express cos r as a fraction in simplest terms

The measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, center of dilation is P and scale factor is 1/3.

In the given triangle ABC, AB=12.4 units, AC=6.7 units and BC=12.7 units

Now, A'B'=12.4/3

A'B'= 4.1 units

A'C'=6.7/3

A'C'= 2.2 units

B'C'=12.7/3

B'C'= 4.2 units

Therefore, the measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.

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If you assume that there is a 0.990.99 percent chance that you will find a prize in the cereal box, the odds are 99:1.

A probability is a measure of how likely or likely it is that a certain event will occur. Probabilities can be represented as percentages between 0% and 100% as well as proportions between 0 and 1.

How likely an event is to occur is determined by the concept of probability. For instance, meteorologists can predict the possibility of rain by looking at weather patterns. In epidemiology, probability theory is used to understand the relationship between exposures as well as the risk of health effects.

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Answer: In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.

Step-by-step explanation: To convert the speed from miles per second to miles per minute, we multiply the speed by the number of seconds per minute. There are 60 seconds per minute, so Venus travels 22 * 60 = 1320 miles per minute.

In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.

Answer:

B. Congruent triangles have both same shape and same size.

C. Corresponding angles and corresponding sides of congruent triangles are equal.

Answer:

5 m/s

Step-by-step explanation:

Divide the distance by Karl's time to find the rate at which Karl was running:

150/30 = 5 meters per second

a) The equation is  y = 4/x².

b) The value of x is 2/9 when y = 25.

What is relationship?

The relation in mathematics is the connection between two or more sets of values. Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.

Given table is

x      1       2        3          4

y      4       1       4/9       1/4.

Given that y is inversely proportional to the square of x.

y∝ 1/x²

y = k/x² where k is proportional constant.

Putting x = 1 and y = 4 in equation y = k/x²:

4 = k/1²

k = 4

Putting x = 2 and y = 1 in equation y = k/x²:

1 = k/2²

k = 4

Putting k = 4 in  y = k/x²:

y = 4/x²

Putting y = 25 in  y = 4/x²

25 = 4/x²

25x² = 4

Divide both sides by 25:

x² = 4/25

Take square root on both sides:

x = 2/5

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Answer:

This answer assumes that the function is A(x) = 100x − 2x^2.  The function as written is A(x) = 100x - (4 or 4x)

The domain is 0 - 50 feet.

Step-by-step explanation:

The area function is a polynomial with a vertex (hghest area possible) at (25,1250).  This is telling us that for a side length of 25 feet, the area is at a maximum of 1250 ft^2.  This is actually not totally correct.  We only need 3 sides of fencing since the school wall will make up the fourth.  The given equation does not seem to allow for this caveat, since it uses 100 feet for all four sides.

Given the equation, the domain for the function A(x) is positive for all values between 0 and 50 feet.  The domain is 0 - 50 feet.

The sample proportion will have the smallest p-value is for Z=3 that can be calculated by taking comparisons between Z=1,2 and 3.

Null hypothesis H0= P=0.45

Alternative hypothesis H1= P>0.45

The null hypothesis assumes that any form of distinction among the selected traits which you see in a fixed of records is because of chance. For example, if the predicted income for the playing recreation are truely same to 0, then any distinction among the common income withinside the records and 0 is because of chance.

H=1000, x1=500, x2=600 and x3=700

P1= x1/h=500/1000=0.5

P2=x2/h=600/1000=0.6

P3=x3/h=700/1000=0.7

Z1=P1-P/(P(1-P)/h)61/2 = 0.5-0.45/(0.45*0.55/1000)^1/2 = 0.32

P-value for Z1=P(Z1>0.32)=0.37748

Z2=P2-P/(P(1-P)/h)61/2 = 0.6-0.45/(0.45*0.55/1000)^1/2 = 0.95

P-value for Z2=P(Z2>0.95)=0.17106

Z3=P3-P/(P(1-P)/h)61/2 = 0.7-0.45/(0.45*0.55/1000)^1/2 = 1.59

P-value for Z3=P(Z3>0.95)=0.055917

Thus, the smallest P-value will be for Z3.

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The f< [tex]f_{max}[/tex] the semicircular disk does not slip at the given instant.

The semicircular disk having a mass of 10 kg.

ω = 4 rad/s,  θ = 60 °

First we have to draw the free body diagram,

Calculate the distance AG.

