Answer:
Solution is 4/9
Explanation:
A box contains:
2 red marbles,
3 white marbles,
4 green marbles,
1 blue marble.
=> Total: 2 + 3 + 4 + 1 = 10
After selected a blue one without replacement, the remaining number: 10 - 1 = 9
=> Probability of drawing a green one: P = 4/9.
Hope this helps!
:)
what value of x in the solution set of -5×-15>10+20
Answer:
ⁱ ʰᵒᵖᵉ ᵗʰⁱˢ ʷᵒᵘˡᵈ ʰᵉˡᵖ ʸᵒᵘ ᵗᵒ ᵍᵉᵗ ʳᵉᵃˡ ᵃⁿˢʷᵉʳ...
What is the length of the line?
square root of 119
square root of 60
13
square root of 17
Answer:
13
Step-by-step explanation:
The line is the hypotenuse of a right triangle that is 5 units high and 12 units wide. The Pythagorean theorem, or the distance formula, tells you the length is ...
length = √(5² +12²) = √(25+144) = √169
length = 13
The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?
Answer:
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
Step-by-step explanation:
Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:
[tex]x + y = 9.9[/tex]
[tex]x^{2} + y^{2} = 53.21[/tex]
First, [tex]x[/tex] is cleared in the first equation:
[tex]x = 9.9 - y[/tex]
Now, the variable is substituted in the second one:
[tex](9.9-y)^{2} + y^{2} = 53.21[/tex]
And some algebra is done in order to simplify the expression:
[tex]98.01-19.8\cdot y +2\cdot y^{2} = 53.21[/tex]
[tex]2\cdot y^{2} -19.8\cdot y +44.8 = 0[/tex]
Roots are found by means of the General Equation for Second-Order Polynomials:
[tex]y_{1} \approx \frac{32}{5}[/tex] and [tex]y_{2} \approx \frac{7}{2}[/tex]
There are two different values for [tex]x[/tex]:
[tex]y = y_{1}[/tex]
[tex]x_{1} = 9.9-6.4[/tex]
[tex]x_{1} = 3.5[/tex]
[tex]y = y_{2}[/tex]
[tex]x_{2} = 9.9 - 3.5[/tex]
[tex]x_{2} = 6.4[/tex]
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample space first.]
Answer:
[tex]p = \frac{4}{9}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Sample space:
All posible outcomes.
First answer - Second answer:
A - A
A - B
A - C
B - A
B - B
B - C
C - A
C - B
C - C
9 possible outcomes.
Probability that neither is B.
A - A
A - C
C - A
C - C
4 possible outcomes.
So
[tex]p = \frac{4}{9}[/tex]
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Circle with centre (0,2) will have the equation
(x)²+(y-2)² = r²
Finding r² by distance formula using P(-7,2)
r² = (-7-0)²+(2-2)²
r² = (-7)²
r² = 49
So substituting in the equation
x²+(y-2)² = 49
When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of the trachea, making a narrower channel for the expelled air to flow through. For a given amount of air to escape in a fixed time, it must move faster through the narrower channel than the wider one. The greater the velocity of the airstream, the greater the force on the foreign object. X rays show that the radius of the circular tracheal tube contracts to about two-thirds of its normal radius during a cough. According to a mathematical model of coughing, the velocity v of the airstream is related to the radius r of the trachea by the equation v(r)= k (r 0- r) r ^ 2, 1/2 r 0 less than r less than r0where k is a constant and r0 is the normal radius of the trachea. The restriction on r is due to the fact that the tracheal wall stiffens under pressure and a contraction greater than 1/2r0 is prevented (otherwise the person would suffocate). Determine the value of r in the interval [1/2r0, r0] at which v has an absolute maximum. How does this compare with experimental evidence?
Answer:
Step-by-step explanation:
(a)
[tex]= kr^2(r_0 - r )[/tex]
[tex]= ( kr_0)r^2 - kr^3 \\\\=>v '(r) = ( 2kr_0 )r -3kr^2\\\\= ( -3k)r^2 + ( 2kr_0 )r[/tex]
v has an absolute maximum when v '(r) = 0
v '(r) = 0 =>
( -3k )r2 + ( 2kr0 )r = 0 =>
r = [ -( 2kr0 ) ± sqrt[ ( 2kr0)2 - ( 4 )( -3k )( 0 ) ] ] / [ ( 2 )( -3k ) ]
= [ -2kr0 ± 2kr0 ] / ( -6k)
= 0 or ( -4kr0 / -6k )
= 0 or (2/3)r0
since [tex]r > (1/2)r_0[/tex] in the given interval,[tex]r =(2/3)r_0[/tex], which matches its experimental value.
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. ModifyingBelow Integral from nothing to nothing With Upper C (y minus z )ds∫C(y−z)ds; C is the helix left angle 12 cosine t comma 12 sine t comma t right angle12cost,12sint,t, for 0 less than or equals t less than or equals 2 pi0≤t≤2π The value of the ordinary integral is nothing.
C is parameterized by
[tex]\vec r(t)=\langle x(t),y(t),z(t)\rangle=\left\langle12\cos t,12\sin t,t\right\rangle[/tex]
for 0 ≤ t ≤ 2π. In the integral, replace y and z as above, and the line element ds is
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{145}\,\mathrm dt[/tex]
So the integral is
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=\sqrt{145}\int_0^{2\pi}(12\sin t-t)\,\mathrm dt[/tex]
sin(t) has period 2π, so that term contributes nothing to the integral, leaving us with
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=-\sqrt{145}\int_0^{2\pi}t\,\mathrm dt=\boxed{-2\pi^2\sqrt{145}}[/tex]
A group consists of five men and five women. Three people are selected to attend a conference.
A. In how many ways can three people be selected from this group of ten?
B. In how many ways can three women be selected from the five women?
C. Find the probability that the selected group will consist of all women.
Answer:
a) 120
b) 10
c) 1/12
Step-by-step explanation:
The number of ways that a sample of r can be selected from a population of n is:
nCr = n! / (r! (n−r)!)
a) 3 people selected from a group of 10
₁₀C₃ = 120
b) 3 women selected from a group of 5
₅C₃ = 10
c) Of the 120 committees that can be chose, 10 are all women. So the probability is 10/120 = 1/12.
It costs Neil $2.88 to make two dozen muffins. He sold the muffins for $.80 each. If Neil sold six dozen muffins how much profit did he make from the sale?
Hi!
So for this you need an equation. It will be 72 • 0.8 - 2.88 • 3
this is bc 12 x 6 is 72 and 3 bc 2 x 3 is 6.
so after you solve it you should get : $48.96..Hope this helped! :))
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final values of the stock, then:______A) A = B = CB) A = B < CC) C < B = AD) A < B < CE) B < A < C
Answer:
E) B < A < C
Step-by-step explanation:
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.
Initial Values are: A, B and C
After one year, A was up 20%, B was down 25%, and C was unchanged.
Values after one year:
A=(100%+20%) of $100=$120 worth of stock.B=(100-25%) of $100=$75 worth of stock.C=100% of $100=$100 worth of stock.For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.
Values after the second year
A=(100%-20%) of $120 =80% of $120=$96 worth of stock.B=(100%+25%) of $75 =125% of $75=$93.75 worth of stock.C=100% of $100 =$100 worth of stock.Therefore, from the final values of the stock, we have that:
B<A<C
The correct option is E.
Trey is estimating the length of a room in his house. The actual length of the room is 17 m. Trey's estimate is 15 m.
Find the absolute error and the percent error of Trey's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Absolute error = 2m
Step-by-step explanation:
Absolute Error = Measured Value - Actual Value
17m - 15m = 2m
Answer:
2m and 11.8%
Step-by-step explanation:
Absolute error is defined mathematically as;
Error/original value
[Original value - estimated value]
[17-15 ] = 2m
The percentage error would be
[Original value - estimated value]/ original value
[17-15 ] /17 × 100%
0.1176 × 100% = 11.76%
11.8%[ to the nearest tenth]
A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt. The recipe can be scaled up to make multiple loaves of bread. Complete the table that shows the quantities to use for multiple loaves of bread.
Answer:
For 2 loaves of bread, 4 cups of flour, 24 tablespoons of water, and 2 teaspoons of salt are required
For 4 loaves of bread, 8 cups of flour, 48 tablespoons of water, and 4 teaspoons of salt are required
Step-by-step explanation:
Given: A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt
To find: the missing terms in the box
Solution:
As for 1 loaf of bread, 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt are required
So, for 2 loaves of bread, double the quantity.
So, for 2 loaves of bread, 2×2=4 cups of flour, 12×2=24 tablespoons of water, and 1×2=2 teaspoons of salt are required
For 4 loaves of bread, double the quantity used to make 2 loaves of bread.
For 4 loaves of bread, 4×2=8 cups of flour, 24×2=48 tablespoons of water, and 2×2=4 teaspoons of salt are required
See the image attached.
Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n =8, p = 0.6, P(3 or fewer) Group of answer choices
Answer:
[tex]P(X \leq 3) = 0.1738[/tex]
Step-by-step explanation:
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.
In this question, we have that:
[tex]n = 8, p = 0.6[/tex]
P(3 or fewer)
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.6)^{0}.(0.4)^{8} = 0.0007[/tex]
[tex]P(X = 1) = C_{8,1}.(0.6)^{1}.(0.4)^{7} = 0.0079[/tex]
[tex]P(X = 2) = C_{8,2}.(0.6)^{2}.(0.4)^{6} = 0.0413[/tex]
[tex]P(X = 3) = C_{8,0}.(0.6)^{3}.(0.4)^{5} = 0.1239[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0007 + 0.0079 + 0.0413 + 0.1239 = 0.1738[/tex]
A cellular phone network uses towers to transit calls. Each tower transmits a circular area. on a grid of a city, the equations given represent the transmission boundaries of the towers. Tell which towers, is any, transmit to a phone located at M(3.5, 4.5).
Tower A: x^2 + y^2 = 9
Tower B: (x - 5)^2 + (y - 3)^2 = 6.25
Tower C: (x - 2)^2 + (y - 5)^2 = 4
Answer:
B
Step-by-step explanation:
Notice that
[tex](3.5-5)^2 + (4.5-3)^2 = 4.5[/tex]
Since 4.5 is less than 6.25, tower B transmits to that phone
Answer:
Towers B and C transmit to the phone.
Step-by-step explanation:
First, let see the location of the center for each tower:
Tower A
[tex]A (x,y) = (0,0)[/tex]
Tower B
[tex]B (x,y) = (5,3)[/tex]
Tower C
[tex]C(x,y) = (2,5)[/tex]
Now, the distance between the location of the phone and any of the towers by means of the Pythagorean equation. The phone is under the influence of a tower only if distance is less than transmission boundaries. Then:
Tower A
[tex]d_{A} = \sqrt{(3.5-0)^{2}+(4.5-0)^{2}}[/tex]
[tex]d_{A} \approx 5.701[/tex]
[tex]d_{A} > 3[/tex]
Tower B
[tex]d_{B} = \sqrt{(3.5-5)^{2}+(4.5-3)^{2}}[/tex]
[tex]d_{B} \approx 2.121[/tex]
[tex]d_{B} < 2.5[/tex]
Tower C
[tex]d_{C} = \sqrt{(3.5-2)^{2}+(4.5-5)^{2}}[/tex]
[tex]d_{C} \approx 1.581[/tex]
[tex]d_{C} < 2[/tex]
Towers B and C transmit to the phone.
Please answer this correctly without making mistakes
Answer:
10.99 inches
Step-by-step explanation:
7*2=14
diameter=14
circumference=diameter*pi
14*3.14=43.96
quarter circle
43.96/4=10.99
10.99 inches
Answer:
the quarter circle's perimeter = 24.99 inch
Step-by-step explanation:
1. Calculate circumference of a complete circle.
2. Divide by 4 and you have the quarter part. (This is the same as multiplying by 0.25).
3. Just like a pie chart, there are 2 sides from the center to the left and right side edge of the quarter circle. Both are equal to the radius r.
4. Add the numbers found in step 2 and step 3 and you will have found the quarter circle's perimeter.
Given: use 3.14 for pi and r = 7 inch
1. Circumference = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * 7 ) = 10.99 inch
3 Since r = 7 and we have to sides.
So you just add 2 * 7 = 14 inch
4. Add 10.99 + 14 = 24.99 inch
How do i solve 3/4 x 4 7/12 =
Answer:
2.9375
Step-by-step explanation:
3/4×47/12
3×47/4×12
141/48
2.9375
Answer:
4x12=48
48+7=55
4 7/12 as an improper fraction is 55/12
multiply the numerator with numerator and denominator with denominator
3x55=165
4x12=48
165/48 can be divided by 3
165/3=55__48/3=16
55/16 is simplified
55/16=3 r 7 so the fraction is 3 7/16
Hope this helps
Step-by-step explanation:
5x + 6y = 32
5x – 6y = 8
Which variable or variables will be eliminated when you add the system of equations?
Answer:
The variable y is eliminated.
Step-by-step explanation:
To add a system of equations, we add the common terms. x with x, y with y and values with values.
In this question:
5x + 6y = 32
5x – 6y = 8
Adding:
5x + 5x + 6y - 6y = 32 + 8
10x = 40
So the variable y is eliminated.
Answer:
10x 40
Step-by-step explanation:
Solve for x
A) 7
B) 10
C) 5
D) -7
Answer:
D) -7
Step-by-step explanation:
[tex] \because \: PQ + QR = PR \\ \therefore \: 2x + 17 + 12 = 22 + x \\ \therefore \: 2x + 29 = 22 + x \\ \therefore \: 2x - x = 22 - 29 \\ \therefore \: x = - 7 \\ [/tex]
You deposit $5000 each year into an account earning 4% interest compounded annually. How much will you have in the account in 35 years?
Answer:
$ 402,722.01
Step-by-step explanation:
Find the largest prime factor of 309^2 - 147^2.
Answer: 2^4*3^5*19
Step-by-step explanation:
You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.
The largest prime factor of 309² - 147² is, 19.
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is,
⇒ 309² - 147²
Now, We can simplify as;
⇒ 309² - 147²
⇒ (309 - 147) (309 + 147)
⇒ 162 × 456
⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19
Thus, The largest prime factor of 309² - 147² is,
⇒ 19
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
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An excavation crew is digging a tunnel under a bay. The crew has dug 573 meters of the tunnel, which is 34 meters past the halfway point. What will be the length of the tunnel when the crew has finished digging?
Answer:
The total length of the tunnel when the crew has finished digging is 1078 meters
Step-by-step explanation:
total length of the tunnel dug by the crew = 573 meters
let the halfway point of the tunnel = h
if the crew digs 34 meters past the halfway point, then we will this equation below;
h + 34 meters = 573 meters
h = 573 - 34
h = 539 meters
halfway point of the tunnel is 539 meters
Then, the total length of the tunnel when the crew has finished digging = 2h
= 2 x 539 meters
= 1078 meters
Therefore, the total length of the tunnel when the crew has finished digging is 1078 meters
81. Restaurants. About 12% of the restaurants in the US are pizzerias, and there are about 70,000 pizzerias in the US. Estimate the total number of restaurants in the United States.
Answer:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
Step-by-step explanation:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
Lauren drove the 75 miles to the coast at 75mph, but got stuck in traffic and averaged 25mph on the way back.
-How many total miles did Lauren drive in this round-trip?
-How many total hours did Lauren drive in this round-trip?
-What was the average speed Lauren was driving during this round-trip?
Answer:
Step-by-step explanation:
1) The distance that Lauren drove to the coast is the same as the distance he drove back from the coast. It means that the total miles that Lauren drove in this round-trip is
75 + 75 = 150 miles
2) time = distance/speed
Time spent in driving to the coast is
75/75 = 1 hour
His return speed is 25 mph
Time spent in driving back from the coast is
75/25 = 3 hours
3) Average speed = total distance/total time
Total distance = 75 + 75 = 150 miles
Total time = 1 + 3 = 4 hours
Average speed = 150/4 = 37.5 mph
Lines sand tare perpendicular. If the slope of line sis 5, what is the slope of
line t?
Answer:
-1/5
Step-by-step explanation:
Perpendicular lines have slopes that are the opposite reciprocal of one another.
The slope of line t is the opposite reciprocal of the slope of line s:
slope of t = -1/(slope of s)
slope of t = -1/5
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
C.
Step-by-step explanation:
Some rectangles can be squares, since they fit the criteria for both if it is a square, but not ALL rectangles can be squares, since squares have ALL 4 sides congruent, whereas rectangles only have 2 sets of sides congruent.
Solve for y 6(y-1/3) = 4(3y-5)
Answer:
y = 3
Step-by-step explanation:
It can work well to start by eliminating parentheses.
6(y -1/3) = 4(3y -5)
6y -2 = 12y -20
18 = 6y . . . . . . . . . add 20-6y to both sides
3 = y . . . . . . . . . . . divide by 6
Answer:
y=3
Step-by-step explanation:
6(y−13)=4(3y−5)
(6)(y)+(6)(−13)=(4)(3y)+(4)(−5)(Distribute)
6y+−2=12y+−20
6y−2=12y−20
Step 2: Subtract 12y from both sides.
6y−2−12y=12y−20−12y
−6y−2=−20
Step 3: Add 2 to both sides.
−6y−2+2=−20+2
−6y=−18
Step 4: Divide both sides by -6.
−6y−6=−18−6
y=3
Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph?
Answer:
Domain : 0 ≤ t ≤ 3
Range : -4 ≤ d ≤ 0
Step-by-step explanation:
The graph attached models the depth of submarine as a function of time.
Points on x-axis represent the time and points on y-axis represent increase in height of the submarine.
Domain of a function is represented by the points on x-axis.
Therefore, Domain : 0 ≤ t ≤ 3
Range of function is represented by te points on y-axis.
Therefore, Range : -4 ≤ d ≤ 0
given:f(x)=x-7 and h(x)=2x+3 write the rule for f(h(x))
Answer:
Step-by-step explanation:
h(x) = 2x + 3
f(2x+3)
2x+3 - 7
2x - 4
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
290
Step-by-step explanation:
(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290
Courtney sold 48 cantaloupes at the farmers' market and had 25 left. Which equation could be used to find x, the number of cantaloupes Courtney had originally?
Answer:
48+25=x
Step-by-step explanation:
Answer:
The answer is D :)
Thank me later.