An image of a sailboat has one triangular sail that is labeled. The base corner labeled as a right angle. The base of the triangle is labeled 14 feet hypotenuse is labeled 38 feet

Answer:

9

Step-by-step explanation:

Answer:

there are nine teachers

Step-by-step explanation:

This can be modeled with the linear function.

f(x) = 530 - 20x

We can model this with a linear function. We know that the initial volume of the tank is 530 gallons, and we know that she uses 20 gallons per week.

So, if the variable x describes the number of weeks, the volume at week x will be 530 gallons minus 20 gallons times x.

This is written as a linear function:

f(x) = 530 - 20x

That function gives the volume left after x weeks.

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Answer: 33

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

Area of a triangle = \(\frac{bh}{2} \\\) (base × height ÷ 2)

A = 6 · 11
       2

A = 66
      2

A = 33

When the level of significance of a test is 5%, you can tell that the probability of committing a Type II error is 95%.

We know that Type I error is the probability of rejecting a null hypothesis when it is true and is represented by α (alpha). And the Type II error is the probability of accepting a null hypothesis when it is false and is represented by β (beta).

Now, Type II error is inversely proportional to the level of significance. As α increases, β decreases and vice versa. Hence, if the level of significance is 5%, then the probability of committing a Type II error is 95%.

So, the probability of committing a Type II error (β) is 95%.

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Answer:

a

Step-by-step explanation:

Answer:

C = A/d - b/d or C = (A - b)/d

Step-by-step explanation:

A = b + cd

A - b = cd

A/d - b/d = c

Answer:

;-; like 100?

Step-by-step explanation:

The answers to the graph that shows the function y = q* are solved and stated above.

       \($e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }\)

Given is a exponential graph as shown in the image.

The coordinates of the point of intersection of the curve with the y-axis is (0, 1).

The function is -

y = qˣ

At x = 1, y = 4. So, we can write -

4 = q

q = 4

y = 4ˣ

y = 4¹⁰

y = 64 x 64 x 64 x 4

y = 1048576

Therefore, the answers to the graph that shows the function y = q* are solved and stated above.

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Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

The relationship between the given equations and the variable T is that they all represent a linear relationship between two variables, where one variable is a constant multiple of the other variable. The constant multiple is given by the coefficient of the variable, which is 0.25, 0.50, 0.40, and 0.75 for the given equations, respectively.

we can use the given table to find the constant of proportionality between the distance from home and time taken to walk that distance. We can do this by calculating the ratio of the distance from home to the time taken at each point, and then finding the average of those ratios. For example, at 10 minutes, the distance from home is 1.5 miles, so the ratio is 1.5/10 = 0.15. Similarly, at 20 minutes, the ratio is 1/20 = 0.05, and at 30 minutes, the ratio is 0.5/30 = 0.0167.

Taking the average of these ratios, we get: (0.15 + 0.05 + 0.0167)/3 = 0.0722 (rounded to four decimal places)
Therefore, the constant of proportionality between the distance from home and time taken to walk that distance is 0.0722, which is a decimal. This means that for every minute you walk, you travel 0.0722 miles away from home, assuming you maintain a constant walking speed.To find the constant of proportionality as a decimal for the given situation, you'll first need to understand the relationship between the time and distance from home. The table provided shows the following information:Time (min) | Distance from home (mi)
10         | 1.5
20         | 1
30         | 0.5
To find the constant of proportionality (k), you can use the formula: k = distance / time Using the first data point (10 minutes, 1.5 miles), calculate the constant of proportionality: k = 1.5 miles / 10 minutes = 0.15 miles per minute So, the constant of proportionality for walking home at a constant rate is 0.15 miles per minute.

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B. Homer was a poet who made use of oral tradition to compose the Iliad and the Odyssey, stories of the Trojan war and its aftermath that were important later Greeks as a means of teaching the aristocratic values of honor and courage.

Homer was significant to education after the collapse of the Mycenaean civilization as he authored the Iliad and Odyssey which became an important source of education for the Greeks in later years.

They were taught to the aristocratic Greeks who learned from the values of honor and courage portrayed in the stories. The poems of Homer were recited and taught for years in the form of an oral tradition by bards until they were written down.

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Answer:

\((- \infty, 2), (2, \infty)\)

Step-by-step explanation:

Given the function:

\(f(x) = \dfrac{x+1}{x-2}\)

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function \(f(x)\) are the values of \(x\) for which the output \(f(x)\) is a valid value.

i.e. The function does not tend to \(\infty\) or does not have \(\frac{0}0\) form.

So, we will check for the values of \(x\) for which \(f(x)\) is not defined.

For value to tend to \(\infty\), denominator will be 0.

\(x-2\neq 0 \\\Rightarrow x \neq 2\)

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function \(f(x)\).

Hence, the answer is:

\(\bold{(- \infty, 2), (2, \infty)}\)     [2 is not included in the domain].

Company B charges a $55 initial price plus an extra $0.90 for every mile traveled. For 70 miles, Company A will charge less than Company B.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

$118 in change and unrestricted mileage

B affects the initial $550 and the cost per mile traveled.

Let m stand for the distance covered.

So inequality is

118 < 55 + 0.90 m

= 0.90 m > 118 - 55

= m > 63/0.90

= m > 70

So for 70 miles above company A changed less than company B.

Complete question:

Karen is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $118 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

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a) The relation R from set A={13, 17, 29, 45} to set B={4, 6, 22, 60} is {(13,4), (13,6), (13,60), (17,6), (17,22), (29,22)}.

b) R is a function from A to B.

a) We need to find all pairs of elements (a, b) such that aRb, where a is an element of set A and b is an element of set B. According to the definition of R, aRb if and only if a+b is a prime number.

Let's start with the first element of set A, which is 13. We need to find all elements of set B that satisfy the condition a+b is a prime number, where a=13. We have:

13+4=17 (prime)

13+6=19 (prime)

13+22=35 (not prime)

13+60=73 (prime)

So, for a=13, the elements of set B that satisfy the condition are 4, 6, and 60. We can repeat this process for the other elements of set A to find all pairs of elements (a, b) such that aRb. The results are:

For a=17, the elements of set B that satisfy the condition are 6 and 22.

For a=29, the element of set B that satisfies the condition is 22.

For a=45, there are no elements of set B that satisfy the condition.

Therefore, the relation R from set A to set B is {(13,4), (13,6), (13,60), (17,6), (17,22), (29,22)}.

b) To determine if R is a function from A to B, we need to check if each element of set A is related to at most one element of set B. In other words, we need to check if there are any duplicate elements in the first coordinate of the ordered pairs in R.

In our case, there are no duplicates in the first coordinate, so each element of set A is related to at most one element of set B. Therefore, R is a function from A to B.

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Answer: Does, 12, 0

Step-by-step explanation:

Because the function has a - in front it is facing downwards which means there is a max at the vertex

To find the vertex you can use x=-b/2a  There is no b so x=0 plug that into equation:

y=-3(0)²+12   y=12   So at (0,12) there is a max

To fill in blanks

does

12

0

Step-by-step explanation:

This is a dome shaped parabola  (because the coefficient of x^2 is negative)

  max occurs at   x = -b/2a      where b = 0   and a = - 3

         so max occurs at x = 0

             plug in x = 0 to find out what that max is

                      max = 12

The rοtatiοn wiII be (x, y) → (y, -x).

Resizing an οbject is accοmpIished thrοugh a change caIIed diIatiοn. The οbjects can be enIarged οr shrunk via diIatiοn. A shape identicaI tο the sοurce image is created by this transfοrmatiοn. The size οf the fοrm dοes, hοwever, differ. A diIatatiοn οught tο either extend οr cοntract the οriginaI fοrm. The scaIe factοr is a phrase used tο describe this transitiοn.

The scaIe factοr is defined as the difference in size between the new and οId images. An estabIished Iοcatiοn in the pIane is the center οf diIatatiοn. The diIatiοn transfοrmatiοn is determined by the scaIe factοr and the center οf diIatiοn.

ABC is rοtated 270 cIοckwise abοut the οrigin tο prοduce A'B'C".

The ruIe that best describes a 270-degree cIοckwise rοtatiοn abοut the οrigin is:

(x, y) → (y, -x)

Hence the rοtatiοn wiII be (x, y) → (y, -x).

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Answer:

$53.30

Step-by-step explanation:

2.5% of 52 is 1.3

1.3 + 52 = 53.30

hope this helped :)

Answer:

$53.30

Step-by-step explanation:

Cost of lunch : $52

Tax : 2.5%

Divide the tax (2.5%) by 100

2.5 ÷ 100 = 0.025

Multiply 0.025 by the cost of the lunch ($52) to get the sales tax.

52 × 0.025 = 1.3

Now, add 1.5 (sales tax) with 52 (cost of lunch).

52 + 1.3 = 53.30

So, the total cost of the lunch + tax is $53.30.

Hope this helped !

Answer: 4=-2x -1 and y=-1 2x

Answer:

The plane have traveled 1512.9 m from the time took off

Step-by-step explanation:

Acceleration \(a = 20m/s^2\)

Initial speed = u = 0

Final speed = v = 246 m/s

Time = t = 93

We are supposed to find how far would the plane have traveled from the time took off

We will use equation of motion

\(v^2=u^2+2as\\(246)^2=2\times 20 \times s\\\frac{(246)^2}{2 \times 20}=s\\1512.9 m=s\)

Hence The plane have traveled 1512.9 m from the time took off

Answer:

100°

Step-by-step explanation:

Since x and the 100 degree angle which is highlighted in blue are vertical to each other, they are parallel to each other as it is vertically opposite angles.

If they are parallel, it means

Angle highlighted in blue = 100°

x = 100°

Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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Answer:

The surface area is 1,070 ft².

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

To find the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3, we need to first find the derivative of r with respect to θ, and then evaluate it at θ = π/3.

Differentiating both sides of the polar equation with respect to θ, we get:

dr/dθ = d/dθ(2 - sinθ)

dr/dθ = -cosθ

So, the derivative of r with respect to θ is -cosθ.

Evaluating this derivative at θ = π/3, we get:

dr/dθ|θ=π/3 = -cos(π/3) = -1/2

Therefore, the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

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i) The marginal rate of substitution (MRS) at the given bundle X = 1 and Y = 16 is 64.

ii) The graph should have the horizontal axis labeled as "X" ranging from 0 to 16, and the vertical axis labeled as "Y" also ranging from 0 to 16. The given bundle X = 1 and Y = 16 should be marked as a point on the graph. The indifference curve that passes through this bundle should be drawn as a curve on the graph, following the equation X * Y = 16. Ensure that the indifference curve passes through the point representing the given bundle accurately.

To find the marginal rate of substitution (MRS) at a given bundle, we need to calculate the ratio of the marginal utilities of the two goods.

Given that the consumer's utility function is U(X, Y) = X^(1/2) * Y^(1/2), and the given bundle is X = 1 and Y = 16, we can proceed with the calculations.

i) MRS:

The marginal utility of X, MUx, is the derivative of the utility function with respect to X:

MUx = ∂U/∂X = (∂/∂X) (X^(1/2) * Y^(1/2))

   = (1/2) * Y^(1/2) * X^(-1/2)

   = (1/2) * Y^(1/2) / X^(1/2)

   = (1/2) * Y/X

Similarly, the marginal utility of Y, MUy, is:

MUy = ∂U/∂Y = (∂/∂Y) (X^(1/2) * Y^(1/2))

   = (1/2) * X^(1/2) * Y^(-1/2)

   = (1/2) * X^(1/2) / Y^(1/2)

   = (1/2) * X/Y^(1/2)

Now we can calculate the MRS by taking the ratio of MUx to MUy:

MRS = MUx / MUy

   = [(1/2) * Y/X] / [(1/2) * X/Y^(1/2)]

   = (Y/X) * (Y^(1/2)/X)

   = Y^(3/2) / X^(3/2)

   = 16^(3/2) / 1^(3/2)

   = 16^(3/2)

   = 64

Therefore, the MRS at the given bundle X = 1 and Y = 16 is 64.

ii) Now, let's draw the graph. Since we are scaling each axis up to 16, the graph will be limited to that range.

On the horizontal axis, plot the amount of good X, ranging from 0 to 16. On the vertical axis, plot the amount of good Y, also ranging from 0 to 16.

Label the axes as "X" and "Y" respectively.

Now, locate the given bundle X = 1 and Y = 16 on the graph by marking a point.

To accurately draw the indifference curve that passes through this bundle, we need to find the equation of the indifference curve.

The utility function U(X, Y) = X^(1/2) * Y^(1/2) represents a perfect complement utility function, implying that the consumer wants to consume X and Y in fixed proportions.

To find the equation of the indifference curve, we set the utility function equal to a constant value, say C.

X^(1/2) * Y^(1/2) = C

Squaring both sides:

X * Y = C²

Now, let's find the value of C for the given bundle X = 1 and Y = 16:

1 * 16 = C²

C² = 16

C = 4

Therefore, the equation of the indifference curve passing through the given bundle is X * Y = 4^2 = 16.

Carefully and accurately draw this indifference curve on the graph, ensuring it passes through the point representing the given bundle X = 1 and Y = 16.

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Answer:

Step-by-step explanation:

Volume = πr²h = πr²12.5 = 245

r ≈ 2.5 cm

Use the fundamental theorem of calculus and the given information the value of f(7) is 15.

First, we know that f'(x) is continuous, which means we can use the fundamental theorem of calculus to find the antiderivative of f'(x), denoted as F(x):

F(x) = ∫ f'(x) dx

Since we know that ∫ 7 5 f'(x) dx = 15, we can use this to find the value of F(7) - F(5):

F(7) - F(5) = ∫ 7 5 f'(x) dx = 15

Next, we can use the fact that f(5) = 13 to find F(5):

F(5) = ∫ f'(x) dx = f(x) + C

f(5) + C = 13

where C is the constant of integration.

Now we can solve for C:

C = 13 - f(5)

Plugging this back into our equation for F(7) - F(5), we get:

F(7) - F(5) = ∫ 7 5 f'(x) dx = 15

F(7) - (f(5) + C) = 15

F(7) = 15 + f(5) + C

F(7) = 15 + 13 - f(5)

F(7) = 28 - f(5)

Finally, we can use the fact that F(7) = f(7) + C to solve for f(7):

f(7) + C = F(7)

f(7) + C = 28 - f(5)

f(7) = 28 - f(5) - C

Substituting C = 13 - f(5), we get:

f(7) = 28 - f(5) - (13 - f(5))

f(7) = 15

Therefore, the value of f(7) is 15.

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