[tex]$$\begin{aligned}A G & =\sqrt{O G^2+O A^2-2 \times O G \times O A \times \cos \theta} \\& =\sqrt{\left(\frac{4 \times 0.4}{3 \pi}\right)^2+0.4^2-2 \times \frac{4 \times 0.4}{3 \pi} \times 0.4 \times \cos 60^{\circ}} \\\end{aligned}$$[/tex]

=0.3477 m.

Calculate the angle ∝.

[tex]$$\begin{aligned}& \frac{\sin \alpha}{O G}=\frac{\sin 60^{\circ}}{0.3477} \\& \alpha=25.01^{\circ}\end{aligned}$$[/tex]

Calculate the normal acceleration at A.

[tex]$$\begin{aligned}a_{A, y} & =\omega^2\left(r_{A O}\right) \\& =4^2 \times 0.4 \\& =6.4 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]

Calculate the acceleration at G.

[tex]& \mathbf{a}_G=\mathbf{a}_A+\boldsymbol{\alpha} \times r_{G / A}-\omega^2\left(\mathbf{r}_{G / A}\right) \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}a_{A, x} \mathbf{i}+a_{A,} \mathbf{j}+\alpha \mathbf{k} \times A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j}) \\-\omega^2[A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j})]\end{array}\right\} \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}0+6.4 \mathbf{j}+\alpha \mathbf{k} \times 0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j}) \\-4^2[0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j})]\end{array}\right\} \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=(0.3151 \alpha-2.352) \mathbf{i}+(0.147 \alpha-1.3584) \mathbf{j}\end{aligned}$$[/tex]

Equate i coefficient:

[tex]-a_{G, x}=0.3151 \alpha-2.352[/tex][tex]-a_{G, x}=0.3151 \alpha-2.352[/tex]

Equate j coefficient:

[tex]$$-a_{G, y}=0.147 \alpha-1.3584$$[/tex]

The free body diagram and the kinematic diagram of the semicircular disk is as follows:

Calculate the mass moment of inertia of the semicircular disk about point O.

[tex]$$\begin{aligned}I_0 & =\frac{1}{2}\left(\frac{1}{2} m r^2\right) \\& =\frac{1}{2}\left(\frac{1}{2} \times 10 \times 0.4^2\right) \\& =0.4 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$[/tex]

Calculate the mass moment of inertia of the semicircular disk about point G.

[tex]$$\begin{aligned}I_G & =I_0-m(O G)^2 \\& =0.4-10\left(\frac{4 \times 0.4}{3 \pi}\right)^2 \\& =0.1118 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$\\[/tex]

Consider moment equilibrium condition about point A.

[tex]$$\begin{aligned}& \sum M_A=I_G \alpha+\sum m a_G d \\& m g(A G \sin \beta)=I_G \alpha+m a_{G, x}(A G \cos \beta)+m a_{G, y}(A G \sin \beta) \\& 10 \times 9.81\left(0.3477 \times \sin 25.01^{\circ}\right)=\left\{\begin{array}{l}0.1118 \alpha+10 a_{G, x}\left(0.3477 \cos 25.01^{\circ}\right) \\+10 a_{G, y}\left(0.3477 \sin 25.01^{\circ}\right)\end{array}\right\} \\& 0.118 \alpha+3.151 a_{G, x}+1.47 a_{G, y}=14.42\end{aligned}$$[/tex]

Solve the equations (1), (2), and (3), the values obtained are as follows:

[tex]$$\begin{aligned}& \alpha=18.04 \mathrm{rad} / \mathrm{s}^2 \\& a_{G, x}=3.333 \mathrm{~m} / \mathrm{s}^2 \\& a_{G, y}=1.294 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]

Consider the force equilibrium along the horizontal direction:

[tex]$$\begin{aligned}& \sum F_x=m a_{G, x} \\& f=m a_{G, x} \\& f=10 \times 3.33\end{aligned}$$[/tex]

f=33.33 N.

Consider the force equilibrium along the vertical direction:

[tex]$$\begin{aligned}& \sum F_y=m a_{G, y} \\& m g-N=m a_{G, y} \\& (10 \times 9.81)-N=10 \times 1.294 \\& N=85.16 \mathrm{~N}\end{aligned}$$[/tex]

Calculate the maximum frictional force at point A.

