Answers
Answer:
8.7cm
Step-by-step explanation:
Pythagorean TheoremPythagoras' Theorem deals with right triangles.
In a right triangle, the triangle has one right angle. The two sides of the triangle that are adjacent to the right angle are called legs, and the side across from the right angle is called a hypotenuse.
Pythagoras' Theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse:
\(LegOne^2+LegTwo^2=Hypotenuse^2\)
Recall that addition obeys the commutative property, meaning that 1+2 is the same as 2+1. This means that the side of the equation could be written as follows:
\(LegTwo^2+LegOne^2=Hypotenuse^2\)
In other words, it doesn't matter which leg we call LegOne, and which leg we call LegTwo (but the Hypotenuse must be the side across from the right angle)
In the equation, the two legs are often simply labeled "a" & "b". Paired with the hypotenuse (often labeled "c"), the equation becomes:
\(a^2+b^2=c^2\)
Finding the Right TriangleObserve that the red diagonal line, EG, cuts the rectangle into two congruent right-triangles (DEG & FGE). As the question asks us to find the length of the diagonal, and the Pythagorean Theorem uses a right triangle (not a rectangle), we'll need to focus on just on one of those two right triangles (there isn't an easy/hard one... it's the same process. I chose to focus on triangle FGE). Simultaneously, while focusing on that one triangle, we'll need to think about the properties of the rectangle as a whole.
Using the rectangle to find the parts of the triangleNote that by definition, the rectangle has 4 congruent angles that are all right angles. Hence, angle F is a right angle, and thus triangle FGE is a right triangle (so we can apply the Pythagorean Theorem).
Since angle F is the right angle, EG is the Hypotenuse. The other two sides, FG and EF, are the legs.
In the diagram, we're given the length of leg FG.
Recall that rectangles are parallelograms, and consequently rectangles have two pairs of opposite congruent sides (the top and the bottom sides are the same length, and the left and the right sides are the same length). Hence, side EF also has a length of 6cm.
Using Pythagoras' TheoremWe can now begin by substituting known values into the equation, and then solving for the unknown:
\((6.3cm)^2+(6cm)^2=c^2\\39.69cm^2+36cm^2=c^2\\75.69cm^2=c^2\)
To solve for c, we would need to apply the Square Root Property.
Square Root Property: If \(x^2=p\), then \(x=\sqrt{p}\) or \(x=-\sqrt{p}\)
While the Square Root Property yields two separate answers (one positive; one negative), accepting that lengths of triangles are generally considered to be positive values, we exclude the negative result:
\(\sqrt{75.69cm^2}=c \\8.7cm=c\)
Note the final result is already rounded to 1 d.p., as requested by the question.
Related Questions
Applications of the Normal Distribution. It turns out that the height (or maximum thickness) of the Blacklip abalones can be modeled very well by a Normal Distribution with mean of 15.4 mm and a standard deviation of 3.7 mm. You are sampling samples of size 20 from this population. You want to calculate the probability that the mean of a sample of size 20 will be 12mm or less. Your first step is to calculate a z- test statistic. What the standard deviation used in this calculation be? Show your calculations on your "scratch paper." Later, check that paper against the feedback information. Here enter your standard deviation value rounded to two decimal places.
Answers
To calculate the z-test statistic, we need to use the standard deviation of the sampling distribution of the sample mean.
The standard deviation of the sampling distribution of the sample mean (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size.
Given that the population standard deviation is 3.7 mm and the sample size is 20, we can calculate the standard deviation of the sampling distribution as follows:
Standard deviation = 3.7 / sqrt(20) ≈ 0.827
Rounding to two decimal places, the standard deviation used in this calculation is 0.83.
Therefore, the standard deviation value is 0.83.
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I need help on this one problem, honestly I've tried this question like 4 times and was all wrong so I don't know. I will send a pic
Answers
Let's use the formula provided:
\(\begin{gathered} A=P(1+r)^t \\ \text{Where:} \\ P=3000 \\ r=0.05 \\ t=4 \\ A=3000(1+0.05)^4 \\ A=3000(1.05)^4 \\ A=3646.51857 \end{gathered}\)Claire i buying 6 pack of index card. Each pack of index card cot $1. 95. The tore where he buy the index card i having a ale in which all item are 20% off. How much doe Claire pend on index card?
Answers
Answer:
2.34
Normally it would be 1.95*6 however since everything is 20% off you need to find 20% of 1.95. You find that by:
Step-by-Solution for What is 20 percent of 1.95: 20 percent *1.95 = (20:100)*1.95 = (20*1.95):100 = 39:100 = 0.39. Now we have 20 percent of 1.95 = 0.39. explanation:
After you find that you multiply it by 6 so it would be 0.39*6 which equals 2.34. I hope this helped! :)
Help 69 points
36 - 7p = -7 ( p - 5)
a) No Solution
b) One Solution
c) Infinite Solutions
Answers
Answer:
a) No Solution
Step-by-step explanation:
36 - 7p = -7(p - 5)
36 - 7p = -7p + 35
1 - 7p = -7p
1 = 0p
so a) No Solution
Answer:
\(36 - 7p = - 7(p - 5) \\ 36 - 7p = - 7p - 7 \times - 5 \\36 - 7p = - 7p + 35 \\ p \: terms \: togather \\ - 7p + 7p = 35 - 36 \\ 0p = - 1 \\ here \: we \: \: have \: 0p \\ so \: no \: solution \\ option(a) \\ thank \: you\)
Miranda has 55 feet of fencing. She wants to use all the fencing to create a rectangular garden. The equation 2l+2w=55, where l is the length of the garden and w is the width, models the scenario. This equation can be used to find on dimension of the garden if the other dimension is known. If Miranda makes the garden 17.5 feet long, how wide should she make it? PLEASE HURRY
Answers
2(17.5) + 2(10) = 55
Circumference & Area of Circles: Question 10
In baseball, the next batter waits in the on-deck circle. If the diameter
of the on-deck circle is 5 feet, what is its approximate circumference?
(Urex= 314)
Select one
01571
o
Answers
Answer:
i got 19.625 if you round it you should get either 20 or 19.6
Step-by-step explanation:
if im wrong sorry
need answer fast in 5 minutes
Answers
Answer:
Each term in pattern B is 9 less than the corresponding term in pattern A.
Use interval notation to represent the domain and range of the following functions. Hint: Start by thinking about the meaning of each function's input and output quantities and the values those quantities can assume.
a. Determine the domain and range of the cos function.
。 Domain:
Preview
• Range:
b. Determine the domain and range of the sin
Preview
function.
。 Domain:
Preview
。 Range:
Preview
c. Determine the domain and range of the tan
function.
• Domain:
Preview
。 Range:
Preview
Answers
c) The range of the tangent function is all real numbers. This can be represented as (-∞, ∞) in interval notation
a. The domain of the cosine function (cos) is all real numbers. This can be represented as (-∞, ∞) in interval notation.
The range of the cosine function is [-1, 1]. This can be represented as [-1, 1] in interval notation.
b. The domain of the sine function (sin) is all real numbers. This can be represented as (-∞, ∞) in interval notation.
The range of the sine function is [-1, 1]. This can be represented as [-1, 1] in interval notation.
c. The domain of the tangent function (tan) is all real numbers except the values where the function is undefined, which occur when the input angle is equal to (2k + 1)π/2, where k is an integer. This can be represented as (-∞, (2k + 1)π/2) ∪ ((2k + 1)π/2, ∞) in interval notation.
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thelma and david built a recycling bin with a volume of 576 cubic feet. the bin is a rectangular prism with a base 12 feet long and 6 feet wide. a rectangular box measuring 12 feet by 6 feet by h feet. what is the height, h of the bin?
Answers
The volume of the recycling bin is given as 576 cubic feet. We know that the bin is a rectangular prism with a base of 12 feet by 6 feet. So, we can use the formula for the volume of a rectangular prism to find the height:
Volume of rectangular prism = base area x height
In this case, the base area is 12 feet x 6 feet = 72 square feet. So, we have:
576 cubic feet = 72 square feet x height
Dividing both sides by 72 square feet, we get:
height = 576 cubic feet / 72 square feet
Simplifying this expression, we get:
height = 8 feet
Therefore, the height of the bin is 8 feet.
