If m<1 = 68 degrees and m<6 = 35 degrees, then find the measures for each of the remaining numbered angles. Justify your answers with definitions and/or theorems.

m<1=68 degrees - Given
m<6=35 degrees - Given

The probabilities are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of students in the problem is given as follows:

17 + 25 + 21 + 37 = 100.

Hence the probabilities are given as follows:

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The value of the equation is A = 1/3

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 0.333...  be equation (1)

Now , the value of A is an irrational number

So , the value of A = 1/3

Therefore , the value of A = 1/3 or A = 2/6

Hence , the equation is A = 1/3

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Answer:

During winter in the Arctic, a lake gets frozen solid with ice. But as spring comes, the ice starts to melt. This happens because the temperature gets warmer and there's more sunlight. It's a natural process that happens every year and shows the change of seasons.

Step-by-step explanation:

Triangle STV is congruent to triangle UTW by SSS congruence postulate

SSS congruence postulate is a statement in geometry that says if three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent.

In other words, if the lengths of the sides of two triangles are the same, then the triangles are the same shape and size. The acronym SSS stands for "side-side-side."

Corresponding Parts of Congruent Triangles are Congruent is abbreviated as CPCTC.

According to the CPCTC theorem, every corresponding component of one triangle is congruent to the other when two triangles are congruent.

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Answer: 10π + 20, or 51.4159, cm

Step-by-step explanation:

The circumference of a circle is calculated using πd. Our d, or diameter, is 20, so the circumference of a full circle would be 20π. However, we only have half of a circle, so that number is halved, resulting in 10π. Now, we just have to add on the cross section, which is equal to the diameter, giving us 10π + 20, or 51.4159, cm.

a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.

b) The rider's minimum height above the ground is of: 5 meters,

c) The horizontal distance is given as follows: x = 0 m and x = 6 m.

The quadratic function in the context of this problem is defined as follows:

y = x²/3- 2x + 8.

In which:

The coefficients are given as follows:

a = 1/3, b = -2, c = 8.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -(-2)/(2/3) = 3.

Hence the y-coordinate of the vertex is given as follows:

y = (3)²/3 - 2(3) + 8 = 5 meters.

Hence the vertex-form definition of the equation is given as follows:

y = 1/3(x - 3)² + 5.

As the function is concave up, the minimum height is of 5 meters.

For the horizontal distance at a height of 8m, we have that:

x²/3 - 2x + 8 = 8

x²/3 - 2x = 0

x(x/3 - 2) = 0.

Hence:

x = 0 m and x = 6 m.

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The maximum height of the ball is 200 feet.

An expression can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

To find the time to the highest point, we need to find the time when the velocity of the ball is equal to zero. The velocity of the ball can be found by taking the derivative of the height equation with respect to time.

The derivative of h with respect to t is:

dh/dt = 32t + 64

Setting the derivative equal to zero and solving for t, we get:

0 = 32t + 64

-64 = 32t

t = -2

So, the time to the highest point is -2 seconds. However, since time cannot be negative in this context, we can say that it takes 2 seconds for the ball to reach its highest point.

To find the maximum height, we can substitute the time of 2 seconds back into the original height equation:

h = 16(2)^2 + 64(2) + 8

h = 64 + 128 + 8

h = 200

So, the maximum height of the ball is 200 feet.

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The complete question is:

Answer:

  (d)  x-axis

Step-by-step explanation:

You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).

The line of reflection is the perpendicular bisector of the segment between a point and its image.

Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':

  y = (-8 +8)/2 = 0/2 = 0

The line y=0 is the x-axis. The line of reflection is the x-axis.

__

Additional comment

Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:

  (x, y) ⇒ (-x, y) . . . . reflection over the y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over the x-axis   ←

  (x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin

Answer:

 (d)  x-axis

Step-by-step explanation:

The stock was worth 40000 dollars in 1998.

Stocks, also known as equities, are securities that represent ownership in a corporation.  The value of your stock holdings is directly tied to the performance of the company and its financial health.

There are two main types of stocks: common stocks and preferred stocks. Common stocks typically offer voting rights, while preferred stocks generally do not. Preferred stocks often offer a fixed dividend, while common stock dividends can vary.

