The value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2. This can be obtained by using Pythagoras' theorem.
Calculate the value of a:This question can be solved using Pythagoras' theorem,
If in a right angled triangle, hypotenuse is the longest side of the triangle and always opposite to the angle 90°, height and base are the two shorter sides which are adjacent to the angle 90°.
If hypotenuse = c, height = a and base = b then,
⇒ hypotenuse² = height² + base²
⇒ c² = a² + b²
Here in the question it is given that,
Hypotenuse of the triangle is c = a√2 6 = a√2 in inches ⇒ c = 6 Height and base is equal and both has the value of a ⇒ height = a and base = aBy using the Pythagoras' theorem we can write that,
⇒ hypotenuse² = height² + base²
⇒ 6² = a² + a²
⇒ 36 = 2a²
By dividing both sides of the equation by 2,
⇒ 18 = a²
⇒ a² = 18
By taking square on both side of the equation,
⇒ a = 3√2 inches
Hence the value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2.
Learn more about Pythagoras' theorem here:
brainly.com/question/9005379
#SPJ1
Volume oblate spheroid
The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.
What is the volume of an oblate spheroid?
In this problem we have the shape of an ellipse centered at origin, whose vertex form is shown below:
x² / a² + y² / b² = 1 (1)
Where a, b are the lengths of the semiaxes, in feet.
An oblate spheroid is generated by revolving half of the ellipse about the y-axis. Oblate spheroids are a kind of ellipse:
x² / a² + y² / b² + z² / a² = 1 (2)
Where a, b, c are the lengths of the semiaxes, in feet.
And the volume of the oblate spheroid is:
V = (4 / 3) · π · a² · b (3)
If we know that a = 3 ft, b = 2 ft, then the volume of the oblate spheroid is:
V = (4 / 3) · π · (3 ft)² · (2 ft)
V ≈ 75.398 ft³
The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.
To learn more on oblate spheroids: https://brainly.com/question/17585663
#SPJ1
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they exercise in a week:
On a grid, Label Hours of Exercise on x axis and Test Scores on y axis. The title of the graph is Test Scores and Exercise. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 12 and 1, 30 and 2.1, 21 and 2.5, 42 and 3.5, 30 and 3.5, 45 and 4, 55 and 5, 45 and 5.5, 60 and 5.5, 70 and 6.5, 40 and 7, 50 and 7.5, 80 and 8, 75, and 8.5, 60 and 9, 75. The ordered pair 9, 15 is circled and labeled as T. All the other points are put in an oval and labeled as P.
Part A: What is the group of points labeled P called? What is the point labeled T called? Give a possible reason for the presence of point T. (5 points)
Part B: Describe the association between students' test scores and the number of hours they exercise. (5 points)
It should be noted that Group A is a cluster of points with similar property or relationship and Point B is an outlier. This is the point outside of the common relationship in the scatterplot
What is a scatterplot?It should be noted that scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.
In this case, the independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.
The association between students' test scores and the number of hours they exercise is that there is a negative tendency. As number of hours spent on computer games increase, the test scores decrease.
Learn more about scatter plot on:
https://brainly.com/question/6592115
#SPJ1
Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 miles per hour faster than the other. If the two buses are 744 miles apart after 6 hours, what is the rate of each bus?
Answer:
53 mph and 71 mph
Step-by-step explanation:
bus 1 rate = x
bus 2 rate = x + 18
rate times time = distance
( x + x+18) * 6 = 744
(2x+18) * 6 = 744
2x + 18 = 124
2x = 106
x = 53 the other bus is 53 + 18 = 71 mph
Someone please help me with this thank you!
Answer:
50°
Step-by-step explanation:
Note EFGH is an isosceles trapezoid.
∠HGF=77° (base angles of an isosceles trapezoid are congruent)
∠EGH=27° (angles in a triangle add to 180°)
∠FGE=50° (angle subtraction postulate)
PLEASE HELP ME WITH THIS QUESTION I NEED HELP
Answer:
True
Step-by-step explanation:
This is true in an equilateral triangle.
What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?
A
(-1, -4)
B
(1, -4)
C
(3, -4)
D
(-3, 12)
Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
VertexConsidering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
Compute the probability of event E if the odds in favor of E are 28 to 29.
Answer:
28/57
Step-by-step explanation:
odds in favor of event occurring = (probability event occurs)/(probability event does not occur)
Let p = probability event occurs.
