Answer:10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
Applying the Pythagoras Theorem
Find the length of the hypotenuse
substitute
Second case
The given lengths are one leg and the hypotenuse
so
Applying the Pythagoras Theorem
Find the length of the other leg
substitute
Find the difference between the two possible lengths of the third side of the triangle
so
Answer:
The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.
Step-by-step explanation:
We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.
And we want to find the difference between the two possible lengths of the third side.
In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+(15)^2=c^2[/tex]
Solve for c:
[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]
In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+b^2=(15)^2[/tex]
Solve for b:
[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]
Therefore, the difference between the two possible lengths for the third side is:
[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]
An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected. what is the value of the z-test statistic?
Answer:
The value of the z-test statistic is [tex]z = 0.68[/tex]
Step-by-step explanation:
An article claims that 12% of trees are infested by a bark beetle.
At the null hypothesis, we test if the proportion is of 12%, that is:
[tex]H_0: p = 0.12[/tex]
At the alternative hypothesis, we test if the proportion is different of 12%, that is:
[tex]H_1: p \neq 0.12[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.12 is tested at the null hypothesis:
This means that [tex]\mu = 0.12, \sigma = \sqrt{0.12*0.88}[/tex]
A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.
This means that [tex]n = 1000, X = \frac{127}{1000} = 0.127[/tex]
What is the value of the z-test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.127 - 0.12}{\frac{\sqrt{0.12*0.88}}{\sqrt{1000}}}[/tex]
[tex]z = 0.68[/tex]
The value of the z-test statistic is [tex]z = 0.68[/tex]
Please help me steps please
10 ft
8 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate .
A = [ ? ] ft2
Nati
If a and b are zeroes of the x2 + 7 x+7, find the value of a−1+b−1−2ab.
9514 1404 393
Answer:
-15
Step-by-step explanation:
If 'a' and 'b' are zeros of the quadratic f(x), its factored form is ...
f(x) = (x -a)(x -b)
and its standard form is ...
f(x) = x^2 -(a+b)x +ab
This tells us that ...
a+b = -7
ab = 7
for the given quadratic.
Then the expression of interest is ...
[tex]a^{-1}+b^{-1}-2ab=\dfrac{1}{a}+\dfrac{1}{b}-2ab=\dfrac{a+b}{ab}-2ab\\\\=\dfrac{-7}{7}-2\cdot7=-1-14=\boxed{-15}[/tex]
HW HELP ASAP PLZZzzzzzzzz
Answer:
Graph 4
Step-by-step explanation:
Point D, not shown below, is one of the four (4) vertices of rectangle ABCD. Find its position and state the coordinate of point D.
Answer:
Hi im not got with graphs
Step-by-step explanation:
w= 2hx - 11x Solve for X. Please and Thank you
Answer:
[tex]{ \tt{ w = 2hx - 11x}} \\ \\ { \bf{w = x(2h - 11)}} \\ \\ { \bf{x = \frac{w}{2h - 11} }}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = \frac{w}{(2h - 11)} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]w = 2hx - 11x[/tex]
[tex]✒ \: w = x \: (2h - 11)[/tex]
[tex]✒ \: x = \frac{w}{(2h - 11)} [/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
What is the probability of randomly selecting a prime number from the first 30 natural numbers?
A. 11/30 ≈ 36.67%
B. 13/30 ≈ 43.33%
C. 1/3 ≈ 33.33%
D. 12/30 = 40%
Answer:
33.33%
Step-by-step explanation:
Prime numbers from 1 to 30 are 2,3,5,7,11,13,17,19,23,29.
So There are 10 prime numbers
Therefore,
P(of randomly selecting a prime number from the first 30 natural numbers)=10/30= 1/3 = 33.33%
Please help me with the correct answer
Answer:
50 books were sold
Step-by-step explanation:
there are 5 books in the Red Crow row, and each book is worth 10 sold.
A community center rents their hall for special events. They charge a fixed fee of $200 plus an hourly fee of $22.50. Lin has $300 to spend on renting the hall for a fundraiser.Using only the money she has, can Lin pay for a 6 hour event? Explain or show your reasoning.
