Answer:
141.78 m
Step-by-step explanation:
Let d = distance of boat from the base of the lighthouse
Tan 10 = 25/d
d tan 10 = 25
d = 25/tan 10
d = 141.78 m
Given f(x)=9+x and g(x)=3x-2, evaluate: fg(x)
Answer:
(f*g)(x) = 3x^2 + 25x - 18
Step-by-step explanation:
(f*g)(x) represents the product of the two functions f and g:
(f*g)(x) = 27x - 18 + 3x^2 - 2x, or, after simplification,
(f*g)(x) = 25x - 18 + 3x^2, or
(f*g)(x) = 3x^2 + 25x - 18
put the cells in the right spot please :(
a rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2 − x 2 . what are the dimensions of such a rectangle with the greatest possible area?
To find the dimensions of the rectangle with the greatest possible area inscribed in the parabola y = 2 - x^2, we need to maximize the area function by determining the x-coordinate where the derivative of the area function is zero.
Let's consider a rectangle with its base on the x-axis, which means its height will be given by the y-coordinate of the parabola. The width of the rectangle will be twice the x-coordinate. Therefore, the area of the rectangle is given by A = 2x(2 - x^2).
To maximize the area, we take the derivative of A with respect to x and set it equal to zero to find critical points. Differentiating A, we get dA/dx = 4 - 6x^2.
Setting 4 - 6x^2 = 0 and solving for x, we find x = ±√(2/3).
Since the rectangle is inscribed, we consider the positive value of x. Therefore, the x-coordinate of the upper corner of the rectangle is √(2/3). Plugging this value back into the equation of the parabola, we get y = 2 - (√(2/3))^2 = 2 - 2/3 = 4/3.
Hence, the dimensions of the rectangle with the greatest possible area are a base of length 2√(2/3) on the x-axis and a height of 4/3.
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Aim High To The Sky
James McDonald
Aim high to the sky,
In all that you do.
Because you just never know,
What it takes to be you.
Be strong and be brave,
But at the same time be kind.
And always be sure,
That you're using your mind.
Based on the poem the reader can conclude that the speaker -
A. feels effort and thoughtfulness to others are all important
B, thinks trying your best is the only important thing
C.feels that success is the most important thing in life
D. thinks that everyone will succeed if they work hard enough
( PLEASE HELP )
Answer:
A
Step-by-step explanation:
Because That's The Main Idea
Help me please!! If you do you will get 25 points :)
Answer:
24 units by 15 units
Step-by-step explanation: To find how many units the length and width are, divide each by 5:
120/5 = 24
75/5= 15
For every 5 feet, there is 1 unit .
PLS hurry!! I'LL MARK BRAINLIEST!
Answer:
A. 5+x-12=2x-7
-7+x+2x-7
x=2x
x-2x=0
-x=0-> x=0
B.
when X=-0.5
5+(-0.5)-12=2 (-0.5)-7
-7.5=-8 (answer does not work)
when X=0
5+0-12=2(0)-7
-7=-7 (answer works)
when x=1
5+1-12=2(1)-7
18=-5 (answer does not work)
Step-by-step explanation:
Answer:
[tex]x=0[/tex]
Step-by-step explanation:
A) From this case you would need to narrow down the whole equation...
Like this: [tex]5+x-12=2x-7[/tex] → [tex]x-7=2x-7[/tex] → [tex]x=0[/tex]
B) To prove that one of these numbers solve the equation, we would have to check it ourselves.
Like this: [tex]5+(-0.5)-12=2(-0.5)-7[/tex] → [tex]-7.5=-8[/tex] (SO THIS WON'T WORK)
[tex]5+0-12=2*0-7[/tex] → [tex]0=0[/tex] (THIS WORKS!)
[tex]5+1-12=2(1)-7[/tex] → [tex]-6=-5[/tex] (NOR DOES THIS WORK)
Therefore: [tex]x=0[/tex] will work to solve the equation correctly
Over the past month, a garment manufacturer produced 800 dresses. The distribution of the amount of fabric required to make the dresses is
not normal.
The average amount of fabric needed to make a dress is 4 yards, with a standard deviation of 2 of a yard. Suppose a series of samples, each
containing 180 dresses, are selected from the dresses produced in the past month.
Would it be appropriate to model the distribution of a sample mean with a normal model?
Answer:
Yes it will be appropriate to model the distribution of a sample mean with a normal model
Step-by-step explanation:
Given that the population is not normal, and the sample is sufficiently large, according to the Central Limit theorem, the distribution of the mean pf the sampling distribution will be approximately normal not withstanding the population from which the sample is obtained. Therefore, the mean, [tex]\overline x[/tex], and the standard deviation, [tex]\dfrac{\sigma}{\sqrt{n} }[/tex], of the sample will be equal to the mean, μ, and standard deviation, σ, of the of the population
Therefore, it will be appropriate to model the distribution of a sample mean with a normal model
Answer:
yes
Step-by-step explanation:
i got it right on plato
solve the following question
Given:
The expressions are:
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]
To find:
The simplified form of the given expressions.
Solution:
We have,
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]
It can be written as:
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{12a^{2+1}bc^3}{40b^4c^2}[/tex]
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{3-2}}{10b^{4-1}}[/tex]
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{1}}{10b^3}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{3a^{3}c}{10b^3}[/tex].
We have,
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]
It can be written as:
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{(x+y)(x-y)}{4(x+y)}\cdot \dfrac{x+y}{x-y}[/tex]
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{x+y}{4}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{x+y}{4}[/tex].
Min is about to roll a six-sided number cube.What is the probability that she will roll an even number? A) 1/4.. B) 1/3 C) 1/2 D) 5/6
Answer:
C) 1/2
Step-by-step explanation:
3 of the 6 numbers on a cube are even. 3/6 = 1/2
Please help, I can’t figure this answer out and I’m really struggling on it!
The exponent on the (x - 1) term include the following: A. 3.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By critically observing the graph of this polynomial function, we can logically deduce that it has a zero of multiplicity 3 at x = 1, a zero of multiplicity 1 at x = 3, and zero of multiplicity 2 at x = 4;
x = 1 ⇒ x - 1 = 0.
(x - 1)³
x = 3 ⇒ x - 3 = 0.
(x - 3)
x = 4 ⇒ x - 4 = 0.
(x - 4)²
Therefore, the required polynomial function is given by;
P(x) = (x - 1)³(x - 3)(x - 4)²
Exponent of (x - 1)³ = 3.
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kohl's rectangular gold garden has an area of 54 square feet wood what would be their dimensions of the garden
Kohl's rectangular gold garden has an area of 54 square feet. To determine the dimensions of the garden, we need to find two numbers whose product is 54.
To find the dimensions of the garden, we can factorize the area of 54 square feet. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Since the garden is rectangular, we are looking for two numbers whose product is 54.
By examining the factors, we can see that the dimensions of the garden could be 6 feet by 9 feet, as their product is indeed 54. Alternatively, the garden could have dimensions of 3 feet by 18 feet, as their product is also 54. Both sets of dimensions result in an area of 54 square feet.
Therefore, the possible dimensions of Kohl's rectangular gold garden could be either 6 feet by 9 feet or 3 feet by 18 feet.
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find the missing angle measurement
Can someone help me with this. Will Mark brainliest.
Answer:
b(-1,-8)
Step-by-step explanation:
assuming x2 and y2 are the coordinates of b.
and x1 and y1 are the coordinates of A
midpoint are (xm, ym)
formula xm= (x1+x2)/2
ym=(y1+y2)/2
Consider the following IVP: y' = ty +t^2, 0<= t<= 2, y(0) = 1 The exact solution of this IVP is y(t) = y = -t^2 – 2(t + 1) + 3et Use Euler's method with step size h = 0.1 to approximate y(1).
The approximate value of y(1) using Euler's method with a step size of h = 0.1 is 1.
Using Euler's method and a step size of h = 0.1, we can use the given initial value problem (IVP) and iterate through the interval [0, 1] in steps of size h to approximate the value of y(1). Let's begin by determining the number of steps required: n = (1-0) / 0.1 = 10.
Utilizing the accompanying recipe, we can repeat through the span beginning with the underlying condition y(0) = 1.
y(i+1) is equivalent to y(i) + h * (t(i) * y(i) + t(i)2), where I is among 0 and n-1, t(i) is equivalent to I * h, and y(i) is the surmised worth of y at t(i).
At each step, we can inexact the upsides of y utilizing the recipe gave:
The approximate value of y(1) is 1, assuming Euler's method and a step size of h = 0.1. y(0) = 1 y(1) y(0) + 0.1 * (0 * y(0) + 02) = 1 + 0.1 * (0 + 0) = 1.
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Note: In the following problem, it is important to show all the steps used to get your answers.
Suppose an imaginary closed economy is characterized by the following:
C = c0 + c1 (Y − T)
T = 300 I = 400 G = 400
C is consumption, Y and YD are, respectively, income and disposable income, T is the level
of taxes, I and G, are, respectively, private investment, and government spending.
c0 and c1 are, respectively, autonomous consumption and the marginal propensity to con-
sume; their values are unknown. However, the expression for private saving, S, is as specified
below.
S = 0.5Y − 500
1. Find the equilibrium values of GDP, consumption, disposable income, and private saving.
(5 points)
2. Find the expression of the investment multiplier in terms of c0 and/or c1. (3 points)
3. Find the values of c0 and c1 and the value of the investment multiplier (Hint: you’ll prob-
ably find c0 is equal to an even number, which is multiple of 2). (5 points)
4. From this question on, you must use when needed the values of c0 and c1 found in the pre-
vious question. Suppose now that the government tax revenue, T, has both autonomous
and endogenous components, in the sense that the tax level depends on the level of in-
come.
T = t0 + t1Y
t0 is the autonomous tax level, and t1 is the marginal tax rate.
Given the values of private investment and government spending mentioned above, find
the expression for the equilibrium GDP in terms of c0, c1, t0 and t1. (4 points)
5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same
level of equilibrium GDP as the one obtained (1). (4 points)
6. Find the expression for the investment multiplier in terms of c1and t1 and possibly c0, and
t0. (4 points)
7. Assume now that private investment, I, increases by 50. Find the change in GDP, ∆Y,
induced by the change in investment, ∆I = 50. (4 points)
8. The government does not like the change in GDP induced by the increase in private in-
vestment. It wants to bring it back to the level found in Question (1). For that purpose, it
has the options to change its spending or to change taxes.
(a) If the government changes its spending alone, find the level of ∆G required to coun-
teract the effect on GDP of the fall in investment. (4 points)
(b) If the government changes instead the level of its autonomous taxes alone, find the
level of ∆t0 required to counteract the effect on GDP of the fall in investment. Explain
what happened. (4 points)
(c) How does ∆G compare to ∆t0? Explain the difference, if there is any. (4 points)
(d) In which direction should the government change its marginal tax rate, t1 (increase
or decrease), if it uses it as the sole policy instrument to counteract the effect of the
change in investment? Explain intuitively your answer. (4 points)
Only need to answer 5-8 questions!!!!