Stocks are bought and sold on stock exchanges, such as the New York Stock Exchange (NYSE) and the NASDAQ.

The value of the stock quintupled every 9 years, which means it increased by a factor of 5 every 9 years. To find the value of the stock in 1998, we need to divide the value in 2016 by 5 raised to the power of the number of 9-year intervals that have passed.

Let's call the value of the stock in 2016 x. Then:

x = million dollars = 1000000

The number of 9-year intervals that have passed is (2016 - 1998) / 9 = 18 / 9 = 2

So, the value of the stock in 1998 is x / (5^2) = 1000000 / (5^2) = 1000000 / 25 = 40000.

Therefore, the stock was worth 40000 dollars in 1998.

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Answer:

  T = 79e^(-kt) +60

Step-by-step explanation:

You want the particular solution to the differential equation ...

  dT +k(T -60)dt = 0 . . . . T(0) = 139

This is a separable differential equation, so we can solve it by separating the variables and integrating each side:

  [tex]\dfrac{dT}{T-60}=-k\,dt\\\\\displaystyle \int{\dfrac{dT}{T-60}}=\int{-k}\,dt\\\\\ln{(T-60)}=-kt+C\\\\T-60=e^{-kt+C}=Ce^{-kt}\qquad\text{take antilogs; values of $C$ are different}[/tex]

Applying the initial condition, we have ...

  139 -60 = C = 79

Then the particular solution is ...

  [tex]\boxed{T=79e^{-kt}+60}[/tex]

The distance, that car will travel in 15 minute, is 28 km.

The formula used to explain the relationship between speed, distance, and time is speed distance time.

That is speed = distance/ time

So, distance = speed * time

Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs.

Given Speed of car = 112 km per hour

Time = 15 minutes = 15/60 hour

Time = 1/4 hour

Distance traveled by car in 15 minute = Speed of car * time

Distance = 112 * 1/4

Distance = 28 km

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Based on the information provided, it can be concluded they will not save enough money to cover their camping site charges.

Charge per person: 6 (charge per person) x 2 = 12 x 10 (number of days) = 120

Tenth charge per night: 18 x 8 (They will stay for 10 days but due to the offer pay for 4 nights if you stay 5, they will pay only 8 nights) = 144

Total: 264

13 x 9 weeks = 117 x 2 (two people are saving) = 234

Based on this, the amount of money they will save is not enough as they will need $30 more to cover their expenses.

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The required polynomial is [tex]12a^{2} -9a+5[/tex]

A polynomial is a expression that contains variables and coefficients, that involves all the four basic arithmetic operations.

Here the given two polynomials are,

[tex]-7a^{2} +3a-9 , 5a^{2} -6a-4[/tex].

subtracting these two polynomials we get,

[tex](5a^{2} -6a-4) - (-7a^{2} +3a-9 ) = 12a^{2} -9a +5[/tex].

Hence, required polynomial is [tex]12^{2} -9a+5.[/tex]

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a) The number of hours the server must work to earn $35 is of: 2.5 hours.

b) The earnings for five hours of work are given as follows: $75.8.

c) As the number of hours worked increases, the earnings also increase.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The points for this problem are given as follows:

(1,10), (2, 27), (3, 45), (4, 55) and (5, 78).

Inserting these points into a calculator, the equation is given as follows:

y = 16.4x - 6.2.

Hence the number of hours needed to earn $35 is given as follows:

35 = 16.4x - 6.2

x = 41.2/16.4

x = 2.5 hours.

The earnings for five hours of work are given as follows:

y = 16.4(5) - 6.2

y = $75.8.

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Answer:

0.2x-0.8

Step-by-step explanation:

In 0.2(x-4), you can multiply 0.2(The number outside of the parentheses) by the numbers inside the parentheses. So, it would be 0.2*x-0.2*4, which is 0.2x-0.2(4), which is 0.2x-0.8.

