The length of the side a is 112.1664 cm.
What is Law of sines?The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides or the opposing angles.
The Law of sines;
Sin A / a = Sin B / b = Sin C/ c
Here, we have two angles 35° and 25° and a side b = 5 ft
Now, sin35°/5 = sin25°/a
a = (0.42) x 5 / (0.57)
a = 3.68
Now the length in feet is 3.68 cm.
Therefore, the length of the side a is 112.1664 cm.
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i need hepl with all of this
The equivalent linear equation to the line 3x + 4y = 15 is the one in the first option:
y = (15 - 3x)/4
Which equation is equivalent to the given one?
Here we have the following linear equation:
3x + 4y = 15
And we want to find an equivalent linear equation where y is isolated in the left side of the equation. So let's isolate the variable.
If we subtract 3x in both sides of the linear equation we will get:
3x + 4y - 3x = 15 - 3x
4y = 15 - 3x
Now we can divide both sides by 4, so we will get:
4y/4 = (15 - 3x)/4
y = (15 - 3x)/4
This is the equation in option 1, so we conclude that the correct option is the first one.
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The temperature Thursday morning was 78 degrees . If the temperature rose 13 degrees by noon, what was the new temperature
The new temperature is 91 degrees, if the temperature is raised by 13 degrees.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The temperature Thursday morning was 78 degrees
If the temperature rose 13 degrees by noon,
We need to find the new temperature
Temperature rose 13 degrees by noon means thirteen degrees is increased by 78.
78 degrees + 13 degrees
91 degrees.
Hence, the new temperature is 91 degrees, if the temperature is raised by 13 degrees.
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Can someone pls im begging help me with this!!
Answer:
31
Step-by-step explanation:
here's the answer :)
Answer:
thnx needed the answer!!
I got it wrong again >:(
find the z score that has 70.54% of the distribution area to its right
The z score that has 70.54% of the distribution area is 9.92
What is a z-score?The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.
For the random variable x, the z-score is;
z = (x - 11)/2
therefore, 70.54% of the area under the curve lies to the right of x,
then the area to the left of x is;
100 - 70.54 = 29.46%
From the standard table, a z-score of -0.54 will yield an area of 29.46% to the left of x.
Therefore, we get;
(x - 11)/2 = -0.54
x - 11 = -0.54(2)
x = 9.92
The z score is 9.92
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Multiply the complex numbers: (1∕2 + 4i)2
Question 18 options:
A) –153∕4 + 8i
B) 153∕4 + 4i
C) 153∕4 + 8i
D) –153∕4 + 4i
Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².
Define complex numbers.Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.
Given,
Complex numbers:;
(1/2 + 4i)²
(a +b )² = a² + b² + 2ab
Multiplying,
(1/2)² + (4i)² + 2(1/2)(4i)
1/4 + 16i² + 4i
i² = -1
1 - 64/4 + 4i
-63/4 + 4i
Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².
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your family is traveling to canada for vacation. you have saved $212 to take for spending money. if 25 canadian dollars is equivalent to $20.08 US dollars, how many canadian dollars will your 212 US dollars become
The number of Canadian dollars your 212 US dollars became is 264.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, you have saved $212 to take for spending money in vacation.
Here, 25 Canadian dollars is equivalent to $20.08 US dollars
Now, number of US dollars = 212/20.08
= 10.56
So, 25 Canadian dollars = 25× The number of US dollars
= 25×10.56
= 264 Canadian dollars
Therefore, the number of Canadian dollars your 212 US dollars became is 264.
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Question 7(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a right triangle.
O5, 12, 13
07, 15, 20
O 5, 8, 14
O 6, 7, 8
Answer: 5, 12, 13
Step-by-step explanation:
the first one
THE FORMULA
a^2 + b^2 = c^2
5^2 + 12^2 = 13^2
5^2 = 25
12^2 = 144
13^2 = 169
IS IT CORRECT???
yes
169-144=25!
Jake had of a cake. He gave
6
2
4
of it to his friend at lunch. How
much more cake does Jake have
left?
Answer:
12 Pieces left!
Step-by-step explanation:
Because, Look. 6 is 1 quarter, He gave some of his other friends less.
If you add 2 + 4, thats 6! 6 is 1 quarter. There is 4 quarters in a cake. SO 6 + 6 12, thats half of a quarter. And then he gets the other half! Good luck!
(24 pieces in his cake)
Fill in the table using this function rule. y=3x+5
The complete table of values of the equation y = 3x + 5 is
x = -2, -1, 0, 1 2
y = -1 2 5 8 11
How to complete the table of values?The complete question is added at the end of this solution
From the question, we have the following equation that can be used in our computation:
y = 3x + 5
From the table of values added at the end of this question, we have the following x values
x = -2, -1, 0, 1 and 2
Substitute x = -2, -1, 0, 1 and 2 in y = 3x + 5
So, we have the following representation
y = 3(-2) + 5 = -1
y = 3(-1) + 5 = 2
y = 3(0) + 5 = 5
y = 3(1) + 5 = 8
y = 3(2) + 5 = 11
So, the complete table of values is
x = -2, -1, 0, 1 2
y = -1 2 5 8 11
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A certain model of a solar panel produces 1,200 KW of power for an area of one square meter,2,400 KW of power for an area of two square meters,and 3,600 KW of power for three square meters. Determine if the amount of power y the solar panel can produce is proportional to the size of x.Then graph.
The amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given data:
A certain model of a solar panel produces 1,200 KW of power for an area of one square meter,2,400 KW of power for an area of two square meters, and 3,600 KW of power for three square meters,
As you can see from the above, the power is linearly dependent on the area, and it can be seen by the following equation,
y = 1200x
Here, y = power and x = area,
Therefore, the amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.
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PLS HELP IM GETTING ABUSED ): 50 POINTS
These items are all on sale with one-third off. What was the full price of each?
Sale price: Original full price:
£32.24 £_________
£86.08 £_________
£105.48 £_________
£230.62 £___________
The full price when the sales price is ;
£32.24 = £96.72
£86.08 is £258.24
£105.48 is £316.44
£230.62 is £691.86
What are the full prices?The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.
Full price = sales price x 3
Full price when the sales price is £32.24 would be;
= 3 x £32.24
= £96.72
Full price when the sales price is £86.08 would be;
= 3 x £86.08 = £258.24
Full price when the sales price is £105.48 would be;
= 3 x £105.48 = £316.44
Full price when the sales price is £230.62 would be;
= 3 x £230.62 = £691.86
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Please help with this!!! Multiply 6x5 7/8
Answer:
35 and 1/4
Step-by-step explanation:
6x47/8
6/1x47/8
282/8
35 1/4 or 35.25
Colleen is searching online for airline tickets.Two weeks ago, the cost to fly. The from Boston to Orlando was $225.Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 Baggage fee with the new ticket price?
Answer:
15
Step-by-step explanation:
The graphs of f(x)= x³ + x² - 6x and g(x) = e^x-3-1 have which of the following features in common?
A. Range
B. X-intercept
C. Y-intercept
D. End behavior
Answer: Range
Step-by-step explanation:
The area of a rectuangular mirror is 10 5/16 square feet. The width of the mirror is 2 3/4 feet. If there is a 4 foot tall space on the wall to hang the mirror will it fit?
The length of the mirror is [tex]3\frac{2}{33}[/tex] feet so it can fit into a wall of 4 feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, The area of a rectangular mirror is [tex]10\frac{5}{6}[/tex] square feet.
The width of the mirror is [tex]2\frac{3}{4}[/tex] feet and assuming the length to be x feet.
∴ (11/4)×x = 65/6.
x = (65/6)×(4/11).
x = 260/66.
x = 130/33.
x = [tex]3\frac{2}{33}[/tex] feet so the mirror can fit in the wall as it is less than 4 feet.
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Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
The slope of the line in the graph is 2/3.
What is a slope?In general, the slope of a line indicates its steepness and direction. The slope of a straight line between two points, say (x1,y1) and (x2,y2), can be easily calculated by subtracting the coordinates of the points. The letter 'm' is commonly used to represent the slope.A line's slope is defined as
Slope = Rise / Run
Can also be written as,
slope(m) = y2 - y1 / x2 - x1
Choose any two points on the line, such as A and B.
It is clear from the graph below that
Rise = y Change = -3-(-1) = -2
Run = x Change = 1 - 4 = -3
In the above formula, substitute these values.
Slope = -2 / -3
= 2/3
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Can somebody help me on this? I thought I got it but then it didn’t turn out as I expected.
Answer: z=34 degrees
Step-by-step explanation:
the total angle of a triangle always adds up to 180
180=44+2z+2z
combine like terms
4z+44=180
4z+44-44=180-44
4z=136
z=34
Men's heights are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, while women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.
(a) What percentage of men must duck when walking through a door that is 72 inches high?
(b) What percentage of women must duck when walking through a door that is 70 inches high?
(c) What door height would allow at least 95% of men to walk through the door without ducking?