[tex]$$\begin{aligned}f_{\max } & =\mu_s N \\& =0.5 \times 85.16 \\f_{\max } & =42.58 \mathrm{~N}\end{aligned}$$[/tex]

Since, f< [tex]f_{max}[/tex]the semicircular disk does not slip at the given instant.

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Answer: 3 boxes

Step-by-step explanation:

she has 3 stuffed animals left and its not manditory to fill a box so you would put the threee remaining into one box

The ratio of purple flower to white flowers is 1:1 for each friend.

A system of arrangement where objects are set at the center position.

In another words the piece that kept in the center position.

As example, for the purpose of decorating a table with flowers, we need to keep the flowers in such a way that all the flowers occupy the center position.

If we want to display a table as centerpieces with white and purple flowers, we must keep the two flowers in the same ratio to look the display more attractive.

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Answer:

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

Simplify the expression:

The solution to the expression y² is 81 when y = -9

From the question, we have the following parameters that can be used in our computation:

y = -9

Also, from the question, we have

y2

Express the exponents in the above expression properly

So, we have the following representation

y²

Substitute the known values in the above equation, so, we have the following representation

y² = (-9)²

Remove the bracket in the expression

'This gives

y² = 9²

Evaluate the exponent

So, we have the following representation

y² = 81

Hence, the solution is 81

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Answer:  The correct answer is 0.0165041148268188

Step-by-step explanation:

Complete division (no rounding precision):

0.442 ÷ 26.7812 = 0.0165041148268188

It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.

What is the percentage increase?

The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original.

It is generally better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.

This is because the percentage raise you receive is applied to your current salary. If you receive a 3% raise first, your salary will be higher when you receive the 9% raise, so the 9% raise will be applied to a higher base salary. This means that you will receive a larger increase in salary overall if you receive the 9% raise first.

For example, let's say you are currently making $50,000 per year. If you receive a 3% raise followed by a 9% raise, your salary would increase to $51,500 after the first raise and then to $56,365 after the second raise, for a total increase of $6,365.

On the other hand, if you receive a 9% raise followed by a 3% raise, your salary would increase to $54,500 after the first raise and then to $56,365 after the second raise, for a total increase of $5,865.

In this example, you would receive a larger increase in salary overall if you received the 9% raise first. This is because the 9% raise is applied to a lower base salary, resulting in a larger increase in salary overall.

Of course, the actual amount of the raise will depend on your current salary and the percentage of the raise. In general, though, it is usually better to receive a larger percentage raise first, followed by a smaller percentage raise.

Hence, It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.

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Answer:

D. Corresponding angles

Step-by-step explanation:

Corresponding angles are angles located on the same side, the intersection of transversal and two or more straight lines. So, answer is D

5. The constant of proportionality is $0.4 per pound

4. The constant of proportionality is  is 3 ounces of almond per ounces of dark chocolate

From the question, we are to determine the constant of proportionality from the given table

From the given information, we have that

There is a proportional relationship between x and y

That is,

y ∝ x

Then,

y = kx

Where k is the constant of proportionality

From the table,

When x = 5 pounds, y = $2

Then,

2 = k × 5

k = $2/5pounds  

k = $0.4/pound

k = $0.4 per pound

4.

x is proportional to y

Then,

y = cx

Where c is the constant of proportionality

From the table,

When x = 3 ounces of dark chocolate, y = 9 ounces of almond

Then,

9 = c × 3

c = 9/3

c = 3 ounces of almond / ounces of dark chocolate

c = 3 ounces of almond per ounces of dark chocolate

Hence, the proportionality constant is 3 ounces of almond per ounces of dark chocolate

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Answer:

ok i can do it if u want then see my m.s.g

The required solutions to the given triangle ABC below as:

(i) sin (B+C/2) = cos (A/2)

(ii) if angle A= 90°, then the value of tan (B+C/2) is is undefined.

Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.

Given that A, B, and C are interior angles of a triangle ABC.