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A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 6 feet. The portion from a point to a vertical line created by two vertices is 6 feet.
Which of the following represents the total area of the figure?
968 ft2
616 ft2
484 ft2.
352ft2
Answers
Area of figure is 484ft².
Define area of rectangle and triangleThe area of a rectangle is the amount of space that is enclosed by its sides. It is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:
Area = length x width
where "length" refers to the longer side of the rectangle, and "width" refers to the shorter side.
The formula for the area of a triangle is:
Area = (base x height) / 2
where "base" refers to the length of the side of the triangle that is parallel to the ground, and "height" refers to the length of a line that is perpendicular to the base and connects the base to the opposite vertex.
Area of figure=Area of 1st triangular part+ Area of rectangular part+ Area of 2nd triangle
=1/2× 22× 8 + 16 ×22 + 1/2 ×4×22
=88+352+44
=484ft².
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Please help, really confused
Answers
11. The probability is 3/9 or 1/3
12. The probability is also 3/9 or 1/3
13. The probability is 8/9
14. The probability is 4/9
At a fire station in Redding, CA, false alarms are received at a mean rate of .1 per day. In a year, what is the probability that fewer than 25 false alarms are received
Answers
How it works:
mean,u= 0.3
days in a year = 365
For poison distribution mean=variance
u=0.3*365= 109.5
standard deviation=sqrt(variance)=sqrt ( 109.5)= 10.46422477
x= 80
x= [Use Continuity Corrector] 79.5
z-score = (X-μ)/σ=(79.5-109, 5)/10.4642= -2.87
Use Excel command "= norm distance (z)" 0.0021
Probability = number of paths to success. A total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.
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Find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
x = √2
Step-by-step explanation:
Here, we want to get the value of x
As we can see, what we have is a right triangle
x faces the angle 30 which makes it the opposite to that angle
the root of 6 is the adjacent to the angle 30
Mathematically, the ratio of the opposite to the adjacent is the tan
Thus;
Tan 30 = x/√6
Tan 30 = 1/√6
1/√3 = x/√6
x = √6/√3
x = √(6/3)
x = √2
Consider a linear system to
X =[ -5 1] X + [1]
[ -1 -2] [1] u
Y =[3 1] X
Find the transfer function of system.
Answers
Transfer Function of the given system is X(s)/U(s)= (1)/[-s^2 + 3s +7].
Given that a linear system toX =[ -5 1] X + [1][ -1 -2] [1] uY =[3 1]
XTransfer Function: It is a mathematical representation of the relationship between the input and output of the linear system.
Mathematically transfer function is represented as Y(s)/U(s)Where U(s) is Laplace Transform of input and Y(s) is Laplace Transform of output.
Here,X =[ -5 1] X + [1][ -1 -2] [1] u
Taking Laplace Transform on both sides.
sX(s)-x(0)=(-5 1)X(s) + u(s)(1)[ -1 -2] [1]Y(s)=[3 1]X(s)
After rearranging the equation (1),X(s)/U(s)= (1)/[s+5 -1]/[-1 s+2]X(s)/U(s)= (1)/[-s^2 + 3s +7]
So, transfer function is given asX(s)/U(s)= (1)/[-s^2 + 3s +7]
Hence, the detail answer for the given question is as follows.
Transfer Function of the given system is X(s)/U(s)= (1)/[-s^2 + 3s +7].
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What’s the solution for (x,y) ?
Answers
Answer:
(-2,-3)
Step-by-step explanation:
appears from graph that is the point of intersection of both lines
somebody who knows how to do least to greatest please help!!
Answers
the bottom 3 are all positive.
least to greatest order would be
clear lake
lake livingston
lake houston
lake conroe
lake travis
hope this helps :)
what is the average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers? $32.50 $20.00 $16.25 $15.84
Answers
The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).
The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.
It can be written as \(\frac{n_1+n_2+.....+n_a}{a}\).
In the given question, the sum of the customer bill is given as $3,250.
And the number of customers served is given to be 200.
Therefore, the average size of a customer's bill is calculated by \(\frac{3250}{200}\)
Which turns out to be $16.25.
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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.
To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:
1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.
Now, calculate the average bill size:
3. Divide the total daily earnings ($3,250) by the number of customers (200).
$3,250 ÷ 200 = $16.25
The average size of a customer's bill at the restaurant is $16.25.
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Use the number line to answer the question. Each tick represents 1 unit. Where is point H located? -4 7 4 -7
Answers
Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.
What is a numerical data?A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegersWhat is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.
Note: Each of the tick represents 1 unit.
Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.
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If two figures are similar but not congruent, which of the following transformations must have occurred?
O dilation
O reflection
O rotation
o translation
Answers
Answer:
c
Step-by-step explanation:
Ali, ben and Cathy share an amount of money in ratio 6:9:10 what fraction of the money does ben get?
Answers
Answer:
Step-by-step explanation:
Let's do an example.
60:90:100
100 plus 90 plus 60 is 250
ben gets 90 of that 250
or 9/25.
a saving account earns interest at a rate of 7% each month. the initial balance is $100. write an exponential function b(m) to model the growth after m months.
Answers
Data:
Initial balance: c
intrest rate: r
time (months)=m
growth: b
c=$100
r=7%=0.07
To an exponential function you have the next general form:
\(y=C(1+r)^t\)In this case
y=b(m)
C=c
r=r
t=m
\(b(m)=100(1+0.07)^m\)add q to p then multiply 5 by the result
Answers
Answer:
q+5p
Step-by-step explanation:
q+px5=q+5p
3(4x - 12) + 8 = 12x - 6
Answers
Answer:
No solution
Step-by-step explanation:
3(4x-12)+8=12x-6
12x-36+8=12x-6
12x-28=12x-6
2.
MNOP is a tetrahedron. Given that the volume of tetrahedron is 75 m²
and the area of the base is 25 m². Find the height of tetrahedron.
Answers
Answer: 9 m
Step-by-step explanation:
\(75=\frac{1}{3}(25)(h)\\\\h=\frac{75}{25/3}=9\)
The expression 2 (L+ w) represents the perimeter of a rectangle with the length I and the width W.
What are the factors of the expression?
А
The factors are the length and the width.
B
The factors are 2, the length, and the width.
c
The factor is the sum of the length and the width.
D
The factors are 2 and the sum of the length and the width.
Answers
Answer: D. 2 and the sum of the length and the width.
Step-by-step explanation:
Add L +w to get one factor. 2 is the other factor.
Factors are what we multiply to get the product.
PLEASE HELP!!!!!
A line intersects the points (-8, -1) and
(1, 8). What is the slope-intercept
equation for this line?
y= [?}x+ _
Answers
Have a great day
:))
Answer:
m=1
c=7
I hope it will be useful.
Which sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent?A)reflection and dilationB)reflection and rotationC)rotation and reflectionD)translation and rotation help please
Answers
The sequence of transformations will be relection and dilation. Then the correct option is A.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.
The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.
Reflection does not change the size and shape of the geometry.
Rotation does not change the size and shape of the geometry.
Translation does not change the size and shape of the geometry.
Dilation does not change the shape but changes the size of the geometry.
Then the correct option is A.
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A regular polygon has 10 sides. What is the measure of each interior angle of the polygon? 36° 1440° 144° 72°
Answers
Answer:
144°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 10, thus
sum = 180° × 8 = 1440°
Each interior angle = 1440° ÷ 10 = 144°
Answer:
144 deg
Step-by-step explanation:
Sum of the measures of the angles of a polygon with n sides:
(n -2)180
For a 10-sided polygon, n = 10.
The sum of the measures is
(10 - 2)180 = (8)180 = 1440
Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is
1440/10 = 144
Answer: 144 deg
Take the sum of 6 and 7 and divide it by the sum of 10 and 3
Answers
Answer:
1
Step-by-step explanation:
(6+7)/(10+3)=1
and hope can help you
Simplify:
(a/b)xy+xy-(5/2)xy
and
(8^3x+1)/(2^x)
Answers
second one.... 512x+1/2x
raise 8 to the power one 3.