5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same level of equilibrium GDP as the one obtained
(1). Solution: Given, T = t0 + t1Y and T = 300
Substituting the given values, we get300 = 200 + t1YGDP, Y = C + I + G + X - M
where, Y = GDP; C = consumption; I = private investment; G = government spending; X = exports; M = imports
We know, C = c0 + c1 (Y − T) Disposable income, YD = Y − T
So, C = c0 + c1 (Y − T) = c0 + c1YD
From the question, S = 0.5Y − 500
We know that, private saving, S = Y − C − T
So, Y − C − T = 0.5Y − 500 ⇒ 0.5Y = C + T + 500
Putting the values,
0.5Y = (c0 + c1YD) + T + 500 ⇒ 0.5Y = (c0 + c1(Y - T)) + T + 500 ⇒ 0.5Y = c0 + c1Y - c1T + T + 500
Solving the above expression, we get
0.5Y - c1Y = c0 - 0.5T + 500 ⇒ 0.5(1-c1)Y = c0 - 0.5T + 500
Hence, Y = (c0 - 0.5T + 500) / (0.5 - c1)
Again, from the question, Y = C + I + G + X - M
Substituting the values we get,
(c0 + c1(Y − T)) + 400 = I + 400 + Y - 500 + X - X0.5Y − 500 + 400 = I + 300 + X − G ⇒ 0.5Y + I = 1200 + G + X
Assuming equilibrium GDP Y = Y*, private investment I = I*, government spending G = G* and net exports X = X*, so0.5Y* + I* = 1200 + G* + X*
Now, from the given information of S, we have S = Y* − C* − T.
Substituting for C* from the equation above, we get S = Y* − (c0 + c1(Y* − T)) − T ⇒ S = Y* − c0 − c1Y* + c1T − T
Substituting for Y* from above, we have S = ((c0 - 0.5T + 500) / (0.5 - c1)) - c0 - c1[((c0 - 0.5T + 500) / (0.5 - c1))] + c1T - T
Now, we need to find the value of t1 when t0 = 200. For this, we need to substitute the value of t0 and Y* in T = t0 + t1YSo, 300 = 200 + t1Y* ⇒ t1 = (300 - 200) / Y* ⇒ t1 = 0.1
Therefore, the value of the marginal tax rate t1 is 0.1.
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Simplify 7a - 3(b - a)
Answer:
10a-3b is your answer
Step-by-step explanation:
7a - 3(b - a)
7a-3b+3a
10a-3b
You roll 2 six sided dice. What are the odds of rolling 2 sixes?
A. 1/6
B. 1/36
C. 1/18
D. 1/12
Marianna is painting a ramp for the school play in the shape of a right triangular prism. The ramp has dimensions as shown below. She will not paint the back or bottom surfaces of the ramp. What is the surface area of the ramp?
Just include the front and sides of the ramp.
A
4 square inches
B
300 square inches
C
2,905 square inches
D
3,672 square inches
Answer: The correct answer will be 4
Step-by-step explanation:
Find the area of this kite.
3 m
5 m
6 m
5 m
Answer:
450m
Step-by-step explanation:
I’m not sure how to solve this problem
Answer:
a
Step-by-step explanation:
Solve for x and the length of segment GH.
Answer:
If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.
45(45) = (2x + 75)(27)
2,025 = (2x + 75)(27)
2x + 75 = 75, so x = 0 and GH = 48
CORRECT ANSWER GETS BRAINLIEST
The difference between two numbers is 15. Find the two numbers if twice the small number plus three times the large number total 75. (Be sure to use let statments and an equation when solving)
Answer:
21 and 6
Step-by-step explanation:
a will be the larger, b the smaller:
a - b = 15
2b + 3a = 75
First, we'll solve the first equation for a in terms of b:
a = b + 15
Then substitute that in for a in the second equation to get a numerical value for b:
2b + 3(b + 15) = 75
2b + 3b + 45 = 75
5b = 30
b = 6
Next, we'll get a numerical value for a:
a - b = 15
a - 6 = 15
a = 21
Check the math:
2(6) + 3(21) = 12 + 63 = 75
Please lmk if you have questions.
consider the vectors v1, v2, v3 in r2 (sketched in the accompanying figure). vectors v1 and v2 are parallel. how many solutions x, y does the system xv1 yv2 = v3 have? argue geometrically.
There is exactly one solution if v3 lies on this line, and no solution otherwise.
Given: vectors v1, v2, v3 in R2
We know that the vectors v1 and v2 are parallel, and we are asked to find the number of solutions of the system xv1 + yv2 = v3. We will argue geometrically.
Let us say that v1 and v2 are not equal to zero and are parallel to the x-axis. We can then write:
v1 = (a, 0)
v2 = (b, 0)
where a and b are nonzero constants. Since v1 and v2 are parallel, their cross-product is zero:
v1 × v2 = a*0 - 0*b = 0
This means that v1 and v2 are linearly dependent. Thus, we can express v2 as a scalar multiple of v1:
v2 = k*v1
where k is a nonzero constant. We can then substitute these expressions into the system and solve for x and y:
xv1 + yv2 = v3
xv1 + y(k*v1) = v3
(x + ky)v1 = v3
Since v1 is nonzero, the equation has a unique solution if and only if (x + ky) is nonzero. But (x + ky) is zero if and only if x = -ky, which is the equation of a line passing through the origin and perpendicular to v1 and v2. Thus, there is exactly one solution if v3 lies on this line, and no solution otherwise.
To see this geometrically, we can sketch the vectors v1, v2, and v3, and the line passing through the origin and perpendicular to v1 and v2. If v3 lies on this line, then there is exactly one solution, which corresponds to the intersection of the line and the vector v3. If v3 does not lie on this line, then there is no solution, since the line does not pass through v3.
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what is the equation for a Vertical Shift 5 units up?
A pizza parlor uses 42 tomatoes for each batch of tomato sauce. About how many batches of sauce can the pizza parlor make from its last shipment of 1,236 tomatoes?
plsssssss help
got 20 mins
the question is: The sin of angle DCB is
Answer:
i. <DCB = [tex]53.13^{o}[/tex]
ii. Sin of <DCB = 0.8
Step-by-step explanation:
Let <DCB be represented by θ, so that;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Thus from the given diagram, we have;
Sin θ = [tex]\frac{4}{5}[/tex]
= 0.8
This implies that,
θ = [tex]Sin^{-1}[/tex] 0.8
= 53.1301
θ = [tex]53.13^{o}[/tex]
Therefore, <DCB = [tex]53.13^{o}[/tex].
So that,
Sin of <DCB = Sin [tex]53.13^{o}[/tex]
= 0.8
Sin of <DCB = 0.8
what goes up a hill with three legs and goes down a hill with four legs?
Answer:
i don't know what goes up with three leg and goes down with 4
Answer:
u
Step-by-step explanation:
Multiple Choice
What is the volume of the pyramid?
A pyramid with height 8 ft and width 7ft.
A. 56 ft³
B.
130 two-thirdsft³
C. 196 ft³
D. 392 ft³
Assume x and y are functions of t.
Evaluate dy/dt for 4xy-3x+4y^3= -76 dx/dt =-8, x=4, and y=-2
The value of dy/dt for the given equation and values is -6.
To evaluate dy/dt, we can differentiate the given equation with respect to t using the chain rule. Starting with the equation 4xy - 3x + 4y^3 = -76, we differentiate both sides with respect to t.
Differentiating each term separately, we get:
(d/dt)(4xy) - (d/dt)(3x) + (d/dt)(4y^3) = 0
Using the chain rule, we can rewrite this as:
4(dy/dt)(x) + 4x(dy/dt) - 3(dx/dt) + 12y^2(dy/dt) = 0
Substituting the given values dx/dt = -8, x = 4, and y = -2, we have:
4(dy/dt)(4) + 4(4)(dy/dt) - 3(-8) + 12(-2)^2(dy/dt) = 0
Simplifying the equation, we get:
16(dy/dt) + 16(dy/dt) + 24 + 48(dy/dt) = 0
80(dy/dt) = -24
(dy/dt) = -24/80
(dy/dt) = -3/10
(dy/dt) = -0.3
Therefore, dy/dt evaluates to -0.3.
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Write the exact value of the side length, in units, of a square whose area in square units is: 100/9
Answer: 10/3 units
Step-by-step explanation: sqrt 100/9= 10/3