To solve the question, we would consider trigonometric ratios of complementary angles.

sin (90° - θ) = cosθ

We know that for ΔABC,

∠A + ∠B + ∠C = 180° (Angle sum property of triangle)

∠B + ∠C = 180° - ∠A

On dividing both sides by 2, we get,

(∠B + ∠C)/2 = (180° - ∠A)/2

(∠B + ∠C)/2 = 90° - ∠A/2

Applying sine angles on both sides:

sin {(∠B + ∠C)/2} = sin (90° - ∠A/2)

Since, sin (90° - θ) = cos θ, we get

sin (∠B + ∠C)/2 = cos A/2

(ii)  if angle A= 90°, then find the value of tan (B+C/2)

If cos A/2 = 0 so ∠A = 90°

sin (∠B + ∠C)/2 = cos A/2 = 0

tan (B+C/2) = ∞

Thus, the value of tan (B+C/2) is undefined.

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Answer:

x intercept= (1.5,0)

y intercept= (0,-2)d

Step-by-step explanation:

Rearrange the equation to be in the form y=mx+c:

4x-1=3y+5

y=(4x-6)/3

y=4/3(x)-2

y intercept= c from equation above =-2

y intercept=-2

x intercept => when y=0

sub 0=y

0=4/3(x)-2

2=4/3(x)

x=1.5

Answer: 73.3%

Step-by-step explanation:

take 44 and divide it by 60

44/60 = 0.0733 repeating

move the decimal place to the right twice

0.0733 --> 73.3%

Answer:

B

Step-by-step explanation:

the shape will reflect b

The interest amount that will be capitalized is $4.04 million.

The entire cost to purchase a good or service is referred to as an expense. A $30 million piece of equipment with a six-year useful life, for instance, is considered a capital expenditure. An expense is something that calls for the transfer of funds, or fortune in general, from one person or group to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students.

The following can be deduced from the information:

Average Expenditure for 2023

= 78 million* 6/6 month + 46 million ** 3/6 month

= 101 million

Amount of interest that should capitalized in 2023 using a specific interest method

= Average expenditure for 2023 * interest rate *6/12 month

= $101 million * 8% * 6/12

= $4.04 million

The interest amount is $4.04 million.

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Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters.The total volume of space available to Takeo is 3,426 cubic centimeters.

To find the total volume of space available to Takeo, first we take the volume of Box 1, which is 2,166 cubic centimeters. Then we take the volume of Box 2, which is 1,260 cubic centimeters. Finally, we add these two volumes together to get the total volume of 3,426 cubic centimeters.Takeo is in the process of packing before his move. He has two boxes to pack and each box has a different volume. Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters. By adding these two volumes together, Takeo has a total volume of 3,426 cubic centimeters of space available to pack before his move.

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The coordinates of ABC are A = (-2, -1) B = (-2, -10) C" = (-14, -1)

The coordinates of the triangle A"B"C" are given as

A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)

The transformation is given as

When these transformations are combined, we have

(x, y) ⇒ (-y/2, x/2)

So, we have

A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)

This gives

A = (-2, -1) B = (-2, -10) C" = (-14, -1)

Hence, the coordinates are A = (-2, -1) B = (-2, -10) C" = (-14, -1)

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Answer:

f(x)=3x+4 and g(x)=2x3

find.

a:fg(x)

b:gf(x)

The transformation from the parent function is a translation by 2 units right and 1 unit up

From the question, we have the following function that can be used in our computation:

f(x) = x³

g(x) = (x − 2)³ - 1

First, we have the transformation to be:

From f(x) = x³ to f'(x) = (x − 2)³

This means the function is translated right by 2 units

Next, we have:

From f'(x) = (x − 2)³ to g(x) = (x − 2)³- 1

This means the function is translated up by 1 unit

Hence, the transformation is 2 units right and 1 unit up

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The value of x in the solution set of the inequality is -4.

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

9(2x+1) < 9x - 18

2x+1 < x - 2

2x < x - 3

x < -3

This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.

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Answer:

-4

Step-by-step explanation:
taking  test

Except table 2, all tables have greater unit rate than the graph.

The required arrangements of tables is  Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rate of graph is

m=20-0/11=20/11=1.818

Similarly, we need to calculate the unit rate for each table.

m1=26-13/14-7=1.81

m2=18-9/10-5=9/5=1.81

m3=34-7/18-9=1.88

m4=42-21/22-11=21/11=1.90

m5=38-19/20-10=1.9

m6=50-25/26-13=25/13=1.923

m7=46-23/24-12=23/12=1.9166

Hence, Except table 2, all tables have greater unit rate than the graph.

The required arrangement of tables is  Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6

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Answer

x=5 y=2

Step-by-step explanation: