An operator at the top of a lighthouse sights a sailboat. The point from which the sighting is made is 25 m above sea level. The angle of depression of the sighting is 10 degrees. How far is the boat from the base of the lighthouse?

Answers

Answer 1

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


Related Questions

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?

Answers

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.

Learn more about derivative here
https://brainly.com/question/29144258



#SPJ11

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.

Answers

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.

Know more about vectors here,

https://brainly.com/question/24256726

#SPJ11

solve the following question

Answers

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].

Write the exact value of the side length, in units, of a square whose area in square units is: 100/9

Answers

Answer: 10/3 units

Step-by-step explanation: sqrt 100/9= 10/3

find the missing angle measurement

Answers

3x+7+10x+17=180
13x+24=180
Subtract 24 from both sides
156/13
x= 12

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?

Answers

Divide the total tomatoes in use by the average amount of tomatoes used in a single batch.

1,236/42 = 29.428 (about 29 batches can be made)

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

Answers

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.

Learn more about chain rule here: brainly.com/question/30764359

#SPJ11

Find the area of this kite.
3 m
5 m
6 m
5 m

Answers

Answer:

450m

Step-by-step explanation:

Can someone help me with this. Will Mark brainliest.

Answers

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

Please help, I can’t figure this answer out and I’m really struggling on it!

Answers

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.

Read more on polynomial and multiplicity here: brainly.com/question/13652616

#SPJ1

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 )

Answers

Answer:

A

Step-by-step explanation:

Because That's The Main Idea

what goes up a hill with three legs and goes down a hill with four legs?

Answers

Answer:

i don't know what goes up with three leg and goes down with 4

Answer:

u

Step-by-step explanation:

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

Answers

Answer:

C) 1/2

Step-by-step explanation:

3 of the 6 numbers on a cube are even. 3/6 = 1/2

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

Answers

Answer: The correct answer will be 4

Step-by-step explanation:

Solve for x and the length of segment GH.

Answers

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

I’m not sure how to solve this problem

Answers

Answer:

a

Step-by-step explanation:

PLS hurry!! I'LL MARK BRAINLIEST!

Answers

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

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)

Answers

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.

Simplify 7a - 3(b - a)​

Answers

Answer:

10a-3b is your answer

Step-by-step explanation:

7a - 3(b - a)

7a-3b+3a

10a-3b

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?

Answers

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

Help me please!! If you do you will get 25 points :)

Answers

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 .

kohl's rectangular gold garden has an area of 54 square feet wood what would be their dimensions of the garden

Answers

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.

Learn more about area here:

https://brainly.com/question/1631786

#SPJ11

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).

Answers

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.

To know more about Euler's method refer to

https://brainly.com/question/30699690

#SPJ11

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!!!!

Answers

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.

To know more about marginal tax rate refer to:

https://brainly.com/question/29418051

#SPJ11

plsssssss help
got 20 mins​
the question is: The sin of angle DCB is

Answers

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

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

Answers

b because l*w*h and then you do multiplication and you get the answer

Given f(x)=9+x and g(x)=3x-2, evaluate: fg(x)

Answers

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

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

Answers

you will have 1/6 odds
You will have 1/12 odds

put the cells in the right spot please :(

Answers

The First one is a eukaryote.
The Second one is a prokaryote.
The Third one is a prokaryote.
The Fourth one is a eukaryote.
The Fifth one is a prokaryote.
The Sixth one is a eukaryote.
The last one is a prokaryote.


Hope it helps.☺️

what is the equation for a Vertical Shift 5 units up?

