Answer:
2/3 + 1/6 + 2/8
=(2×8+1×4+2×3)/24
=(16+4+6)/24
=26/24
=13/12
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Man on cliff observes a boat at angle of depression of 30 which is approaching the shore at uniform speed. 6 minutes later, the angle of depression of boat is 60. Find time taken by boat to reach shore?
Answer:
Step-by-step explanation:
Let the speed be x km/h
Let the time be t
In △ADC,
tan30°=
h
xt
3
1
=
h
xt
h= xt
In △ABD,
tan60°=
h
x(6+t)
h=
x(t+6)
3
xt=
x(t+6)
3t=6+t
t=3 seconds
∴ total time taken=6+3=9 seconds
Decrease 520 by 60%.
Answer:
208
Step-by-step explanation:
60 percent of 520 is 312
520 subtract 312 is 208
Answer:
208
Step-by-step explanation:
(520)-60% of 520
(520)-3×104
520-312
=208
Hope it helps you
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Is 9x2 42x 49 a perfect square trinomial?
No, 9x2 42x 49 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."
No, 9x2 42x 49 is not a perfect square trinomial. A perfect square trinomial is a polynomial of the form a2 + 2ab + b2,
where a and b are numbers or variables.
9x2 42x 49 does not fit this pattern, as it does not involve two terms whose sum is multiplied by itself.
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A report states that of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with confidence
To estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with confidence, a sample size of 384 would be needed.
How big of a sample is required to confidently estimate the true percentage of homeowners having vegetable gardens to within 6 percentage points?This can be calculated using a sample size calculator and the given margin of error and desired confidence level.The size of the sample needed can be calculated using the formula n = (z2 * p * (1-p)) / e2, where n is the size of the sample, z is the z-score associated with the desired confidence level (1.96 for 95% confidence), p is the estimated proportion of home owners having a vegetable garden, and e is the margin of error (6 percentage points).Assuming a conservative estimate of p = 0.50, the sample size needed to estimate the true proportion of home owners having a vegetable garden to within 6 percentage points with 95% confidence is:n = (1.962 * 0.50 * 0.50) / (0.06)2 = 384.9 ≈ 385Therefore, a sample size of 385 home owners is needed to estimate the true proportion of home owners having a vegetable garden to within 6 percentage points with 95% confidence.The equation is: n = (z_alpha/2)^2 * (p*(1-p)) / e^2 Where n is the sample size, z_alpha/2 is the z-score for the desired confidence level (e.g., z = 1.96 for a 95% confidence level), p is the estimated population proportion, and e is the margin of error. For this example, we can assume a 95% confidence level (z = 1.96), a population size of N = 100,000, and a margin of error of 6 percentage points (e = 0.06). Plugging these values into the sample size equation, the required sample size is n = (1.96/2)^2 * (0.5*(1-0.5)) / 0.06^2 This gives us a sample size of n = 384.To learn more about the Theory of Confidence Intervals refer to:
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plsplsplsplsplspls help me
Find the measure of an interior angle of a regular hexagon
Therefore , the solution of the given problem of angles comes out to be
Each inner angle of a regular hexagon measures 120 degrees.
Exactly what angles are there?Two rays that converging at the vertex, or center, of an angular structure in geometry make up the structure. We refer to these rays as the faces of the angle. Two beams may well be able to create any angle within just a planar depending on their location. Additionally, an angle is created when two planes intersect. .
Given: A standard hexagon
Measure each internal angle of a standard hexagon.
Solution:
(n - 2) x 180° is the formula for the sum of lengths of a polygon's inner angles.
Every side of a regular polygon is the same length, and every angle is the same size.
A hexagon has six sides.
Find the total of the measurements of the internal angles of a hexagon by substituting n = 6 in (n - 2) x 180n latitude in step 1.
=> (n - 2) * 180°
=> (6 - 2) * 180°
=>4 * 180°
=> 720°
Step 2: Since a regular hexagon has six sides and all of its sides and angles are equal in size, divide by six to obtain the dimensions of each inner angle.
=> 720° /6
=> 120°
Each internal angle of such a regular polygon is 120 degrees in length.
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Researchers will conduct a year-long investigation of walking and cholesterol levels in adults. They will select a random sample of 100 adults from the target population to participate as subjects in the study. (a) One aspect of the study is to record the number of miles each subject walks per day. The researchers are deciding whether to have subjects wear an activity tracker to record the data or to have subjects keep a daily journal of the miles they walk each day. Describe what bias could be introduced by keeping the daily journal instead of wearing the activity tracker.
