ABCDE is a circle centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and DE = 14 cm. The radius of the circle is r

Answer: 120

Step-by-step explanation:

[tex]\displaystyle\\10.8:0.09=\\\\\frac{10.8}{0.09}=\\\\\frac{10.8(100)}{0.09(100)}=\\\\\frac{1080}{9} =\\\\\frac{9(120)}{9}=\\\\120[/tex]

This operation is equivalent to:

It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.

As we can see, h(x) have terms with x + 4, so if we call:

We can see that h(x) becomes:

And if we substitute g(x) by x, we will get the expression of the ouside function f(x):

This way, we have:

So, the functions are:

Answer:

y = 5

Step-by-step explanation:

the equation of a horizontal line, parallel to the x- axis is

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 5, 5 ) and (0, 5 ) with y- coordinates 5 , then

y = 5 ← equation of line

Answer:

1422.5778

Step-by-step explanation:

8.89x8.89=79.0321. 79.0321x18=1422.5778

Answer:

Answer down below!

Step-by-step explanation:

(Part a):

So we have the information that after 20 minutes, the submarine descended 480 feet.

To find how many feet it descended per minute, all we need to do is divide 480 and 20 which will give us 24

Every 1 minute, the submarine descended 24 feet.

(Part b):

Now that we have how many feet it descended per minute, we have to make an expression that goes along with it.

Our unknown variable in this case will have to have to be the feet.

We can use the letter f to express that. We can also use the letter m to express our minutes in the end

So after 24(f) = m

(Part c):

After 5 Minutes: 120 ft

After 10 Minutes: 240 ft

After 15 Minutes: 360 ft

After 18 Minutes: 432 ft

The elevation is 848 feet.

The word elevation is often used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying aeroplanes or orbiting satellites, and depth is used to describe locations below the surface.

A geographical feature's elevation is determined by how high it is above the mean sea level (MSL). Accordingly, elevation is the distance between the height that corresponds to the ocean's surface and the top of the feature.

Given:

Hilda hiked up 530 feet,

down 602 feet,

up 1003 feet,

and down 89 feet to get to the lake.

Taking all similar cases together

Hiked up

= 530 + 1003

= 1533 feet

and, hiked down

=602+83

= 685

Thus, the elevation is

= 1533 - 685

= 848

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The best description for the sequence of transformation used is; Rigid Transformations.

In mathematics, a rigid transformation is defined as a geometric transformation of a defined Euclidean space that does not change or preserves the Euclidean distance that is between every pair of points. Examples of this rigid transformations are rotations, translations, reflections e.t.c

Now, from the given transformation, the first thing to notice is that the transformation does not change the distance between pair of points in the diagram. Secondly, it is neither only a translation nor reflection as it is more than  one transformation that was used and so it can be described as a rigid transformation.

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The total number of students that are on the team is e. 210 if the ratio of  freshmen to sophomores to juniors to seniors is 1:3:4:6

As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;

Freshmen = 1x

Sophomores = 3x

Juniors = 4x

Seniors = 6x

As the number of juniors on the team is 60, therefore;

4x = 60

To determine the value of x we divide both sides by 4;

4x/4 = 60/4

x = 15

Now the total number of students can be found by substituting the value of x;

1x + 3x + 4x + 6x

1(15) + 3(15) + 4(15) + 6(15) = 210

Hence, the total number of students on the team is 210.

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A measure of the probability that the sample's average IQ is below 987 is 44.70 %.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.

The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.

Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.

Z-score = (X- μ)/σ

             = (98-100)/15

             = -0.1333

P value for this z score equals 0.4470 which is 44.70 %

Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.

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The evaluation of the composite function (g o f)(0) is -4

A composite function is generally a function that is written inside another function.

Therefore, let's solve the composite function below:

f(x) = 1x

g(x) = x - 4

Let's find (g o f)(0)

Therefore,

(g o f)(x) = g(f(x))

Hence,

(g o f)(0) = g(f(0))

f(0) = 1(0) = 0

Therefore, let's substitute f(0) in g(x)

(g o f)(0) = 0 - 4

(g o f)(0) =  - 4

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Answer:

Step-by-step explanation:

We are looking for a new number which is 350 more than 400.

We will get the new number by adding 350 to 400.

We write it down as:

400+350=750

Therefore your answer is; 750

Answer: 750

Step-by-step explanation: You add both of them 350+400...

The student's first error was in step 1.

Step 1 should involve plotting a point at (0, 1).

Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).

Step 3, connecting the points with a line was correct.

In this question, we have been given an equation of line y + 5 = - 3/4 (x - 8)

We need to describe and correct the error a student made when graphing y + 5 = - 3/4 (x - 8).

Consider given equation.

y + 5 = - 3/4 (x - 8)

y + 5 = - 3/4 x - (-3/4) 8

y + 5 = -3/4 x + 6

y = (-3/4)x + 6 - 5

y = -3/4 x + 1

Here,

slope(m) = (-3/4)

and y-intercept (c) = (0, 1)

Therefore, the student's first error was in step 1.

Step 1 should involve plotting a point at (0, 1).

Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).

Step 3, connecting the points with a line was correct.

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Mandy must to walk a distance of 24.73 units towards Mark.

Given:

Mark is standing at 35th Street and 21st Avenue, so his location can be determined using the coordinates (35,21)

Mandy is positioned at 59th Street and 15th Avenue, hence her position's coordinates are as follows: (59,15).

We must now determine the distance Mandy must travel if Mark stays where he is and walks to meet him.

