y - 6 = 0 ................ equation 1
x - 4 = 0 ................ equation 2
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Answer:
15
Problem:
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Step-by-step explanation:
First we find 3*5 using rule a*b = 2ab - 3b.
3*5=2(3)(5)-3(5)
3*5=30-15
3*5=15
Now we are left with 2*15 in which we will still use the rule a*b=2ab-3b.
2*15=2(2)(15)-3(15)
2*15=60-45
2*15=15
Therefore, 2*(3*5)=15.
Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?
Answer:
[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]
[tex](b)\ t = 6[/tex]
[tex](c)\ t = 1.7[/tex]
Step-by-step explanation:
Given
[tex]G_0 = 100[/tex] --- initial
[tex]G(1) = 120[/tex] --- after 1 year
[tex]r \to rate[/tex]
Solving (a): The expression for g
Since the rate is constant, the distribution of G follows:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(1) = 120[/tex] implies that:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]120 = G_0 * e^{r*1}[/tex]
Substitute [tex]G_0 = 100[/tex]
[tex]120 = 100 * e^{r[/tex]
Divide both sides by 100
[tex]1.2 = e^{r[/tex]
Take natural logarithm of both sides
[tex]\ln(1.2) = \ln(e^r)[/tex]
[tex]0.1823 = r[/tex]
[tex]r = 0.1823[/tex]
So, the expression for G is:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(t) = 100 *e^{0.1823t}[/tex]
Solving (b): t when G(t) = 300
We have:
[tex]G(t) = 100 *e^{0.1823t}[/tex]
[tex]300 = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]3 = e^{0.1823t}[/tex]
Take natural logarithm
[tex]\ln(3) = \ln(e^{0.1823t})[/tex]
[tex]1.099 = 0.1823t[/tex]
Solve for t
[tex]t = \frac{1.099}{0.1823}[/tex]
[tex]t = 6[/tex] --- approximated
Solving (c): When there will be no grass
Reduction at a rate of 80 tons per year implies that:
[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]
To solve for t, we set G(t) = 0
[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]
Rewrite as
[tex]80t = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]0.8t = e^{0.1823t}[/tex]
Take natural logarithm of both sides
[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]
[tex]\ln( 0.8t) = 0.1823t[/tex]
Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]
[tex]t = 1.7[/tex]
I need help with this math problem
Answer: A) (x + 12) and (x + 9)
Step-by-step explanation:
You need to get x^2 + 21x + 108.
A) (x + 12) (x + 9) = x^2 + 12x + 9x + 108 = x^2 + 21x + 108
B) (x - 12) (x - 9) = x^2 - 9x - 12x + 108 = x^2 -21x + 108
C) (x - 27) (x - 4) = x^2 - 4x - 27x + 108 = x^2 - 31x + 108
D) (x + 27) (x + 4) = x^2 + 27x + 4x + 31 = x^2 + 31x + 31
So, the answer is A).
Answer fast please and thank you!
Step-by-step explanation:
everything can be found in the picture
Please I really need help
=======================================================
Explanation:
The triangular face has area of base*height/2 = 8*2/2 = 16/2 = 8 square feet.
Multiply this with the depth of the prism to get 8*12 = 96 cubic feet
----------
For any prism, the volume formula is
V = (area of base)*(depth of prism)
The term "depth" can be replaced with "height" and it's the same idea.
In this problem, we have a triangular prism because the parallel sides are triangles.
What is the difference of the polynomials?
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
Answers:
A.) -x^3 + 6x^2 + 9
B.) -x^3 + 2x^2 - 9
C.) 5x^3 - 2x^2 - 2x - 9
D.) 5x^3 - 2x^2 + 2x + 9
Answer:
D
Step-by-step explanation:
We want to find the difference between the two polynomials:
[tex](5x^3+4x^2)-(6x^2-2x-9)[/tex]
Distribute the negative:
[tex]=(5x^3+4x^2)+(-6x^2+2x+9)[/tex]
Rearrange the terms:
[tex]=(5x^3)+(4x^2-6x^2)+(2x)+(9)[/tex]
Combine like terms. Hence:
[tex]=5x^3-2x^2+2x+9[/tex]
Our answer is D.
An engineering consulting firm wanted to evaluate the diameter of rivet heads. The following data represent the diameters (in hundredths of an inch) for a random sample of 25 rivet heads:
(20 pts) 6.81 6.79 6.69 6.59 6.65 6.60 6.74 6.70 6.76 6.84 6.81 6.71 6.66 6.76 6.76 6.77 6.72 6.68 6.71 6.79 6.72 6.72 6.72 6.79 6.83
a. Set up a 95% confidence interval estimate of the average diameter of rivet heads (in hundredths of an inch)
b. Set up a 95% CI estimate of the standard deviation of the diameter rivet heads (in hundredths of an inch)
Answer:
a)CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % = ( 0.05 < σ < 0.089 ) ( in hundredths of an inch)
Step-by-step explanation:
From the problem statement, we have a manufacturing process and we we assume a normal distribution, from sample data:
x = 6.7328 and s = 0.0644
a) CI 95 % = ( x ± t(c) * s/√n )
t(c) df = n -1 df = 25 - 1 df = 24
CI = 95 % α = 5 % α = 0.05 α /2 = 0.025
Then from t-student table t(c) = 2.060
s/√n = 0.0644/ √ 25 s/√n = 0.01288
CI 95 % = ( x ± t(c) * s/√n ) = ( 6.7328 ± 2.060*0.01288)
CI 95 % = ( 6.7328 ± 0.02653 )
CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % of the variance is:
CI 95 % = ( ( n - 1 ) * s² / χ²₁ - α/₂ ≤ σ² ≤ ( n - 1 )*s² / χ²α/₂ )
( n - 1 ) * s² = ( 25 - 1 ) * (0.0644)² = 24* 0.00414
( n - 1 ) * s² = 0.09936
And from χ² table we look for values of
χ² α/₂ ,df df = 24 and α/2 = 0.025
χ² (0.025,24) = 12.40 and χ²₁ - α/₂ = χ² (0.975, 24)
χ² (0.975, 24) = 39.36
Then
CI 95 % = ( 0.09936 / 39.36 ≤ σ² ≤ 0.09936 / 12.40)
CI 95 % = ( 0.0025 ≤ σ² ≤ 0.0080)
Then for the standard deviation, we take the square root of that interval
CI 95 % = ( 0.05 < σ < 0.089 )
What is the value of z2 if 3z1 = 6 + 18i and z1 + z2 = 5 + 9i?
Answer:
z2=-3-3i
Step-by-step explanation:
3z1+0z2=6+18i
z1+z2=5+9i (×3)
3z1+3z2=15+27i
3z1+0z2=6+18i (-) =
-3z2=9+9i
z2=-3÷(9+9i)
z2=-3-3i
the solution set for -2x[tex]-2x^{2}+12x=0[/tex]
Which expression can be used to convert 22 Australian dollars to US dollar
Answer:26.4
Step-by-step explanation:1.2 x22
When an airplane is 35,000 feet from an air traffic control tower, the angle of elevation between the tower and the airplane is.
What is the approximate altitude, a, of the plane at this point?
A. 45,689 feet
B. 26,812 feet
C. 29,369 feet
D. 41,711 feet
Answer:
26,812 ft
Step-by-step explanation:
The drawing given is very helpful in this case. When solving problems like this, it's important to realize what trigonometric ratio we're going to use. From the given angle (50°), we are given the hypotenuse (35,000 ft) and we're trying to solve for the opposite side ([tex]a[/tex]).
So since we're trying to find the opposite side side and we have the hypotenuse, we should try to find a trigonmetric ratio between the opposite side and the hypotenuse. Using SOH-CAH-TOA, hopefully you can see that we should pick SOH (i.e. [tex]\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]). Therefore, we can set up our equation given the angle [tex]\theta=50^\circ[/tex].
[tex]\sin(50^\circ)=\frac{a}{35000}[/tex]
Since we're solving for [tex]a[/tex], we can just rearrange to get [tex]a=35000\sin(50^\circ)=26812[/tex]
Therefore, the plane's altitude [tex]a[/tex] is 26,812 ft.
The approximation altitude of the plane at 35,000 feet from an air traffic control tower will be 26812 feet hence option (B) will be correct.
What is a trigonometric function?the trigonometric functions are real functions for only an angle of a right-angled triangle to ratios of two side lengths.
The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
Given that 35000 feet are the distance between a plane and the air traffic control tower.
Hypotaneous = 35000 feet
The angle of elevation is 50°
By trigonometric function sin
Sinx = perpendicular/hypotaneous
Sin50° = Altitude/35000
Altitute = 35000 × sin50°
Altitude = 26811.55 ≈ 26812 feet will be the correct answer.
For more information about the trigonometric function
brainly.com/question/1143565
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Câu ca dao sau đây bị chi phối bởi luật bài trung, Giải thích tại sao?
“Có yêu, thì yêu cho chắc,
Bằng như trúc trắc, thì trục trặc cho luôn”.
Answer:
Hi Are you from Vietnam?
Step-by-step explanation:
Sorry i cant understand
im filipino
You are riding your bike and notice the square sign above. You mentally draw a
straight line from point A to C. Describe the angle relationship between /_DCA and
/_BCA.
===========================================================
Explanation:
When using the SSS congruence rule, we can prove that triangle DCA is congruent to triangle BCA.
Since the triangles are congruent, the corresponding pieces angle DCA and angle BCA are equal in measure (if they weren't, then the triangles wouldn't be congruent).
Recall that any square has four right angles, ie all angles are 90 degrees each. Angle DCB is cut in half to get 90/2 = 45.
The angles DCA and DCB are 45 degrees each.
Perimeter of a 14cm,10cm,6cm and 20cm shape?
Answer:
The perimeter is 50 cm.
Step-by-step explanation:
P= 14 + 10 + 6 + 20= 50 cm
HELP HELP HELP HELP solve this
Answer:
77
Step-by-step explanation:
put these numbers in order of size, smallest to largest 4.5,-1,-3,-3.5,3
Answer:
-3.5, -3, -1, 3, 4.5
Step-by-step explanation:
Answer:
-3.5, -3, -1, 3, 4.5 because the higher the negative is, the lower the number.
what is the midpoint with the line segments with end points (-4, 6) (2,-1)
Answer:
(-1, 5/2)
Step-by-step explanation:
Midpoint = (-4 + 2)/ 2 , (6 - 1)/2
= (-2/2), (5/2)
= (-1, 5/2)
Answer:
Step-by-step explanation:
The midpoints of two coordinate is = [tex]\frac{x2 + x1}{2}[/tex] , [tex]\frac{y2 +y1}{2}[/tex].
Let x2 = 2
x1 = -4
y2 = -1
y1 = 6
Solution:
[tex]\frac{2+-4}{2} , \frac{-1+6}{2} \\\\\\= (-1,\frac{5}{2})[/tex]
How many ways can a person toss a coin 16 times so that the number of heads is between 7 and 14 inclusive
50626 ways with a probability of 0.77
Step-by-step explanation:If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2
If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4
If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.
Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.
From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;
Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]
Where;
n = number of tosses
x = number of selection
number of ways of getting 7 heads;
n = 16
x = 7
=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]
=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]
=> C₁₆, ₇ = 11440
number of ways of getting 8 heads;
n = 16
x = 8
=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]
=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]
=> C₁₆, ₈ = 12870
number of ways of getting 9 heads;
n = 16
x = 9
=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]
=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]
=> C₁₆, ₉ = 11440
number of ways of getting 10 heads;
n = 16
x = 10
=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]
=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]
=> C₁₆, ₁₀ = 8008
number of ways of getting 11 heads;
n = 16
x = 11
=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]
=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]
=> C₁₆, ₁₁ = 4368
number of ways of getting 12 heads;
n = 16
x = 12
=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]
=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]
=> C₁₆, ₁₂ = 1820
number of ways of getting 13 heads;
n = 16
x = 13
=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]
=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]
=> C₁₆, ₁₃ = 560
number of ways of getting 14 heads;
n = 16
x = 14
=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]
=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]
=> C₁₆, ₁₄ = 120
Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e
11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways
P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]
= [tex]\frac{50626}{65536}[/tex]
= 0.77
An angle measures. What is the measure of its complement? (b) An angle measures 48 . What is measure 26 of its supplement?
3x – 4(x - 4) + 4 = 13
Solve for x step by step
Please answer quickly
Answer:
7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
=> 3x - 4x + 16 + 4 = 13
=> - x + 20 = 13
=> - x = 13 - 20
=> - x = - 7
=> x = 7
Answer:
x = 7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
3x - 4x + 16 + 4 = 13
-x + 20 = 13
-x + 20 - 20 = 13 - 20
-x = -7
(-x = -7)/-1
x = 7
Hope this helps.
. Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
B làm k cho mình KQ với
27. Find the length of the segment LK. (G.CO.C.10)
Show your work! (2pts)
J
1
3x
L
K
X + 6
Click to add speaker notes
Answer:
9
Step-by-step explanation:
the only thing we can say for sure is that JL is splitting the triangle and also its baseline IK in half.
so, both sides of the baseline must be equal :
3x = x + 6
2x = 6
x = 3
=> LK = x + 6 = 3 + 6 = 9
A cone has a height of 3 feet. The diameter of the base is 8 feet. What is the approximate volume of the cone in feet to the nearest hundreth?
Answer:
12.56 feet cubed
Step-by-step explanation:
Diameter of 8= radius of 4
4 x 3.14=12.56
12.56x3=37.68
37.68/3=12.56
Consider the following statement. For every integer m, 7m + 4 is not divisible by 7. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Suppose that there is an integer m such that 7m + 4 is divisible by 7.Subtracting 4m from both sides of the equation gives 7 = 4k − 4m = 4(k − m).By definition of divisibility 4m + 7 = 4k, for some integer k.By definition of divisibility 7m + 4 = 7k for some integer k.Dividing both sides of the equation by 7 results in 4 7 = k − m.Dividing both sides of the equation by 4 results in 7 4 = k − m.But k − m is an integer and 7 4 is not an integer.Suppose that there is an integer m such that 7m + 4 is not divisible by 7.But k − m is an integer and 4 7 is not an integer.Subtracting 7m from both sides of the equation gives 4 = 7k − 7m = 7(k − m).
Answer:
A proof for the statement by selecting the given sentences are as follows;
Suppose there is an integer m such that 7·m + 4 is divisible by 7
By definition of divisibility, 7·m + 4 = 7·k for some integer k
Subtracting 7·m from both sides of the equation gives 4 = 7·k - 7·m = 7·(k - m)
Dividing both sides of the equation by 7 results in 4/7 = k - m
But k - m is an integer and 4/7 is not an integer
Therefore, for every integer m, 7·m + 4 is not divisible by 7
Step-by-step explanation:
The given equation can be expressed as follows;
Where 7·m + 4 is divisible by 7, we have;
7·m + 4 = 7·k
Where 'k' is an integer
We have;
7·m + 4 - 7·m = 4 = 7·k - 7·m
∴ k - m = 4/7, where k - m is an integer
∴ k - m cannot be equal to 4/7, from which we have;
7·m + 4 cannot be divisible by 7.
Please answer part A and B.
Answer:
Percent who walk 45%
Percent in car 22.5%
Step-by-step explanation:
The total number of students is
36+26+18 = 80
Percent who walk is 36/80 = .45 =45%
Percent in car is 18/80 =.225= 22.5%
Given g(x) -x + 4, solve for a when g(x) = 8.
Answer:
x = 12
Step-by-step explanation:
g(x) - × + 4 =0
put g(x) = 8
so, 8 - x + 4 = 0
x = 12
Answer:
x = - 4
Step-by-step explanation:
Given g(x) = - x + 4 and g(x) = 8 , the equate the right sides, that is
- x + 4 = 8 ( subtract 4 from both sides )
- x = 4 ( multiply both sides by - 1 )
x = - 4
What is the equation of the directrix of the parabola?
Y=3
Y=-3
X=3
X=-3
Answer:
its x=-3
Step-by-step explanation:
Help me pleassseeeee
Answer:
8x+(-20x)
Step-by-step explanation:
Find the area of the composite area
Sarah bought a TV for £250
Three years later she sold it for £180
Work out her percentage loss
Answer:
36%
Step-by-step explanation:
Step-by-step explanation:
Loss percentage= loss/cost× 100%
250-180=70
70/180=0.3888
0.3888×100%=39%