Answer:
No, 6 hours would cost $335, 35 over her limit of $300.
Step-by-step explanation:
she has to pay $200 plus 22.50 for every hour she rents. So, if she rents for 6 hours, she has to pay $200 + 6(22.50) or $200 + 135=335. She only has $300 so she can’t afford the event.
Solve the system 6x -2y+z= -2 2x+ 3y - 3z =11 x+ 6y=31
Answer:
x = 1
y = 5
z = 2
Step-by-step explanation:
System of equations:
6x - 2y + z = -2
2x + 3y - 3z = 11
x + 6y = 31
Isolate one variable in any of the equations:
x + 6y = 31
x = 31 - 6y
Plug in this value for x in another equation:
6(31 - 6y) - 2y + z = -2
186 - 36y - 2y + z = -2
186 - 38y + z = -2
-38y + z = -188
z = -188 + 38y
Plug in these values in the remaining equation:
2(31 - 6y) + 3y - 3(-188 + 38y) = 11
62 - 12y + 3y + 564 - 114y = 11
626 - 12y + 3y - 114y = 11
626 - 9y - 114y = 11
626 - 123y = 11
-123y = -615
y = 5
Plug in value of y into our other answers to solve for x and z:
x = 31 - 6(5)
x = 31 - 30
x = 1
z = -188 + 38(5)
z = -188 + 190
z = 2
Check your work:
6x - 2y + z = -2
6(1) - 2(5) + 2 = -2
6 - 10 + 2 = -2
-4 + 2 = -2
-2 = -2
Correct!
*Note there are several ways to solve for these types of problems. I used substitution*
If you drive at a constant speed of 60 miles/hour find the time it would take to travel each of the distances in the following chart. Here are the formulas:
d = s ⋅t
or
t = ds
a. Find the time for each distance. Show your work for at least one trial.
Distance in Miles Time in Hours
10
20
30
40
50
60
b. Graph the points and label the axis
c. What does this graph mean?
Answer:
b bc it is i got it right
Step-by-step explanation:
can someone help me with this question
Answer:
its C or A bro
Step-by-step explanation:
tính dz(0,1) của hàm ẩn (x,y) xác định bởi hệ thức x² + 2y + z = ye^x²
Answer:
???
Step-by-step explanation:
asaan ang sasagutan
Eli will photograph a wedding for a flat fee of $880 or for an hourly rate of $120. For what lengths of time would the hourly rate be less expensive?
The hourly rate would be less expensive if the wedding was less than ___ hours long.
Answer:
7 hours
Just divide 880/120 = 7.3333333
So if 7*120 = 840
An hour more would be more expensive.
(4x+ 5 = 20
Which best describes the circled part of the statement?
Expression
Coefficient
Term
Variable
Answer:
B) Coefficient.
Step-by-step explanation:
The coefficient is the numerical constant in the given term.
For example, the given term is 4x, in which:
4 is the coefficient.
x is the variable.
5 is the constant.
20 is another constant.
~
How many solutions are there to the equation below?
8(x-3) = 7x- 20
Answer:
x = 4 (ONE solution)
Step-by-step explanation:
This is a first order linear equation, so we can expect 1 solution.
Multiplying out the left side, we get:
8x - 24 = 7x - 20, which simplifies to:
x = 4 (ONE solution)
how to write 403.225 in words and how do i get the answer. Thanks!!!!
the sum of three consecutive even number is 27
What is the midpoint of the line segment connecting the points (-4, 5) and (4,7)?
Answer:
(0,6)
Step-by-step explanation:
Answer:
(0,6)
Step-by-step explanation:
We need to find the midpoint of the line segment having end points (-4,5) and (4,7). So, here we can use the Midpoint Formula :-
Points :- (-4,5) and (4,7).