Then the probability the event does not occur is 1 - p.
Let the odds = a/b.
a/b = p/(1 - p)
a(1 - p) = bp
a - ap = bp
bp + ap = a
p(a + b) = a
p = a/(a + b)
p = 28/(28 + 29)
p = 28/57
As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
If the odds in favor of an event E are "a to b," then the probability of E is given by:
P(E) = a / (a + b)
In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.
So, using the formula above, we can compute the probability of E as:
P(E) = 28 / (28 + 29)
P(E) = 28 / 57
Therefore, the probability of event E is 28/57 or approximately 0.4912.
For more details regarding probability, visit:
https://brainly.com/question/30034780
#SPJ2
I am confused. Can somebody explain this to me?
Maryann can paint a wall in 45 minutes. It takes her brother Junior 1 hour and 45 minutes to paint the same wall. How many minutes would it take Maryann and Junior to paint the wall, if they work together? Answer as a decimal to the nearest tenth.
Answer: If they worked together, it would take 31.5 minutes
Step-by-step explanation:
There's a certain formula for equations like this:
[tex]\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}[/tex]
t1= the time it took for the first person to complete the task.
t2= the time it took for the second person to complete the task.
tb= the time it took for both of them to complete the task.
We have the values for both t1 and t2, but not for tb.
t1= 45
t2= 105
tb= x
[tex]\frac{1}{45} +\frac{1}{105} = \frac{1}{x}[/tex]
Now it's simple algebra, and all we need to do is solve for x
The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.
[tex]\frac{315}{45} + \frac{315}{105} = \frac{315}{x}[/tex]
This will simplify nicely, so now we just need to get x on the other side.[tex]7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x[/tex]
[tex]10x = 315 \\\\x = 31.5[/tex]
. What are the values a b and c In the following quadratic equation ? -6x^2-8x+12=0
Answer:
a = -6
b = -8
c = 12
Step-by-step explanation:
Quadratic equations follow the general structure:
ax² + bx + c = 0
In this equation, "a" and "b" serve as coefficients which modify the variables and "c" represents the y-intercept. Since the given equation is in the quadratic form, you can easily identify which values match the variables.
-6x² - 8x + 12 = 0
a = -6
b = -8
c = 12
AMERICAN AIRLINES HAS A POLICY OF BOOKING AS MANY AS 15 PEOPLE ON AN AIRPLANE THAT CAN SEAT ONLY 14. (PAST STUDIES HAVE REVEALED THAT ONLY
85% OF THE BOOKED PASSENGERS ACTUALLY ARRIVE FOR THE FLIGHTS.) FIND THE PROBABILITY THAT IF AMERICAN AIRLINES BOOKS 15 PEOPLE, NOT ENOUGH SEATS
WILL BE AVAILABLE
Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
n = 15, p = 0.85.
The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874[/tex]
0.0874 = 8.74% probability that not enough seats will be available.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
find the zeros x^4-2x^3-44x^2-88x-32
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
What are the zeros of a polynomial expression?The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.
For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.
From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:
Using the rational root theorem:
[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]
[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]
By factorization, we have:
= (x + 2) (x + 4) (x² - 8x - 4)
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
Learn more about zeros of polynomial here:
https://brainly.com/question/2833285
#SPJ1
The Bourassas decide to sell a home for $440,000. They are charged a real estate commission of 8% of the selling price, title insurance that is 1.4% of the selling price, and an escrow fee of $775.
(a)
What amount (in dollars) do the Bourassas receive after fees?
$
(b)
What percentage of the selling price was fees? Round to the nearest tenth of a percent.
%
The amount received net of expenses is $397865 and the percentage of the sale price was 10%.
Given that Bourassas decides to sell a house for $ 440,000. You will be charged a real estate fee of 8% of the sale price, property insurance of 1.4% of the sale price, and an escrow fee of $ 775.
The declared retail price is $ 440,000.
Real estate commission = 8% of the sale price
Real Estate Fee = (8/100) × 440000
Real Estate Fee = 8 × 4400
Real Estate Fee = $ 35,200
Security insurance costs of the title = 1.4% of the sale price
Cost of title insurance = (1.4 / 100) × 440 000
Cost of title insurance = 1.4 × 4400
Title Insurance Cost = $ 6160
The escrow fee assigned is $ 775.