Approximately 95% of men must duck when walking through a door that is 72 inches high. Approximately 5% of women must duck when walking through the door. The door height that would allow at least 95% of men to walk through the door without ducking is 74 inches.
The mean height of men is 69.0 inches and the standard deviation is 2.8 inches, while the mean height of women is 63.6 inches and the standard deviation is 2.5 inches.
(a) To find the percentage of men who must duck when walking through a door that is 72 inches high, we first need to find the percentage of men whose height is less than 72 inches.
The height of the door is 72 inches, which is 3 inches above the mean height of men.
Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.
Therefore, approximately 95% of men are between 69.0 - 5.6 = 63.4 inches and 69.0 + 5.6 = 74.6 inches tall.
If the height of the door is 72 inches, approximately 95% of men must duck when walking through the door.
(b) To find the percentage of women who must duck when walking through a door that is 70 inches high, we first need to find the percentage of women whose height is less than 70 inches.
The height of the door is 70 inches, which is 6.4 inches above the mean height of women.
Since the standard deviation is 2.5 inches, this means that approximately 95% of women are within 2.5 * 2 = 5 inches of the mean height. Therefore, approximately 95% of women are between 63.6 - 5 = 58.6 inches and 63.6 + 5 = 68.6 inches tall.
If the height of the door is 70 inches, approximately 5% of women must duck when walking through the door.
(c) To find the door height that would allow at least 95% of men to walk through the door without ducking, we need to find the height that is within 2 standard deviations of the mean height of men.
Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.
Therefore, the door height that would allow at least 95% of men to walk through the door without ducking is 69.0 + 5.6 = 74
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find the value of a + 4 when a = 13
Answer:
17
Step-by-step explanation:
13 + 4 = 17
Determining the Value of an Unknown
What is the value of n in the equation --(2n + 4) + 6 = -9 + 4(2n + 1)?
The value of n in the given equation is 1.
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given equation,
-1/2 (2n + 4) + 6 = -9 + 4(2n + 1)
Now, solve for n
first, solve the brackets
-1/2 * 2n + (-1/2) * 4 + 6 = -9 + 4*2n + 4 * 1
-n - 2 + 6 = -9 + 8n + 4
Solve the constants on both the sides,
-n + 4 = 8n - 5
Now, take out n value one side and constant terms other side
-n - 8n = -5 - 4
-9n = -9
Cancel out -9 from both the sides,
n = 1
Hence, the value of n in the given equation is 1.
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Please help me on number 13?
HEEEEEEEP
(b) A certain arcade game gives players tickets. The table below shows the
number of tickets a player gets for the number of points.
Tickets
Points
32
4
56
8
CO
63
9
O Each point does not always give the same number of tickets.
Each point appears to give the same numb of tickets.
Predicted number of tickets for getting 10 point:
Answer:
Step-by-step explanation: Can u show the picture of the table so i can understand this better
What percent of 16x is 4x?
4x is 25 percent of 16x.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Let the percentage be P.
Now,
P% of 16x = 4x
P/100 x 16x = 4x
P/100 = 4x/16x
P/100 = 1/4
P = 100/4
P = 25
This means,
25% of 16x is 4x.
We can cross-check.
= 25% of 16x
= 1/4 x 16x
= 4x
Thus,
25 percent of 16x is 4x.
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Jennifer has 76 inches of string to make bracelets. She uses 8 inches for each bracelet. How many bracelets can she make?
Look at the equation below
y = 2x - 2
Which situation is best described by the situation?
a. The temperature at 2:00 am is 2 degrees celsius and rises 2 degrees each hour for x hours.
b. The temperature at 2:00 am is 2 degrees and rises 2 degrees each hour for x hours.
c. The temperature at 2:00 am is 2 degrees and drops 2 degrees each hour for x hours
d. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours
The situation that is best described by the situation is that D. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.
Which situation is best described by the situation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the equation is given as:
y = 2x - 2.
This illustrates that the temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.
In conclusion, the correct option is D.
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What property is 13(20x5)
Answer: The distributive property
Step-by-step explanation: The distributive property ALWAYS has 1 number that is outside the parentheses. I know you didn't ask for this, but you can use the distributive property to write an equivalent expression by multiplying (or distributing) the 13 by every # inside the parentheses, so your new equation would look like 260 x 65. I hoped this explanation and example help you understand now.
Which one is it?? Pls helpppp
Answer:
6x-3=15
Step-by-step explanation:
what is the value of h if h2=441?
Answer:
[tex]h=\pm 21[/tex]
Step-by-step explanation:
[tex]h^2=441 \implies h=\pm \sqrt{441}=\pm 21[/tex]