Using Midpoint Formula ,
[tex]\rm\implies Midpoint =\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)[/tex]
Substitute the respective values ,
[tex]\rm\implies Midpoint =\bigg(\dfrac{-4+4}{2},\dfrac{7+5}{2}\bigg)[/tex]
Simplify the numbers ,
[tex]\rm\implies Midpoint =\bigg(\dfrac{0}{2},\dfrac{12}{2}\bigg)[/tex]
This equals to ,
[tex]\rm\implies \boxed{\blue{\rm Midpoint =\bigg( 0,6\bigg)}}[/tex]
Hence the midpoint is (0,6) .
Which statement best describes the areas and perimeters of the figures below?
Answer:
They have different areas and different perimeters
Two angles are supplementary. One is 25° more than four times the other. Find the measures of the angles.
Answer:
100
Step-by-step explanation:
I believe it is this answer bur don't hold me to. If it is wrong I'm sorry in advance
Answer:
The two angles are 31° and 149°
Step-by-step explanation:
Let the two supplementary angles be , x and y.
Then, x + y = 180° ----- ( 1 )
Given : one is 25° more than 4 times other
Let y = 25° + 4x ------ ( 2 )
Substitute ( 2 ) in ( 1 ) :
x + y = 180°
x + 25° +4x = 180°
x + 4x = 180° - 25°
5x = 155°
x = 31°
Substitute x in ( 2 ) :
y = 25° + 4x
= 25 + 4 ( 31 )
= 25 + 124
= 149°
(Right angle Trigonometry) Please help me solve and explain!
Answer:
31.3
Step-by-step explanation:
Reference angle given = 56.1°
Hypotenuse = 56.1
Adjacent side = x = ?
We would apply CAH, which is:
Cos 56.1° = Adj/Hyp
Cos 56.1° = x/56.1
56.1 × Cos 56.1° = x
31.2895006 = x
x = 31.3 (approximated to the nearest tenth)
y=5px+5x2+p2 differential equation
Answer:
Step-by-step explanation:
y=5px+5x2+p2
y=10p2x2p
Which of the following graphs show a
proportional relationship?
Choose all answers that apply:
Help me please I only have 20min left to do this
Answer:
A
Step-by-step explanation:
Match the statement using the diagram
9514 1404 393
Answer:
d, b, c, a, e
Step-by-step explanation:
The order of the letters in the congruence statement tells you ...
ΔQOP ≅ ΔABC
∠Q ≅ ∠A
∠O ≅ ∠B ≅ 115°
∠P ≅ ∠C
QO ≅ AB = 5 m
OP ≅ BC = 8 m
PQ ≅ CA
GIVING OUT BRAINLIEST HELP ME PLEASE !! PLS 10 PTS
Answer:
x2+y2-12x24y+36=36.
2
+
y
2
−
12
x
+
18
y
=
−
36
Step-by-step explanation:
Answer:
Step-by-step explanation:
(x^2-12x+36) + (y^2-24y+144-144) = 0
(X-6)^2 + (y-12)^2=144
Triangle KLM is similar to triangle NOP. Find the measure of side OP. Round your answer to the nearest tenth if necessary
Answer:
OP = 43.7
Step-by-step explanation:
since the triangle is similar use these ratios.
LM/OP = LK/ON
9/OP = 7/34
do cross multiplication
OP*7 = 34*9
OP = 306/7
OP = 43.71
OP = 43.7
Answer:
OP = 50
because that is the answer
Which input value produces the same output value for the two functions
X=-12
X=-9
X=-6
X=-3
Imara used these steps to find the length of the hypotenuse of the right triangle.
3 squares are positioned to form a right triangle. The small square is labeled 15, medium square is 20, and large square is not labeled.
Step 1: Find the area of the square with side lengths of 20: 400
Step 2: Find the area of the square with side lengths of 15: 225
Step 3: Find the sum of the areas of the two squares: 625
Step 4: State the length of the hypotenuse: 625
Answer:
C, "She could have found the sum of 15 and 20 and then squared the sum."
Step-by-step explanation:
I just took the test on Edge :)
The answer is C, I got it right on edge.
Have a nice day everyone <3.