(a) - Subjects may enter a false information or data, or mistakes can be done while entering the data.
(b) - The researcher can use the results of the study to make generalization to the entire population.
Bias
A bias can be defined as the tendency of facts to be distorted or subjective rather than being objective. It's a deviation from the facts.
generalization
It is the tendency to respond in the same way to different but similar stimuli.
A representative sample can be defined as a sample drawn from an entire population such that it is a subset of it and has similar characteristics as the population group.
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What is the midpoint formula of quadratic equation?
The midpoint formula of a quadratic equation is given by: x = -b/(2a), where a, b and c are the coefficients of the quadratic equation ax2 + bx + c = 0.
This formula is used to determine the midpoint of the roots of a quadratic equation. It works by taking the coefficients of the equation and plugging them into the formula. The result of the formula will be the x-coordinate of the midpoint of the two roots.
This formula is useful when solving quadratic equations, because it allows us to quickly find the midpoint of the two roots without having to solve for both roots first. It is also useful for graphing the quadratic equation, as it reveals the location of the vertex of the parabola. Knowing the midpoint of the two roots also makes it easier to determine the nature of the roots, whether they are real or imaginary.
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2. Use the Pythagorean Theorem to find x. Show your work!
The value of x using Pythagorean theorem is 14.05 units
What is an equation?An equation shows how two or more numbers and variables are related to each other.
Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:
hypotenuse² = adjacent² + opposite²
In the diagram, using Pythagoras theorem:
22² = (x + 1)² + (x + 2)²
484 = x² + 2x + 1 + (x² + 4x + 4)
2x² + 6x + 5 = 484
2x² + 6x - 479 = 0
x = 14.05
The value of x is 14.05 units
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-x+6=-2(x+2)-5
Solve for x
Answer:
x = -15
Step-by-step explanation:
-x+6=-2(x+2)-5
Solve for x
-x + 6 = -2(x + 2) - 5
-x + 6 = -2x - 4 - 5
x = -15
------------------------
check- (-15) + 6 = -2(-15 + 2) - 5
21 = 21
the answer is goodx = -15
For which values of x does each expression make sense? square root of x-2 over square root of x-3
the answer is x>3
this is the answer becuase x-3 cannot be 0 because tou cant divide by zero and it cant be negative because it is in the square root notation which cant be negative without the use of inaginary numbers
What is the value of the expression shown below?
-28+42-12+(-16) + 7
A.14
B. 7
C.-7
D.-14
The height (h) in meters, of an item d days
can be modeled using the equation, h(d) = 3(5/4)^x
What does the fraction 5/4
represent in this equation?
Therefore, the fraction 5/4 in this equation represents the growth factor of the height of the item over time.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
Define numerator or denominator.The total number of equally sized components chosen is shown in the numerator. The denominator, however, shows the total number of equal pieces.
The fraction 5/4 in this equation represents the growth factor of the height of the item over time. The value of 3 in front of the fraction is the initial height and the exponent x represents the number of days that have passed, so the height of the item increases by a factor of 5/4 for every additional day. The height equation represents exponential growth.
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Equivalent fractions for 1 3/4 and 1 4/5 using 20 as the common denominator
Answer: 1 3/4 = 35/20 and 1 4/5 = 36/20
Step-by-step explanation:
1 3/4 = 7/4
Multiply top and bottom by 5 to get 35/20
1 4/5 = 9/5
Multiply top and bottom by 4 to get 36/20
The length of an object in feet is equal to 3 times it's length in yards. The length of the boat is 36 feet. Write and solve a multiplication equation to find the length of the boat in yards
In linear equation ,The length of waterslide is 12 yards.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given that,
The length of an object object in feet is equal to 3 times it’s length in yards
The length of wall water side slide is 36 feet
Let "y" be the length of object in yards
From given,
Length in feet = 3 times length in yards
36 = 3 * y
3y = 36
y = 36/3
y = 12
Thus length of waterslide is 12 yards.
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A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 98
Tails 102
Determine the experimental probability of landing on heads.
102%
98%
50%
49%
probability of landing on heads - 49 %
Answer:
49%
Step-by-step explanation:
Which statement about the offer are true ? Check all that apply
Answer: The first and third options are correct.
Step-by-step explanation:
GIVEN: An exterior stud wall with brick veneer is 11 ft tall and 40 ft long. 25 % of the area of the wall is windows (glass, frame and sash). FIND: Total weight of the wall and the average dead load in lb/ft of the length of the wall (per foot of wall length) that the wall exerts on the floor.
The total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.
To find the total weight of the wall and the average dead load per foot of wall length, we need to calculate the total area of the wall and the area of the windows, then use that information to determine the weight of the remaining brick veneer.
First, we calculate the total area of the wall by multiplying the length and height:
40 ft * 11 ft = 440 ft²
Next, we calculate the area of the windows by multiplying the total area of the wall by 25% (the percentage of the wall that is windows):
440 ft² * 0.25 = 110 ft²
Now we can find the area of the brick veneer by subtracting the area of the windows from the total area of the wall:
440 ft² - 110 ft² = 330 ft²
To find the weight of the brick veneer, we can assume a weight of 150 lb/ft². We can calculate this by multiplying the area of the brick veneer by the weight per square foot:
330 ft² * 150 lb/ft² = 49,500 lb
Now to find the average dead load in lb/ft of the length of the wall, we divide the total weight of the wall by the total length of the wall:
49500 lb / 40 ft = 1237.5 lb/ft
So the total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.
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(5 points) 2. The coordinates of the vertices of ARST are R(1, 6), S(5, 3), and T(3,-2). Triangle R'S'T' is the image of ARST after a reflection in x = -1. Graph and state the coordinates of the vertices of AR'S'T'.
The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).
The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -
R' (1, -6)
S' (5, -3)
T' (3, 2)
The graph is attached.
Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
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The distance that an object falls varies directly as the square of the time the object is in motion. If an object falls for 3 seconds, it will fall 144. 9 feet. To estimate the height of a cliff, a person drops a stone at the edge of the cliff and measures how long it takes for the stone to reach the base. If it takes 3. 5 seconds, what is the height of the cliff?
As per the given equation the height of the cliff is 196.225 feet.
How to calculate the distance of an object in motion?We know that the distance an object falls varies directly as the square of the time it is in motion, meaning that the distance is proportional to the square of the time. If we let d be the distance fallen and t be the time, we can write this relationship as [tex]d = kt^2[/tex] for some constant of proportionality k.
We also know that when an object falls for 3 seconds, it falls 144.9 feet. We can use this information to find the value of k:
[tex]144.9 = k(3^2)[/tex]
k = 16.1
Now that we know the value of k, we can use it to find the distance fallen when the time is 3.5 seconds:
[tex]d = kt^2\\d = 16.1(3.5^2)\\d = 16.1(12.25)\\d = 196.225[/tex]
So, the height of the cliff is 196.225 feet.
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n% of 400 = 150
please HELLPPP
Answer:
150 of 400 can be written as:
150400To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
150400 × 100100= (150 × 100400) × 1100 = 37.5100Therefore, the answer is 37.5%
If you are using a calculator, simply enter 150÷400×100 which will give you 37.5 as the answer.
sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read
The number of books that Sofia read is 32 books and the brother read 8 books.
How to calculate the number of books read?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, Sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read
Let the number of books read by the brother = x
Number of books read by Sofia = 4x
Therefore, x + 4x = 40
5x = 40.
Divide
x = 40 / 5
x = 8
The brother read 8 books
Sofia read = 4x
= 4 × 8
= 32 books.
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please help me with this!!
Answer: The answer is no, they are not proportional
Step-by-step explanation:
Let, third proportional is x 0.8 : 0.2 : : 0.2 : x = 0.8/0.2 = 0.2/x = x = 0.2 × 0.2/0.8 × 10 = 1/20 = 0.05 Hence, here third proportional is 0.05
The quadrilaterals ABCD and JKLM are similar.
Find the length x of JK.
B
K
A
U
S
3. 5
2. 1
3
M
2. 1 L
D
3
c
X
0
X 5 ?
The length x of JK is 3.6 units
Here, quadrilaterals ABCD and JKLM are similar.
We know that the corresponding sides of similar triangles are in proportion.
So, by definition of similar triangles,
AB/JK = BC/KL = CD/LM = AD/JM
To find: the length x of JK
So, consider an equation
AB/JK = AD/JM
Substitute the length of each side in above equation.
4/x = 2/1.8
(4 × 1.8)/x = 2
(4 × 1.8)/2 = x
x = 2 × 1.8
x = 3.6
Therefore, the length of JK = 3.6 units
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Tracy took a test and had 24 questions. She got 5/6 of the questions correct. How many questions did she answer correctly? Write an equation to model your work
Tracy got 20 questions correct in her test.
