Answer:
Hello,
Step-by-step explanation:
AB=DC=b, AD=BC=a
p=BD, q=AC
angle ABC=x
[tex]AB^4+AD^4+AB^2*AD^2=AC^2*BD^2\\\\b^4+a^4+b^2a^2=(a^2+b^2+2abcos(X))(a^2+b^2-2abcos(X)\\\\(a^2+b^2+2a^2b^2)-a^2b^2=((a^2+b^2)^2-4a^2b^2*cos^2(X))\\\\\\4a^2b^2cos^2(X)=a^2b^2\\\\\\cos^2(X)=\dfrac{1}{4} \\\\(cos(X)-\dfrac{1}{2} )(cos(X)+\dfrac{1}{2} )=0\\cos(x)=\frac{1}{2} \ or\ cos(X)=\dfrac{-1}{2} \\\\\\X=60^o =\dfrac{\pi}{3} rad \ or \ X=120^o=\dfrac{4\pi}{3} rad\\\\\\\\Product=\dfrac{\pi}{3}*\dfrac{4\pi}{3} =\boxed{\dfrac{4\pi^2}{9}}\\[/tex]
A piece of art is in the shape of an equilateral triangle with sides of 7 inches each. Find the area of the piece of art to the nearest tenth. Explain how you know.
Answer:
21.2 in²
Step-by-step explanation:
The area of an equilateral triangle is given as :
Area, A = √3/4 * a²
Where, a = side length of the equilateral triangle
a = 7 inches ; Recall that all sides of an equilateral triangle are the same.
Put a = 7 in the equation :
A = √3/4 * a²
A = √3/4 * 7²
A = 0.4330127 * 49
A = 21.217 in²
Area, A = 21.2 in²
PLEEASE HELP ME IM RUNNING LATE
If mC = 49 , find the values of x and y.
Answer:
m∠y=41
m∠x=90
Step-by-step explanation:
It is an isosceles triangle, so m∠B=49 too
49+49=98
180-98=82
82÷2=41
m∠y=41
41+49=90
180-90=90
m∠x=90
I need help with this
Answer:
C
The lines will intersect once because this systems has one solution
Step-by-step explanation:
Start by putting everything into slope intercept form (AKA y=mx+b
2x-4y=3
2x-3=4y
y= .5x-.75
And the other one
7y-5x=8
-5x-8= -7y
y=(5x+8)/7
Because their slopes are different there's an intersection
Because their y intercepts are different there's only 1 solution
4, 1 and 0, -4 on a graph
Answer:
Hope this will help.
Assume that thermometer readings are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in celsius degrees)
Between -1.42 and 1.61
The probability of getting a reading between -1.42 degrees C and 1.61 degreesC is_______ ( round to four decimal places as needed)
Answer:
The probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.
Step-by-step explanation:
We are given that
[tex]Mean,\mu=0[/tex] degree C
Standard deviation, [tex]\sigma=1[/tex] degree C
We have to find the probability of the reading between -1.42 and 1.61.
[tex]P(-1.42<x<1.61)=P(\frac{-1.42-0}{1}<\frac{x-\mu}{\sigma}<\frac{1.61-0}{1})[/tex]
[tex]P(-1.42<x<1.61)=P(-1.42<Z<1.61)[/tex]
[tex]P(-1.42<x<1.61)=P(Z<1.61)-P(Z<-1.42)[/tex]
Using the formula
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
[tex]P(-1.42<x<1.61)=0.94630-0.07780[/tex]
[tex]P(-1.42<x<1.61)=0.8685[/tex]
Hence, the probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.
Write down all the Subsets of {20,40}
Answer:
{20}, {40}, {20,40}, { }
A person can see the top of a building at an angle of 65°. The person is standing 50 ft away from
the building and has an eye level of 5 ft. How tall is the building to the nearest tenth of a foot?
O 107.2 ft
O 112.2 ft
O 50.3 ft
O 26.1 ft
9514 1404 393
Answer:
(b) 112.2 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
For the given geometry, this becomes ...
tan(65°) = (height above eye level)/(50 ft)
Then we have ...
(height above eye level) = (50 ft)tan(65°) = 107.2 ft
Adding the height of eye level will give us the height of the building.
building height = (eye level height) + (height above eye level)
building height = (5 ft) + (107.2 ft)
building height = 112.2 ft
[tex]8-x/(x-3)(x-4)[/tex]
How to do this please help
Answer:
[tex]\frac{1}{9}[/tex] feet³
Step-by-step explanation:
[tex]\frac{1}{3}[/tex]×[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{2}[/tex]=[tex]\frac{2}{18}[/tex]=[tex]\frac{1}{9}[/tex]
Answer:
V = 1/9 ft^3
Step-by-step explanation:
The volume is given by
V = l*w*h where l = length, w = width, h = height
V = 1/3 * 2/3 * 1/2
V = 2/9*1/2
V = 1/9 ft^3
The birth rate of a population is b(t) = 2000e0.023t people per year and the death rate is d(t)= 1410e0.017t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.) people
Answer: 7118
Step-by-step explanation:
Given
Birth rate is [tex]b(t)=2000e^{0.023t}[/tex]
Death rate is [tex]d(t)=1410e^{0.017t}[/tex]
Area between them is given by
[tex]\Rightarrow A=\int _0^{10}2000e^{0.023t}-1410e^{0.017t}dt\\\Rightarrow A=\int _0^{10}2000e^{0.023t}dt-\int _0^{10}1410e^{0.017t}dt\\\Rightarrow A=22486.95652 -15368.99999\\\Rightarrow A=7117.95652[/tex]
Thus, the area between the curves is [tex]7117.95652\approx 7118[/tex]
Please help!!!!!!!!!!!!
9514 1404 393
Answer:
(c) 16°
Step-by-step explanation:
The external angle at P is half the difference of the intercepted arcs:
P = (90° -58°)/2 = 32°/2
P = 16°
Halp me please. This questions is killing me. I need the answer. Solve $3a + 4b = a - 8b + 24$ for $a$ in terms of $b$.
Answer:
a=12-6b
Step-by-step explanation:
move b and a to their respective sides, getting a = -6b+12
tada :)
As per linear equation, the value of 'a' in terms of 'b' will be
a = 12 - 6b.
What is a linear equation?A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.
Given, (3a + 4b) = (a - 8b + 24)
⇒ 3a - a = - 8b + 24 - 4b
⇒ 2a = - 12b + 24
⇒ a = (- 12b + 24)/2
⇒ a = - 6b + 12
⇒ a = 12 - 6b
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help with plz thank you
Your answer is in the attachment..
Hope the answer helps you..
.
.
Select it as the BRAINLIEST..
Answer:
38. skipping by 3s
14, 17, 20, 23, 26, 29, 32, 35, 38
Someone help me pls !!!!!
Answer:
1)a
the problem asks"what PERCENT of 5 is 4?"
2)part
it gives both the percent and the whole, so your left with the part
3)Whole
4 is a part which is 80%
Step-by-step explanation:
The global surface water area is 361, 132,000 square metres. Calculate the volume of water needed to cause a 3mm in sea level.
Answer:
The volume of water is 396 cubic meter.
Step-by-step explanation:
Area of water, A = 132000 square meter
Height, h = 3 mm = 0.003 m
The volume of water is given by
V = Area x height
V = 132000 x 0.003
V = 396 cubic meter.
what value of n make an equation??
Answer:
[tex]\frac{4}{27}[/tex]
Step-by-step explanation:
simplify the terms on both sides;
12*18*n=32
n*216=32
n=32/216
simplified --> 4/27
you can check by plugging it back into the equation;
12*n*3*6=4*8
12*(4/27)*3*6=32
216*(4/27)=32
32=32
A. Two numbers are in the ratio 5:7. When 3 is added to each number, the new ratio becomes 3 : 4. Find the numbers.
Answer:
answer is 3 and ratio of two different numbers
PLEASE HELP WILL MARK BRAINLIEST
Using the table above, if the reserve requirement is 10%, then the additional amount the bank could loan out is
$40,000
$60,000
$300,000
$340,000
$1,800,000
Simplify 12w + 2 (w + 3)
Answer:
= 14w + 6
Step-by-step explanation:
= 12w + 2w + 6
Add similar elements: 12w + 2w = 14w
= 14w + 6
please help asap! i rlly need help on this
A. y=x+7
B. y= x-7
C. y=-5x+2
D. y=5x+2
A television stand at Wiles' Discount Mart is $187, and the sales tax is 6%. What is the amount of tax to be paid for the TV?
Answer:
$11.22
Step-by-step explanation:
100% = 187
1% = 187/100 = $1.87
6% = 1%×6 = 1.87×6 = $11.22
Answer:
In this case, you need to calculate the 6% of the price, which is 187 $.
We only need to multiply the price (187) by the percentage (6%):
187 * 0.06 = 11.22
So the tax would be $11.22
Which ratio expresses the scale used to create this drawing?
1 square=10 yards
Answer:
option B
Step-by-step explanation:
option B
gdyfudjfjghfhguftduc
In the triangle shown below (not to scale), what is the angle gamma, y, when
A=6.8, B= 8.4, and C = 11.5? Answer in degrees rounded to at least
the nearest hundredth.
ILL GIVE YOU BRAINLIEST!
Answer:
γ = 97.77°
Step-by-step explanation:
A = 6.8
B = 8.4
C = 11.5
To find γ, apply the angle version of the Law of Cosines:
Cos γ = (A² + B² - C²)/(2AB)
Plug in the values
Cos γ = (6.8² + 8.4² - 11.5²)/(2*6.8*8.4)
Cos γ = -15.45/114.24
Cos γ = -0.1352
γ = Cos^{-1}(-0.1352)
γ = 97.77° (nearest hundredth)
Find X?
please help?
Look at one side of the triangle. It forms a right triangle with 45 degree angles.
A 45 degree triangle the base and height are the same, so the height would also be 26.
The hypotenuse(x) of a 45 degree right triangle is the side length time the sqrt(2)
The answer is: 26 sqrt(2)
p=2,-3 and Q= -1,4. Evaluate 3q-2p
Answer:
When p=2 , q=-1
3q-2p
3(-1) - 2(2)
(3)-4
-1
When p=-3 , q=4
3(4)-2(-3)
(12 )-(-6)
=18
A new restaurant sells cheeseburgers for 6$, french fries for 3$, and salads for 8$ On opening night, the restaurant sold items and made 1070$. They sold 4 times as many fries as salads. How many cheeseburgers were sold?
Answer:
25 cheeseburger
Step-by-step explanation:
I checked and get that 4 times fries as many as salad means that fries = 4 times Salad.
Brainliest please~
25 cheeseburgers were sold.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Let cheeseburger be x
Price of x = 6
Let French Fries be y
Price of y = 3
Let salads be z
Price of z=8
x+ y+ z =220
6x + 3y + 8z = 1070
4 y = z 4 times as many as
= 4 times - Fries is more than Salad
Substitute 3 in 1
x + 4 z + z =220
x+5z =220
Substitute 3 in 2
6x + 12z +8z = 1070
6x + 20z = 1070
3x + 10z - 535
From 4: x=220-5z
Substitute into 3 (220-5z) +10z = 535
660 - 15z+10z=535
- 5z = - 125
z = 25
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A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution.
(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.
The probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. 0.03310
The probability that their hospital stay is greater than 6 days, rounded to five decimal places. 0.96610
We are given the following information in the question:
Mean, =7.37 days
Standard Deviation, σ = 0.75 days
We are given that the distribution of hospital stays is a bell-shaped distribution that is a normal distribution.
What is the formula for z score?[tex]z_{score}=\frac{x-\mu }{\sigma}[/tex]
a) P( hospital stay is from 5 to 6 days)
[tex]P(5\leq x\leq 6)=P(\frac{5-7.37}{0.75} \leq z\frac{6-7.37}{0.37})\\=P(-3.16\leq z\leq -1.827)\\=0.034-0.001\\=0.0310\\=3.10%[/tex]
[tex]P(5\leq x\leq 6)=3.31%[/tex]
b) P(hospital stay is greater than 6 days)
P(x > 6)
Calculation of the value from the standard regular z table, we have,
[tex]P(x > 6)=P(z\leq -1.827)[/tex]
[tex]P(x > 6)=1-0.0339\\=0.0399\\=0.96610\\=96.61%[/tex]
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PLEASE i need the answers!!!!!!!!!
I have no time please if you know the answer please tell MEEE!!!!!!!!!!!
Answer:
5x^2(2-3x)
(n+4)(x+y)
Step-by-step explanation:
5. A Ferris wheel at an amusement park measures 16m in diameter. It makes 3 rotations
every minute. The bottom of the Ferris wheel is 1m above the ground. Riders board the
Ferris wheel at the minimum point.
a) Determine the equation that models Emily's height (m) with respect to time (in seconds)
above ground. [3A]
b) A 12m tree stands near the Ferris wheel. For how long (in seconds) is Emily higher than
the tree during the first rotation? Round to 2 decimal places. [4A]
Following are the responses to the given points:
For point a:
[tex]Diameter\ (d)= 16\ m\\\\[/tex]
Calculating the 3 rotations for every minute:
Calculating time for completing 1 rotation:
[tex]1\ rotation=\frac{60}{3}= 20\ second\\\\period=20 \ second\\\\[/tex]
The standard form of the equation of the sine and cosine function is:
[tex]y=A \sin \{ B(x-c)\} +D\\\\y=A \cos \{ B(x-c)\} +D\\\\[/tex]
Calculating the Amplitue:
[tex]A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\[/tex]
Calculating the phase shift:
for [tex]\sin[/tex] function: [tex]c=5[/tex]
for [tex]\cos[/tex] function: [tex]c=10[/tex]
Calculating the vertical shift:
[tex]\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\[/tex]
For point b:
[tex]y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\[/tex]
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There are two independent file servers in a web site. Either file server works with a probability of 0.6. And this web site is up if either file server is working. The probability that the web site is up is _____.
Answer:
The probability that the web site is up is 0.84 = 84%.
Step-by-step explanation:
For each web server, there are only two possible outcomes. Either it is working, or it is not. The probability of a web server being working is independent of any other web server, which meas that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Either file server works with a probability of 0.6.
This means that [tex]p = 0.6[/tex]
Two servers.
This means that [tex]n = 2[/tex]
The probability that the web site is up is
At least one server working, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84[/tex]
The probability that the web site is up is 0.84 = 84%.
