2} m\\[/tex]
Height of Dorsal fin on scuplture = [tex](\frac{1}{6})(1\frac{1}{2} )\\[/tex]
= [tex](\frac{1}{6} )(\frac{3}{2}) \\= \frac{3}{12} \\= \frac{1}{4}m or 0.25m[/tex]
Read the excerpt from Black Boy.
The boys scattered, yelling, nursing their heads, staring at
me in utter disbelief. They had never seen such frenzy. I
stood panting, egging them on, taunting them to come on
and fight.
What is the connotative meaning of frenzy as it is used in this
excerpt?
-Negative; it describes a violent reaction based on
rage.
-Positive; it develops a sense of excitement.
-Negative; it suggests a complete mental breakdown.
-Positive; it emphasizes strength and courage
Answer:
Negative; it describes a violent reaction based on rage.
Step-by-step explanation:
My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
Find the length of the third side. If necessary, write in simplest radical form.
[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}[/tex]
Which measure is of an angle that is coterminal with a 425° angle?
425° – (1,000n)°, for any integer n
425° – (840n)°, for any integer n
425° + (960n)°, for any integer n
425° + (1,440n)°, for any integer n
The measure of angle that is coterminal with 425° is 425° + (1440n)°
What are coterminal angles?Coterminal angles are angles in multiples of the angles in standard positions examples(360°).
It is mostly gotten by adding 360° or multiples of 360 to the angle.
One of the unique behavior of coterminal angles is that their sine, cosine and tangent are equal.
Analysis:
From the options, the only one with an addition of 360 or multiples of 360 is 425 + 1440n
If we put n = 1, the coterminal angle gotten is 1865.
if we find the sine of 425°, we get 0.9063 which is same as the sine of 1865°.
In conclusion, the coterminal angle to 425° is 425° + (1440n)°.
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Answer:
B. 425° – (840n)°, for any integer n
DOES the given value make the inequalities true? x + 9 > 21, when x = 15?
Answer:
Yes.
Step-by-step explanation:
When [tex]x=15[/tex],
[tex]x+9=15+9=24 > 21[/tex].
Answer:
Yes this is true
Step-by-step explanation:
24 is greater than 21; which means this statement is always true.
What is the partial fraction decomposition, I know D is wrong
[tex]\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}[/tex]
For f(x) = 2x+1 and g(x)=x^2-7, find (f+ g)(x).
OA. 2x²-15
OB.x²+2x-6
OC. 2x³-6
OD. x²+2x+8
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 ← in standard form
The value of (f + g)(x) is x² + 2x - 6.
What are arithmetical operations?Arithmetic operations are a set of four basic operations to be performed to add, subtract, multiply or divide two or more quantities. They include the study of numbers including order of operations which are useful in all the other parts of mathematics such as algebra, data handling, and geometry.
Given are two functions, f(x) = 2x+1 and g(x) = x²-7, we are asked to find
(f + g)(x),
So we know,
(f + g)(x) = f(x) + g(x)
Therefore,
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7
= x² + 2x - 6
Hence the value of (f + g)(x) is x² + 2x - 6.
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Simplify (8z - 10) ÷ (-2) + 5(z - 1).
OZ
OZ-1
Oz-2
Answer:
A) z
Step-by-step explanation:
(8z - 10) ÷ (-2) + 5(z - 1)
1. Rewrite:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+5(z-1)$}[/tex]
2. Distribute 5
[tex]\large \textsf{$5(z-1)$}\\\\\large \textsf{$5(z)+5(-1)$}\\\\\large \textsf{$5z-5$}[/tex]
Now we have:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}[/tex]
3. Reduce the fraction:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}\\\\\large \textsf{$-4x+5+5z-5$}[/tex]
4. Combine like terms:
[tex]\large \textsf{$-4x+5+5z-5$}=\large \textsf{z}[/tex]
Final answer: z
Hope this helps!
A family wants to make a 20% downpayment on a house that costs $20,000, which of the amount is the downpayment?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 20000}}{\left( \cfrac{20}{100} \right)20000}\implies 4000\qquad \impliedby downpayment[/tex]
Toni participates in a 10-mile charity walk. For each mile she walks, a sponsor will donate $9 to the charity. The graph represents the function that models the amount of money the sponsor will donate given the number of miles, x, Toni walks. what is the domain of the fuction
The domain of the function when Toni participates in a 10-mile charity walk will be [0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90]
What is a function?It should be noted that a function simply means a relation that's used to express a variable with another variable.
In this case, it should be noted that a domain simply means the set of possible values of the independent variable. The function here is 9x. The domain is all x-values or inputs of a function. Therefore, the domain is depicted above.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the resulting values to the corresponding limits.
The correct solution to the limits of x in the tiles can be seen below.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex][tex]\mathbf{ = -\dfrac{1}{52} }[/tex][tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex][tex]\mathbf{=\dfrac{1}{79} }[/tex][tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]= -31 [tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex][tex]\mathbf{ =\dfrac{1}{98}}[/tex]What are the corresponding limits of x?The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.
From the given diagram, we have:
1.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex]
So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }[/tex]
Simplifying the quadratic equation, we have:
[tex]\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }[/tex]
Replacing the value of x = 9
[tex]\mathbf{ = (-\dfrac{1}{9+43}) }[/tex]
[tex]\mathbf{ = -\dfrac{1}{52} }[/tex]
2.
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex]
-x²-63x+568 is positive when x → 8⁻.Thus |-x²-63x+568| = -x²-63x+568
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }[/tex]
[tex]\mathbf{=\dfrac{1}{8+71} }[/tex]
[tex]\mathbf{=\dfrac{1}{79} }[/tex]
3.
[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]
x -7 is positive, therefore |x-7| = x - 7[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-x-24)}[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-7-24)}[/tex]
= -31
4.
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex]
x-6 is negative when x → 6⁻. Therefore, |x-6| = -x + 6[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }[/tex]
[tex]\mathbf{ =\dfrac{1}{98}}[/tex]
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Meril Starts driving at 14 00
What is the mode: 18,21,22,18,19
Answer:
18
Step-by-step explanation:
Mode = modal class (Recurring)
The number/value that appears the most which in this case is 18 because it can be seen twice.
Bob's living room floor is a rectangle that measures 9 feet by 12 feet. what is the diagonal distance, in feet, across the floor.
Answer:
15
Step-by-step explanation:
For this question you would need to do a squared + b squared so 9x9 is 91 + 12x12 which is 144. you add the two up then find the square root of that which should make your answer 15
Which of the following expressions is equivalent to the one shown below?
OA. 5.-11
OB. (-11)
14
OC.
(-11)
D. (-11)
145
The expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
Indices expressionGiven the expression as shown below
(-11/15)⁵
This expression means that we are to raise the value -11 and 14 raised to the power of 5 individually as shown:
(-11/15)⁵ = (-11)⁵/(15)⁵
Hence the expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
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What is the exact value of x
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
Anyone please help me, deadline is tomorrow.༎ຶ‿༎ຶ wahhhhhhhh huhuhu
mean is average, add all numbers and divide by quantity of numbers.
Median is the middle value, list the numbers from smallest to largest and find the middle number.
mode is the number that appears the most.
1. Mean = 6
Median = 5
Mode = 6
2. Mean = 86.1
Median = 86.5
Mode = 85
Help please thank you
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other. The supplementary angles are 153° and 27°. The Complementary angles are 34° and 56°.
What are Supplementary Angles?When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
What are Complementary Angles?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
The supplementary angles are 153° and 27°.
The Complementary angles are 34° and 56°.
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A car leaves its garage and travels for 30km on a bearing of 145, then 10 km on a bearing of 250 Calculate a) the distance travelled from the starting point b) the bearing of the starting point from the car.
The distance travelled from the starting point is 29 km , the bearing is 344 degree
The missing diagram is attached with the answer.
What is Bearing Angle ?It is the horizontal angle between the object and another object.
It is given that the car starts from point travels for 30km on a bearing of 145, then 10 km on a bearing of 250
(a) the distance travelled from the starting point
It can be understood from the diagram that
To determine the distance , b is to determined4
By applying Cosine rule
b² = a² +c²-2ac cos[tex]\rm \theta[/tex]
b² = 10² +30² - 2* 30*10 cos75
b² = 100+900 -600* 0.2588
b² = 100-155.2914
b² = 844.7
b = 29 km
Therefore the distance travelled from the starting point is 29 km.
(b) the bearing of the starting point from the car.
To determine the bearing ,
angle C has to be determined
By sine rule
sin C / c = sin B / b
sin C = sin 75 * 30 / 29
sin C = 0.9970
C = sin⁻¹ 0.9970
C = 85.59 degree
angle C = α +70 degree
α = 15.59 degree
Bearing = 70 + 20 + 9 0 + 90+74 = 244 degree
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Hurry help
If p is true and ~ q is false, then p -> ~ q is ____ false.
-Sometimes
-Always
-Never
Answer:
Never
Step-by-step explanation:
If p is true and ~ q is false, then p -> ~ q is ____ false
This translates to:
true -> true
So it will never be false.
i need some help doing this
PLEASE HELP I WILL GIVE BRAINLIEST!!
Find an angle in the range between 0 and 2ㅠ radians that is coterminal with
-ㅠ/2
a) 7ㅠ/2
b) 3ㅠ/2
C) 5ㅠ/2
d) ㅠ/2
The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.
How to find a coterminal angle?
For any angle A, all the coterminal angles are of the form:
B = A + n*(2ㅠ).
Where n is an integer different than zero.
In this case, the angle is A = -ㅠ/2
So the coterminal angles are of the form:
B = -ㅠ/2 + n*(2ㅠ)
We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:
B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2
Then we can conclude that the correct option is b.
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Omg I can't work this one out, help!!
You can also check whether I did wrong on the other ones but help me on the last question
Answer:
a) 26 tickets
b) £5
c) chips, pastie and a soft drink
Step-by-step explanation:
Given:
Price of one ticket = £7.50Total available to spend = £200Part (a)
Greatest number of tickets = total available to spend ÷ cost of one ticket
= 200 ÷ 7.5
= 26.66666...
= 26 tickets
(We can't round up, as 27 tickets would cost £202.50)
Part (b)
Money left = Total available spend - cost of 26 tickets
= 200 - (26 × 7.50)
= 200 - 195
= £5
Part (c)
Cost of 3 items = £10 - change
= £10 - £4.70
= £5.30
One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.
If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.
Pastie + Soft Drink = £1.60 + £1.30 = £2.90
So he can buy: chips, pastie and a soft drink