Tracy took a test in which there are 24 questions, out of which Tracy got 5/6 correct.
Hence he got 24 x 5/6 = 20 questions correct.
An equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign.
So ,an equation to model this would be:
x = 24 x 5/6
where x is the number of questions tracy answered correctly.
Hence Tracy answered 20 questions correctly.
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28 = 4/5x - 8 what value of x makes the equation true?
Answer:
1.6285
Step-by-step explanation:
28 = 4/5x-8
Cross multiply
140x-224=4
140x =224+4
140x = 228
x = 228/140
x = 1.6285
12[6.3+3(1.9)] what comes first
The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ 12 × [6.3 + 3 × (1.9)]
Simplify the numerical expression, then we have
⇒ 12 × [6.3 + 3 × (1.9)]
⇒ 12 × [6.3 + 5.7]
⇒ 12 × 12
⇒ 144
The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.
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Jackson picked apples for his family. He picked a total of 6 pounds. He took 2
3
4
pounds to his aunt and 1
7
8
pounds to his mother. How many pounds of apples were left to give to his grandmother? Use the numbers and symbols to write an equation that represents the problem, then solve the equation. Symbols may be used more than once or not at all.
2
3
4
1
7
8
6 y + =
PLEASE HELPPPPPPPP
"17/8" pounds of apples were left to give to his grandmother.
Since we have given that
The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.
The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.
The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.
So, the total quantity left for his grandmother is given by
first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.
After subtracting from what he picked.
⇒13/2-(11/4+13/8)
⇒13/2-(22+13/8)
⇒13/2-(35/8)
⇒52-35/8
⇒17/8
Hence, 17/8 pounds are left for his grandmother.
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Qasim is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Qasim have to pay for parking if he left his car in the lot for 6 hours? How much would Qasim have to pay if he left his car in the lot for t hours?
Answer:
23; 11 + 2t
Step-by-step explanation:
So let's start with the equation and then plug in the 6 hours:
Because we start with 11 dollars just to enter, our equation would start like this:
11 +
Also, 2 dollars for every hour. One hour could be represented as 1t, or just t:
11 + 2t (2 dollars for every t, every hour)
So now the equation is 11 dollars starting entry plus 2 dollars every hour
Now all we have to do is replace t with the number of hours:
11 + 2(6) = answer
11 + 12 = answer
23 = answer
A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of cards in each suit. Rochelle chooses a card from the deck, records the suit, and replaces the card. Her results are shown in the table. Cards Suit Observed Frequency Clubs 29 Spades 13 Hearts 15 Diamonds 23 How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart
The theoretical likelihood of selecting a heart is 1/16 times higher than the actual likelihood.
In the given question, we have to find the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart.
We are aware that a deck's total number of cards= 52
Total number of hearts = 13
Then the theoretical probability of getting a heart = Number of cards have hearts/Total cards
Then the theoretical probability of getting a heart = 13/52
Then the theoretical probability of getting a heart = 1/4
Then the theoretical probability of getting a heart = 0.25
Cards chosen by Rochelle : Clubs 29, Spades 13, Hearts 15, Diamonds 23
Total cards = 80
The experimental likelihood of experiencing a heart attack = Number of cards have hearts/Total cards
The experimental likelihood of experiencing a heart attack = 15/80
The experimental likelihood of experiencing a heart attack = 3/16
The experimental likelihood of experiencing a heart attack = 0.185
Since, 0.25 > 0.1875 so, Theoretical probability > Experimental probability
and,
Theoretical probability = 0.25-0.1875
Theoretical probability = 0.0625
Theoretical probability = 625/10000
Theoretical probability = 1/16
Hence, the theoretical likelihood of selecting a heart is 1/16 times higher than the actual likelihood.
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Audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (–1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The reasonable solutions for this situation is (1, 3.5) and (2, 2)
What is Graph?A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.
Audrey has x pounds of red grapes and y pounds of green grapes.
She has less than 5 pounds of grapes in all, hence:
x + y < 5
Also, x ≥ 0, y ≥ 0
a) The option (–1, 2) is wrong because x = -1 < 0
b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5
c) The option (2, 2) is correct because 2 + 2 = 4 < 5
d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.
e) The option (5, 0) is wrong because 5 + 0 is not less than 5
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