Answers

f(x) = x2 + 5

This function comes from the basic function f(x) = x2 with the constant 5 added to the outside. This gives the basic function a vertical shift UP 5 units.
Other Questions
Which of these are characteristics of herbaceous stems? (Select all that apply.)A. dont increase in diameterB. more pliableC. stiffD. thin 20 PIONTSWhich statement correctly compares individuals in earlier stages of development with those in the generativity vs. stagnation stage? Individuals in earlier stages care about romance and sex, while those in the generativity vs. stagnation stage no longer do. Individuals in earlier stages are developing their brainpower, while those in the generativity vs. stagnation stage are beginning to experience cognitive decline. Individuals in earlier stages are more reliant on the older generations, while those in the generativity vs. stagnation stage are concerned with giving to the next. Individuals in earlier stages experience more stable emotions, while those in the generativity vs. stagnation stage are prone to anxiety and depression. Discussion Question 01-09 a. Explain the typical shapes of the marginal-benefit and marginal-cost curves. The marginal-benefit curve is upward sloping. The marginal-cost curve is upward sloping. b. With these curves, the optimal allocation of resources to a particular product will occur when MB MC c. If current output is such that marginal cost exceeds marginal benefit, should more or fewer resources be allocated to this product? Fewer Select the correct comparison Listen to Julie describe her neighborhood in Montral, Canada, and answer the question. You may copy and paste the accented characters from this list if needed: Quand est-ce que sa mre fait des courses?https://lti.flvsgl.com/flvs-cat-content/9tp8jav8uatei8imeo54a1hu6h/flvs-cat-session/educator_french2_v13_3_gs/module05/lesson06/interactives/05_06_05/screen4.mp3 as a result of the distribution, quinlan corporation has a realized loss of $fill in the blank 2 of whic Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent. At the 0.10 level of significance, is there sufficient evidence to reject the null hypothesis? The line passes through the points (3, 7) and (4, 9) The grocery store is mile from Katies house and the gas station is 0.5 mile from Katies house.Which comparison of these distances is both true and correctly justified?A. Because 0.5 < , the gas station is closer than the grocery store.B. Because 0.5 < , the grocery store is closer than the gas station.C. Because < 0.5, the gas station is closer than the grocery store.D. Because < 0.5, the grocery store is closer than the gas station. When a real zero x = a of a polynomial function fis of even multiplicity, the graph of f ---Select-- the x-axis at x = a, and when it is of odd multiplicity, thegraph of f ---Select-- the x-axis at x = a. NEED TO SUBMIT THIS IN 10 MINS, PLS HELP!!!! HELP ME PLSA native of Houston, Texas, she served in the Texas Senate (1967-1973) and in the U.S. House (1973-1979), becoming the first African American woman to do so from Texas since Reconstruction. Kay Bailey Hutchinson Miriam Ferguson Ann Richards Barbara Jordan Select all the representations that are appropriate for comparing bite strength to weight for different carnivores. 1. Scatter plot 2. Box plot 3. Histogram 4. Table 5. Dot plot The following information was extracted from the consolidated financial statements for 2020 and 2021 of Bahrain Company and its 70% owned Sitra Inc. 1. Sales revenue amount to $430,000. 2. Cost of goo Which is the BEST statement of what the speaker wants?A) to become a political leaderB)to no longer have to plant cropsC) to be treated fairly and equallyD) to move to a country that respects women An assignment model with 3 tasks and 4 resources will have how many constraints, assuming no special constraints and not including non-negativity? 1278413Which of the following is not part of assignment models?Binary ConstraintsResourcesTasksWarehousesAll of the above are a part of assignment models.Which of the following statements will lead to an infeasible solution?Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 4 resources.Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources.The supply for Node A is 550 and the supply for Node B is 600. The demand for Node C is 700. The demand for Node D is 400.The supply for Node A is 375 and the supply for Node B is 525. The demand for Node C is 450 and the demand for Node D is 500.More than one option above will lead to an infeasible solution. Help Read the following passage:"Scrabble players, rejoice! Exult! Savor! Pick whatever word you have the letters to spell. Today Merriam-Webster announced it hasadded 300 new words to the official Scrabble dictionary. Players will most appreciate additions in four categories."Two-letter words, like new entries 'OK' and 'ew' are especially useful in Scrabble. They make it easier to form parallel, overlappingwords, and are also good when nothing else seems to work."Words spelled with 'q' but not 'u' are prized because it's so hard to draw both letters at the same time. Now the category has two newmembers, 'qapik' and 'qapiks.' There are so few of these words that any addition is a big help, even if no one knows what it means. (Aqapik is a unit of money in Azerbaijan.)"Buzz words and foreign words are great because most people think they aren't allowed. Newly acceptable buzz words include'sheeple,' 'yowza,' and 'twerk. Play these and now legal foreign words such as 'bibimbap' and 'schneid' with a guilty look, and you may beable to trick your opponents into making a losing challenge."The main idea of this reading is that Scrabble players will be most happy with certain kinds of additions to the official Scrabble dictionary.Which selection below is a minor supporting detail of the reading?O It's rare to draw both a "q" and a "u."O Tricking an opponent into challenging a newly legal word is a good Scrabble strategy.O Merriam-Webster publishes the official Scrabble dictionary.O Scrabble players will be especially pleased to have access to more two-letter, "q" without "u," foreign, and buzz words, Kei buys a table and 12 chairs. Each chair cost the same price. The table cost $165. The total cost for the table and 12 chairs is $ 465. What is the cost of one chair? Which expression is equivalent to -8?O-2-3-392-3