We can use the distance formula to determine this:

D = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1})^{2} } }[/tex]

Here,

(x₁, y₁) =  (35, 21)

(x₂, y₂) = (59, 15)

Then,

D = [tex]\sqrt{(59-35)^{2}+(21-15)^{2} }[/tex]

D = [tex]\sqrt{24^{2} +6^{2} }[/tex]

D = [tex]\sqrt{576+36}[/tex]

D = √612

D = 24.73

That is,

Mandy must to walk a distance of 24.73 units towards Mark.

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The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

The given equation is 3x+3y²+6y+3=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Left

Vertex: (0, -1)

Focus: (-1/4, -1)

Axis of symmetry: y=-1

Directrix: x = 1/4

The coordinate points to plot (2, 0.41), (-2, -2.41), (-1, 0), (-1, -2) and (0, -1).

The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

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Answer:

6.3 * 10^3

Step-by-step explanation:

6.3 * 10^3

:]

To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation, i.e, a new weight function, as follows: We want the elements with maximum weight to have minimum weight and. In other words, two weight functions need to be mutually opposite in this sense. Therefore, if we denote the maximum weight of all the elements with w ∗ : w ∗ = max w(x) x ∈ S we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly. Since we want the weight function to be strictly positive, we finish our construction with: w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation,

or a new weight function, as follows:

We want the elements with maximum weight to have minimum weight a In other words, two weight functions need to be mutually opposite in this sense.

Therefore, if we denote the maximum weight of all the elements with

w ∗ : w ∗ = max w(x) x ∈ S

we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly.

Since we want the weight function to be strictly positive, we finish our construction with:

w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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Answer:

-3

Step-by-step explanation:

It was quite easy

Answer:

Step-by-step explanation: factor out x2

from the expression x2 (x+11) -3x-33

Factor out-3 from the expression x2 (x-+11) -3(x+11)

Factor out x+11 your solution is x2 (x+11) (x-3).

The annual percentage yield is 1.55% for any account if the interest is compounded daily.

Given that Island bank is advertising a special 1.55% APR for long-term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily.

Principal (P) = $40000

Interest rate(r) = 1.55% = 0.0155

Number of periods (n) = 365

The formula for Annual Percentage Yield (APY) for an account that is compounded continuously is given as

APY = [1 + (r/n)ⁿ - 1]

Substitute the values in the formula to get

= [1 + (0.0155/365)³⁶⁵ - 1]

= [1 + 0.000042)³⁶⁵ - 1]

= [1.000042]³⁶⁵- 1

= 1.015448 - 1

= 1.55%

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Answer:

400

Step-by-step explanation:

=

1

We know that:

3 R=4% 1 = 48

T =3 R = 4% into formula 48 2 Substitute

1=Prt

48= Prt

Solve the equation:

3 × 0.04x= 48

3

X = 400

so Pablo invested 400$

The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

So, the flat rate is $7 and we're charged $0.65 per mile:

Then the suitable expression will be:

Cost if we traveled 15 miles:

So, 0.65x = y where x = 15.

It would cost $9.75 for 15 miles.

Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

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The measure of angle A is found as 115 degrees.

For the given question, the values of the angles are given.

A=(3x-35)

B=(x-35)

c=x

We know that the sum of all angles in a triangle is 180.

A + B + C = 180

Put the values;

3x-35 + x-35 + x = 180

Simplifying;

5x - 70 = 180

5x = 250

x = 50

Put the values in the angles;

Angles A = 3×50 - 35

Angles A = 115

Thus, the measure of angle A is found as 115 degrees.

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Answer:

a)

f(1/2) = 2

g(-1) = -3/2

Step-by-step explanation:

for f(x) = 2x + 1 substitute the x with 1/2

2(1/2) +  1 then solve

1+1

2

for g(x) = 3x - 1/2x + 1 substitute with -1

3(-1) - 1/2(-1) +1 then solve

-3 + 1/2 + 1

-3/2

The probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

Given that, we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e., they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution.

Therefore, the probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

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"Your question is incomplete, probably the complete question/missing part is:"

Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:

1. Flip the coin.

2. Flip the coin again.

3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.

(a) Show that the result is equally likely to be either heads or tails.

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

If she wants to meet her target distance 3/20 steps need to be taken.

Emily made the decision to walk 4/5 kilometers every day in order to keep healthy. She walked a distance of 2/5 miles to work and a distance of 1 mile for lunch.

The desired range is 4/5 miles.

walked for 2/5 miles and for 1/4 miles.

Total miles walked is [tex]\frac{2}{5} + \frac{1}{4}[/tex]

= [tex]\frac{13}{20}[/tex]

Mileage walked overall is +

LCD is 20

add the fractions after matching the denominators

The desired range is 4 to 5 miles.

Now deduct the distance you walked from the goal distance.

[tex]\frac{4}{5} - \frac{13}{20} \\\\\frac{16}{20} - \frac{13}{20} \\\\\frac{3}{20}[/tex]

the required walking distance is 3/20

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Answer:

y= -3x+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

So, you have to isolate the variable. Think of it as finding how many plants she gave fertilizer to. 0.4n+8=25, when moving the 8 to the other side, it becomes negative. 0.4n=25-8. 0.4n=17. You then find the variable n. think of it as dividing 17 by 0.4 or multiplying n a certain number of times to find the number of plants.17/0.4 is 42.5. therefore, she gave 42 plants fertilizer, depending on what your teacher wanted to count. If she says round down, 42. If she wants to round up, 43. If she wants to be specific, 42.5. I would personally put the decimal.

y = f(2x)  ⇒ Shrink the graph of function f(X) by half horizontally .

What is function and example?

y = f((1/2)x)) ⇒ Stretch the graph of f(x) horizontally by factor 2 .

y=2f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

                     Shrink the graph twice ( vertically) .

y = f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

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