(a) In determining the amount received after deducting the sale price of the property commission, title insurance and escrow fees, we receive
Amount received after fees = sale price - real estate commission - title insurance - escrow fees
Amount received after fees = 440000-35200-6160-775
The amount received after fees = $397865
(b) To find the percentage of sale price, add together all the terms real estate commission, title insurance and escrow fees and divide by the sale price we get
Percentage of selling price=((35200+6160+775)/440000)×100
Percentage of sale price = (42135/440000) × 100
Percentage of sale price = 9.57
Percentage of sale price = 10% (rounded down)
Hence Bourassas decides to sell a house for $440,000, then the amount Bourassas will receive after expenses is $397,865 and the percentage of the sale price of expenses is 10%.
Learn more about selling price from here brainly.com/question/11067377
#SPJ1
When it is Noon (12 pm) in London, it is 10pm in Sydney, Australia. Dan in London rings his friend Boski in Sydney at 15:30pm on Christmas Day. What time is it in Sydney?
A. 1am
B. 1:30am
C. 2am
S. 2:30am
The time at Sydney when Dan rings his friend is 1 : 30 am (option B).
What is the time at Sydney?The first step is determine the time difference between London and Sydney.
Time difference = time at Sydney - time at London
( 12 + 10pm) - 12pm
22pm - 12pm = 10 hours
The second step is to add the time difference to the time it was when Dan rang.
15 : 30 pm + 10pm = 25 : 30
We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30
25 : 30 - 24 = 1 : 30 am
To learn more about how to calculate time, please check: https://brainly.com/question/26290873
#SPJ1
72 is 15% of what number?
Answer: 480
Step-by-step explanation:
72/3 is 5% of the number we are looking for.
72/3=24
24*20 will be 100%
480 is 100%
72 is 15% of what number?
Quantity %
72---------------15
x---------------100
We solve
[tex]\boldsymbol{\sf{x=\dfrac{72\times100 }{15}=\dfrac{7200}{15}=480 }}[/tex]
Answer: 72 is 15% of 480.
ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/18034746
Answers for number 32 and 31
Answer:
32: X=54
31: Xx54+74
What is the slope of the line that passes through the points (8, 0) and (-4, -8)?
Write your answer in simplest form.
Answer:
Step-by-step explanation:
(-8 - 0)/(-4 - 8)= -8/-12 = 2/3
The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
How to estimate the slope of the line?The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.
Using the slope formula [tex](y_2 - y_1)/(x_2 - x_1)[/tex]
[tex]x_1 = 8, y_1 = 0[/tex] and [tex]x_2 = -4 , y_2= -8[/tex]
slope [tex]= (y_2 - y_1)/(x_2 - x_1)[/tex]
= ((-8) - 0) / ((-4) - (8))
= (-8) / (-12) = (-2) / (-3)
= 0.66667
Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
To learn more about the slope of the line refer to:
https://brainly.com/question/16949303
#SPJ9
I need help… a lot of it im so confused
[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]
2)[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]
3)[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]
4)
[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]
5)[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]
6)[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]
7)[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]
8)[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]
9)[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]
HELPP PLSSS I NEED HELP!!!
Answer:
(3+3) x (3+1)
Step-by-step explanation:
free
We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.
Solution :» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
Which pair of functions are inverses of each other? O A. F(a) = I - 9 and g(2) = 2*9 O B. Ax) = 5x - 11 and g(a) = 2+11 O C. F(a) = V2m and g(2) = (3) ° O D. f(a) = ; + 8 and g(x) = 6x - 8 SUBMIT
The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
How to determine the function and the inverse?The complete question is added as an attachment
Function 1
f(x) = 5x - 11 and g(x) = (x + 11)/5
Represent 5x - 11 with y in f(x) = 5x - 11
y = 5x - 11
Swap x and y
x = 5y - 11
Add 11 to both sides
x + 11 = 5y
Divide by 5
y = (x + 11)/5
Express as a function
g(x) = (x + 11)/5
From the question, we have:
f(x) = 5x - 11 and g(x) = (x + 11)/5
This means that the function g(x) is an inverse of the function f(x)
Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
Read more about inverse function at:
https://brainly.com/question/14391067
#SPJ1
what is 7/8 - 1/2 as a fraction
Answer: 3/8
Step-by-step explanation:
1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8
ASAP help me with this question
Answer:
SAS and SSA
Kindly award branliest
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.
The criterias that guarantee congruence are :
SSSSASASAAAS[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct options are : b, c, d, eFind the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
Answer:
no mode
Step-by-step explanation:
no number appears more than once
therefore there is no mode
Find the gradient of the line joining the points P(2,5) and Q(4,-2).
How many grams of the isotope remains after 90 days?
Answer:
84,08964 [gr.].
Step-by-step explanation:
for more details see in the attachment.
Find the surface area of the composite figure 4 cm 13 cm 3 cm 4 cm 12 cm SA = [?] cm² 5 cm 3 cm.
Find one possible missing coordinate so that the point becomes a solution to the given inequality.
(x,6) is a solution to 6x−6>y .
Answer:
Step-by-step explanation:
6x-6>y
put y=6
6x-6>6
6x>12
x>12/6
x>2
(3,6) is one solution.
A barn that holds hay for the cows is shown below. If you see the hay for $1.50 per cubic foot, how much money could
you make if the barn is completely full?
If the price of 1 cubic foot of hay is $10 then the money needed is $15.
Given the price of 1 cubic foot of hay be $10 and the amount of hay be $1.50.
We are required to find the amount of money needed to buy the hay.
We know that the amount of money that can be spend on something is the product of price of one unit and number of units.
Product is the result when two numbers are multiplied with each other.
Total money =Price of 1 cubic foot*$1.50
=10*1.50
=$15
Hence if the price of 1 cubic foot of hay is $10 then the money needed is $15.
Learn more about product at https://brainly.com/question/10873737
#SPJ1
Question is incomplete, the right question is as under:
1.5 cubic foot hay is required to fill a room completely. Calculate the amount we have to pay to fill the room completely if the price of 1 cubic foot is $10?
P = √mx_ £x MX t make x the subject
[tex]p = \sqrt{ \frac{mx}{t} } - t {}^{2}x \: \: make \: x \: the \: subject [/tex]
So, making x subject of the formula, x = [m - 2pt³ ±√(m² - 4pt²m)]/{2t⁵}
How to make x subject of the formula?Since p = √(mx/t) - t²x
So, p + t²x = √(mx/t)
Squaring both sides, we have
(p + t²x)² = [√(mx/t)]²
p² + 2pt²x + t⁴x² = mx/t
Multiplying through by t,we have
(p² + 2pt²x + t⁴x²)t = mx/t × t
p²t + 2pt³x + t⁵x² = mx
p²t + 2pt³x + t⁵x² - mx = 0
t⁵x² + 2pt³x - mx + p²t = 0
t⁵x² + (2pt³ - m)x + p²t = 0
Using the quadratic formula, we find x.
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]
where
a = t⁵, b = (2pt³ - m) and c = p²tSubstituting the values of the variables into the equation, we have
[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
So, making x subject of the formula, [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
Learn more about subject of formula here:
https://brainly.com/question/25334090
#SPJ1
1 Which is the greatest 4- digit number divisible by 6?......
As fast as when u are running to save ur mom life
Answer:
The greatest four-digit number that is divisible by 6 is 9996
Step-by-step explanation:
9,996 / 6 = 1,666
Which of the following is the solution to 8√3 + 7√3?
15√9
15√6
15√3
56√3
Which of the following is the solution to √15 * √45 simplified?
√675
8√3
15√15
15√3
Which of the following is the solution to 15√10 - 3√10?
12√10
5√10
12√100
45√10
Answer:
Q1: Third Choice. 15√3
Q2: Fourth Choice. 15√3
Q3: First Choice. 12√10
Step-by-step explanation:
Question 1: Which of the following is the solution to 8√3 + 7√3?Given expression
8√3 + 7√3
Simplify by addition
Remember that terms with the same radical part can add together directly
= (8 + 7) √3
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Question 2: Which of the following is the solution to √15 * √45 simplified?Given expression
√15 × √45
Factorize each radical
= √(3 × 5) × √(9 × 5)
= √3 × √5 × √9 × √5
Simplify necessary radicals
= √3 × √5 × 3 × √5
= 3 × √3 × √5 × √5
Simplify by multiplication
When radicals multiply, combine them under one radical sign
= 3√3 × √(5 × 5)
= 3√3 × 5
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Questions 3: Which of the following is the solution to 15√10 - 3√10?Given expression
15√10 - 3√10
Simplify by subtraction
Remember that terms with the same radical part can subtract each other directly
= (15 - 3) √10
[tex]\Large\boxed{=12\sqrt{10} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions