Answer:
Hypotenuse is the longest side in a triangle.
a^2=b^2+c^2.
5^2=4^2+c^2.
c^2=25-16.
c^2=9.
c=√9.
c=3cm.
If eight persons are having dinner together, in how many different ways can three order chicken, four order steak, and one order lobster
Answer:
Total number of ways= 144 ways
Step-by-step explanation:
Number of ways 3 can order chicken
= 3!
= 3*2*1
= 6
Number of ways 4 can order steak
= 4!
= 4*3*2*1
= 24
Number of ways 1 can order lobster
= 1!
= 1
Total number of ways= 24*6*1
Total number of ways= 144 ways
The total number of different ways is 144.
Calculation of the total no of ways:Since If eight persons are having dinner together.And, there is three order chicken, four order steak, and one order lobster
Now
Number of ways 3 can order chicken
= 3!
[tex]= 3\times 2\times 1[/tex]
= 6
Now
Number of ways 4 can order steak
= 4!
[tex]= 4\times 3\times 2\times 1[/tex]
= 24
Now Number of ways 1 can order lobster
= 1!
= 1
So, total should be
[tex]= 24\times 6\times 1[/tex]
= 144 ways
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What is the correct reason for statement 3?
Point C is the midpoint of a segment AB . What are the coordinates of point B, if: A(–1, 3), C( 1, –1)
Answer:
(3,-5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates together and divide by 2
The x coordinate is
(x1+x2)/2
We know one point and the midpoint
( -1+x)/2 = 1
Multiply by 2
-1 +x = 2
Add 1
x =2+1
x=3
To find the y coordinate of the midpoint, add the y coordinates together and divide by 2
The y coordinate is
(y1+y2)/2
We know one point and the midpoint
(3+y)/2 = -1
Multiply by 2
3+y = -2
Subtract 3
y = -2-3
y =-5
The other endpoint is (3,-5)
Answer:
B(3, -5)
Step-by-step explantion
We know that these formulas can be used to find the mid point between 2 points on a graph
[tex]\frac{a_{1} +b_{1}}{2}= c_{1}\\ \frac{a_{2} +b_{2}}{2} =c_{2}[/tex]
Now we plot these points in
A(-1, 3), C(1, -1)
[tex]\frac{-1+b_{1}}{2} =1 \\\frac{3+b_{2}}{2} =1[/tex]
And we can find that
[tex]b_{1}= 3\\b_{2}=-5[/tex]
Therefore we get the answer of (3, -5)
Hope that helped you with your problem!! :)
The sum of two numbers is 48. The larger number is 7 less than four times the smaller number. Find the numbers.
Answer:
Larger number = 37
Smaller Number = 11
Step-by-step explanation:
Lets take x as the bigger number and y as the smaller number
x + y = 48
What do we know?
The larger number is 7 less than four times the smaller number
so 4y - 7 = x
Lets replace the equation obove with x
4y - 7 + y = 48
5y - 7 = 48
5y = 48 + 7
y = 55/5
y = 11
Then multiply 11 by 4 11 times 4 = 44 and subtract by 7 44 - 7 = 37
To recheck add 37 to 11 and u should get 48
Solve the following math problem. Show your work.
My mom gave me 25 cents. I shared 10 cents with my brother. How much money do I have left?
Answer:
15
Step-by-step explanation:
25-10=15
You take out 10 cents and u have 15 left
The number 18 is a counterexample for which of the following conditional statements?
Answer:
The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.
Step-by-step explanation:
To find : The number 18 is a counterexample for which of the following conditional statements?
Solution :
For a conditional statement to be true then it is true for all cases that satisfy the condition.
A counterexample is given to prove a conditional statement false.
Now, Examine all the conditions
A. If a number is divisible by 2, it is even.
18 is even and divisible by 2 - True
B. If a number is odd, then it is not divisible by 2.
18 is not odd so it is divisible by 2 - True
C. If a number is even, then it ends with 0, 2, 4, 6, or 8.
18 ends with 8 so it is even - True
D. If a number is divisible by 2, then it is also divisible by 4.
18 is divisible by 2 but 18 is not divisible by 4 - False
Therefore, The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.
One serving of a certain brand of yogurt contains 7g of fat. The low-fat version contains 38.25% less fat per serving. How many grams of fat does one serving the low-fat yogurt contain?
Answer:
7g-100%
x-38,25
38,25*7:100=2,6775g
7g-2,6775g=4,4325g
Step-by-step explanation:
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
106
Step-by-step explanation:
The area of one of the triangles is 1/2*5*3
The area is 7.5, but there are 2 triangles so the combined area is 15
The area for whole rectangle is 7*(5+3+5)=7*13=91
So the total area is 91+15= 106
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
Answer:
(B) {6,6,7}
Step-by-step explanation:
A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:
[tex]a^{2} = b^{2}+c^{2}-2\cdot b \cdot c \cdot \cos \theta[/tex]
Where [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are sides of the triangle and [tex]\theta[/tex] is the angle opposite to side [tex]a[/tex]. Now, let is clear the cosine function:
[tex]2\cdot a \cdot b\cdot \cos \theta = b^{2}+c^{2}-a^{2}[/tex]
[tex]\cos \theta = \frac{b^{2}+c^{2}-a^{2}}{2\cdot b \cdot c}[/tex]
Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:
a) [tex]a = 2[/tex], [tex]b = 5[/tex], [tex]c = 9[/tex]
[tex]\cos \theta =\frac{5^{2}+9^{2}-2^{2}}{2\cdot (5)\cdot (9)}[/tex]
[tex]\cos \theta = 1.133[/tex] (Absurd)
The triplet does not represent a triangle.
b) [tex]a = 6[/tex], [tex]b = 6[/tex], [tex]c = 7[/tex]
[tex]\cos \theta =\frac{6^{2}+7^{2}-6^{2}}{2\cdot (6)\cdot (7)}[/tex]
[tex]\cos \theta = 0.583[/tex] (Reasonable)
The triplet represents a triangle.
c) [tex]a = 6[/tex], [tex]b = 4[/tex], [tex]c = 2[/tex]
[tex]\cos \theta = \frac{4^{2}+2^{2}-6^{2}}{2\cdot (4)\cdot (2)}[/tex]
[tex]\cos \theta = -1[/tex] (Absurd)
The triplet does not represent a triangle, but a straight line.
d) [tex]a = 7[/tex], [tex]b = 8[/tex], [tex]c = 1[/tex]
[tex]\cos \theta = \frac{8^{2}+1^{2}-7^{2}}{2\cdot (8)\cdot (1)}[/tex]
[tex]\cos \theta = 1[/tex] (Absurd)
The triplet does not represent a triangle, but a straight line.
Hence, the correct answer is B.
Course Activity: Relationships Betwee
5 of 16
Question
Mark says that the number 2 is a rational number
because he can write it as the fraction ?
Is Mark correct? Why or why not?
Answer:
yes
Step-by-step explanation:
A rational number is in the form p/q where p and q are both integers and the denominator q is not equal to zero. This means that the set of all real numbers are rational numbers.
Since q can be any integer apart from zero, it means that all integers are rational numbers i.e for q = 1.
Hence 2 which can be written as fraction as 2/1 is a rational number since the denominator (q = 1) is a non zero number
Answer:
Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.
Step-by-step explanation:
Vivian is going to do some yard work, but she needs to leave her house at 1:00 to go to a football game. She is going to mow the lawn for 1 hour and 10 minutesl, trim some bushes for 30 minutes, and put down some mulch for 35 minutes. She will also need 20 minutes to shower and get dressed. What time should she start the work so she will be ready at 1/00 ?
Answer:
10:25
Step-by-step explanation:
mow the lawn 1:10
trim bushes: 0:30
put down mulch: 0:35
shower: 0:20
Total time = 1:10 + 0:30 + 0:35 + 0:20 = 1:95 = 2:35
She needs 2 hours and 35 minutes to do everything.
1:00 p.m. = 13:00
13:00 - 2:35 = 12:60 - 2:35 = 10:25
She should start work at 10:35 a.m.
Find the nth Taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 3 P4(x) =
Answer:
P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
Step-by-step explanation:
Given:
f(x) = ln(x)
n = 4
c = 3
To find:
nth Taylor polynomial for the function, centered at c
Solution:
The Taylor series for f(x) = ln x centered at 3 is:
[tex]P_{n}(x) = f(c) + \frac{f'(c)}{1!}(x-c)+\frac{f''(c)}{2!}(x-c)^{2} +\frac{f'''(c)}{3!}(x-c)^{3}+...+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since c = 3 So,
[tex]P_{4}(x) = f(3) + \frac{f'(3)}{1!}(x-3)+\frac{f''(3)}{2!}(x-3)^{2} +\frac{f'''(3)}{3!}(x-3)^{3}+...+\frac{f^{n} (3)}{n!}(x-3)^{n}[/tex]
Now
f(3) = ln 3
f'(x) = 1/x ⇒ f'(3) = 1/3
f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9
f'''(x) = 2/x³ ⇒ f'''(3) = 2/3³ = 2/27
f[tex]^{(4)}[/tex] (x) = -6/x⁴ ⇒ f[tex]^{(4)}[/tex] (3) = -6/3⁴ = -6/81 = - 2/27
So Taylor polynomial for n=4 is:
P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴
help a girl out pls.........
Answer:
Hey there!
The solution is (1, 2) because that is where the lines intersect.
Hope this helps :)
City planners are designing a new dog park. The park will be a square. The area of the park is the square of the side length: area=2802 feet2. Without using a calculator, what is the area of the dog park? Use polynomial identities to support your answer. (thank you)
Step-by-step explanation:
A = 280² ft²
A = (200 + 80)² ft²
A = [200² + 2(200)(80) + 80²] ft²
A = (40000 + 32000 + 6400) ft²
A = 78400 ft²
The required area of the dog park using polynomial is 6771204 feet².
What is polynomial?Polynomial is an algebraic expression that has more than two terms. In other words, it is a combination of different variables with mathematical operations.
Given that,
The area of the park = square of the side length a = 2802 feet².
To find the area of the park, using polynomial use
Formula of area of square = (a)²
= (2802)²
= (2800 + 2)²
Use formula (a + b)² = a² + b² + 2ab
= (2800)² + (2)² + 2 x 2800 x 2
= 6,760,000 + 4 + 11200
= 6771204 feet²
The required area of the dog park is 6771204 feet².
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which of the folowing has a value that is less than zero.
a.) (-6)2
Answer:
the answer is the letter A
Answer:
A
Step-by-step explanation:
It's A because -6 * 2 equals -12 which is less than zero
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (XY) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y)
midpoint (5. - 12), endpoint (4-7)
The other endpoint is
(Type an ordered pair)
Answer:
(6, -17)
Step-by-step explanation:
Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:
The midpoint formula is given as [tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex].
Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.
Let the other endpoint be [tex] (x_1, y_1) [/tex]
Midpoint = M(5, -12)
Let the given endpoint = [tex] (4, -7) = (x_2, y_2) [/tex]
Thus:
[tex] M(5, -12) = (\frac{x_1 + 4}{2}, \frac{y_1 +(-7)}{2}) [/tex]
Rewrite the equation to find the coordinates of the other endpoints
[tex] 5 = \frac{x_1 + 4}{2} [/tex] and [tex] -12 = \frac{y_1 - 7}{2} [/tex]
Solve for each:
[tex] 5 = \frac{x_1 + 4}{2} [/tex]
[tex] 5*2 = \frac{x_1 + 4}{2}*2 [/tex]
[tex] 10 = x_1 + 4 [/tex]
[tex] 10 - 4 = x_1 + 4 - 4 [/tex]
[tex] 6 = x_1 [/tex]
[tex] x_1 = 6 [/tex]
[tex] -12 = \frac{y_1 - 7}{2} [/tex]
[tex] -12*2 = \frac{y_1 - 7}{2}*2 [/tex]
[tex] -24 = y_1 - 7 [/tex]
[tex] -24 + 7 = y_1 - 7 + 7 [/tex]
[tex] -17 = y_1 [/tex]
[tex] y_1 = -17 [/tex]
Ordered pair of the other endpoint is (6, -17)
There are 14 books on a shelf. .5 of them are new. The rest of them are used. What is the ratio of all books on the shelf to used books?
Answer:
9/14
Step-by-step explanation:
what is the surface area means
Answer:
that is the outsider part.of something
the sum of the areas of all the faces of a three dimension figure or in 3-D shapes
write 7*7*7 in standard form
Answer:
Step-by-step explanation:
343
Answer:
7^3
Step-by-step explanation:
7 to the power of 3. Because there are 3, 7's so you are multiplying 7 3 times
According to a recent pol, 29 % of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. Assume the standard deviation from the recent studies is accurate and known. According to recent studies, cholesterol levels in healthy adults from the area average about 205 mg/dL, with a standard deviation of about 25 mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of40 healthy adults from the region is taken,What is the probability that the mean cholesterol level of the sample will be between 200 and 210
Answer:
Step-by-step explanation:
The mean value μ = 205 , standard deviation of population σ = 25
no of people n = 40
standard deviation of sample of 40 people = σ / √n
σ₁ = 25 / √ 40 = 3.95
probability between 200 and 205
P ( 200 < X < 205 ) = P ( Z= (210 - 205) / 3.95 - P ( Z= (200 - 205) / 3.95
= P ( Z = + 1.26 ) - P ( - 1.26 )
= .8962 - .1038
= .7924
Probability is 79.24 % .
How many subsets are there of the set N = {1, 42, 65, 12, 31, 27}?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{64}}}}}[/tex]
Step-by-step explanation:
If ' n ' is the cardinal number of a set, the number of subsets of a given set can be obtained by using the formula 2ⁿ
Given,
N = { 1 , 42 , 65 , 12 , 31 , 27 }
where n ( total number of elements ) = 6
So, the number of possible subsets of set N :
= 2ⁿ
= 2⁶
= 2 × 2 × 2 × 2 × 2 × 2
= 64
Hope I helped!
Best regards!!
A movie rental company offers a membership plan that costs $10/month and charges $2 to rent each movie.How many movies can a member rent in one month and spend at most $24
Answer:
7 movies
Step-by-step explanation:
Given
membership cost for 1 month = $10
rent for 1 movie = $2
Maximum money to be spent by a member = $24
Let the no. of movie rented by x
Thus, total rent for x movies = x* rent for 1 movie = x*$2 = $2x
Total spending for 1 month = membership cost for 1 month + total rent for x movies
Total spending for 1 month = 10 +2x
Given that he can spend at most $24
Total spending for 1 month <= 24
10 + 2x <= 24
2x <= 24-10
2x <= 14
x <= 14/2
x <= 7
Thus, movies rented can be less than or equal to 7.
since we have to find the maximum movies rented in 23, it will be 7
Thus, at most 7 movies can be rented.
This exercise examines the accuracy of various branch predictors for the following repeating pattern (e.g., in a loop) of branch outcomes: T, NT, T, T, NT.
a. What is the accuracy of always-taken and always-not-taken predictors for this sequence of branch outcomes?
b. What is the accuracy of the 2-bit predictor for the first four branches in this pattern, assuming that the predictor starts off in the bottom left state (predict not taken)?
c. What is the accuracy of the 2-bit predictor if this pattern is repeated forever?
Answer:
attached below is the missing part of the question and the solution
A) 60%, 40%
B) 25%
C) 60%
Step-by-step explanation:
a) The accuracy of always-taken for this sequence of branch outcomes = 60%
The accuracy of always -not-taken for this sequence of branch outcomes = 40%
b) The accuracy of the 2-bit predictor for the first four branches assuming that the predictor starts off in the bottom left state = 25%
C)the accuracy of the 2-bit predictor if this pattern is repeated forever = 60% ( was stopped after the fourth iteration because the fourth and third iterations are the same) =
how many kilometres are there in 1 metre
Answer:
0.001km
1km is 1000m
So, 1m is 1m divided by 1000km
Which gives 0.001km
There are 0.001 kilometres in 1 metre.
1000 metre =1 kilometre
1 metre=1/1000 kilometre
Express (-3 - i) - (5 + 3i) in the form of a + ib.
Answer:
Step-by-step explanation:
=-3-i-5-3i
=-8-4i
Find all values of in the interval [0, 2π] that satisfy the equation. Enter your answers from smallest to largest. (Enter NONE in any unused answer blanks.) $$ 2\sin^2(x) = 1 $$
Answer:
π/4 and 3π/4Step-by-step explanation:
Given the equation [tex]2\sin^2(x) = 1 \\[/tex], we are to find all the values of x in the interval [0, 2π] that satisfies the equation.
Simplifying the equation:
[tex]2\sin^2(x) = 1 \\\\sin^2x = \frac{1}{2} \\\\[/tex]
Square both sides of the equation;
[tex]\sqrt{sin^2x } = \sqrt{\frac{1}{2} } \\\\sin(x) = \sqrt{0.5}\\ \\sin(x) = 0.7071\\\\x = sin^{-1}0.7071\\\\x \approx 45^0[/tex]
The general formula for sin(x) is x = nπ + (-1)ⁿ∝ where n = 0, 1, 2, 3...
Since ∝ = 45° = π/4.
x = nπ + (-1)ⁿπ/4
when n = 1
x = π + (-1)¹π/4
x = π - π/4
x = 3π/4
Hence the values of x within the given interval are π/4 and 3π/4
Which expression has a value of 74?
Please help
Answer:
x+5y+2z sry if itss wrong lol
Step-by-step explanation:
Part C
Kelvin wants to know whether his father, Arnold, skied three times as long without falling as anyone else in the family did. He can check using the
inequality 3w < 356, where w is the time in seconds that each person skied. Plug the values for the time skied by each person into the inequality to
find the answer
B
I
u
X
Font Sizes
A- A - E 3 E 3
Person
Time Skied Plugged into True or False?
(seconds) 3w <356
Answer
Kelvin 223 669 < 356
Lori 55 165 < 356
Vanessa 265 795 < 356
Devon 172 516 < 356
Celia 112 336 < 356
Step-by-step explanation:
8. The ratio of cats to dogs in a particular animal shelter is 11:3. If there are 154 total animals in
the shelter, how many of them are dogs?
33 animals at the shelter are dogs.
how much time with it take for 450 to yield 81 as interest at 4.5 per annum of simple interesst
Answer:
4 years
Step-by-step explanation:
The formula for simple interest is useful here.
I = Prt
where P is the principal invested at rate r for t years.
Fill in the given values and solve for t:
81 = 450×0.045×t
81/20.25 = t = 4
It will take 4 years for 450 to yield 81.