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

the geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex]

the geometric mean of 6 and 8 is then

[tex]\sqrt{6(8)}[/tex]

= [tex]\sqrt{48}[/tex] ← express as factors

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex]

Answer:

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

Step-by-step explanation:

To find the inverse of F(x), we need to follow these steps:

Step 1: Replace F(x) with y:

y = 5x^2 - 10x + 7

Step 2: Solve for x in terms of y:

y = 5x^2 - 10x + 7

y - 7 = 5x^2 - 10x

5x^2 - 10x = y - 7

5(x^2 - 2x) = y - 7

Completing the square:

5(x^2 - 2x + 1) = y - 7 + 5

5(x - 1)^2 = y - 2

x - 1 = ±sqrt((y-2)/5)

x = 1 ± sqrt((y-2)/5)

Step 3: Replace x with F^-1(x):

F^-1(x) = 1 ± sqrt((x-2)/5)

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

The options which are equal to, or a good estimate of the ratio include:

8 out of 1, 000 :

8 / 100 :

8 out of 1, 000 is a ratio that can be shown to be :

= 8 / 1, 000 x 100 %

= 0. 008 x 100 %

= 0. 8 %

0. 8 % is less than 1 %.

8 / 100 is a ratio that would be:

= 8 / 100 x 100 %

= 8 %

This is almost 10 % as it is 2 % away.

8 / 100 = 0. 08

2 / 25 = 0. 08

These two ratios are therefore equal.

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The most correct answer is D ( 3,-2) . Because in the 2 equations above when you enter the value x= 3 in equation I and II, it produces y=-2.

In the question above, there are two equations.

y=-(½)x - ½ (eq I)

y=-(⅔)x (eq II)

To find which x and y values satisfy these two equations in options A,B,C,D, we have to substitute one by one to prove:

A.(-2, 3)

we substitute the value x=-2 into equation I

y=-(½)x - ½

y= -(½) (-2) -½

y=1-½

y= ½ ( This means that option A is not valid, because it should give y a value of 3)

B.(-1,0)

we substitute the value x=-1 into equation I

y=-(½)x - ½

y= -(½) (-1) -½

y= ½ - ½

y= 0

Then, we try to substitute the value x=-1 into equation II

y=-(⅔)x

y= -(⅔) (-1)

y= ⅔ ( This means option B is not valid, because it should result in y being 0)

C.(1, 2)

we substitute the value x=1 into equation I

y=-(½)x - ½

y= -(½) (1) -½

y= -½ - ½

y= -1 ( This means option C is not valid, because it should result in y being 2)

D. (3,-2)

we substitute the value x=3 into equation I

y=-(½)x - ½

y= -(½) (3) -½

y= -3/2- ½

y=-4/2

y= -2

Then, we try to substitute the value x=3 into equation II

y=-(⅔)x

y= -(⅔) (3)

y=-2

The option D satisfies equations I and II,

Therefore the answer is option D.

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The average velocity of the object from t = 2 and t = 4 is equal to - 48 feet per second.

In this problem we find the case of an object thrown upward, whose height (h(t)), in feet, as a function of time (t), in seconds, is represented by a quadratic equation. We need to determine the average velocity (u) of the object by means of secant line formula:

u = [h(4) - h(2)] / (4 - 2)

Where:

If we know that h(t) = - 16 · t² + 48 · t + 120, then the average velocity is:

t = 2

h(2) = - 16 · 2² + 48 · 2 + 120

h(2) = 152 ft

t = 4

h(4) = - 16 · 4² + 48 · 4 + 120

h(4) = 56 ft

u = (56 ft - 152 ft) / (4 s - 2 s)

u = - 48 ft / s

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The balance after 6 years is $2108.

percentage, a relative value indicating hundredth parts of any quantity.

Given that savings account earns 4% annual simple interest.

The principal is $1700.

We need to find the balance after 6 years.

The formula for simple interest I=Prt

I = interest

P = principal ($1700)

r = annual interest rate (4%)

t = time in years (6)

So the interest earned in 6 years is:

I = 1700× 4×6 / 100 = $408

The balance after 6 years is the sum of the principal and the interest earned:

1700 + 408 = $2108.

Hence,  the balance after 6 years is $2108.

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Answer: 4/5 and 5/6 are not equivalent to 2/3 because they represent different fractions. 4/5 represents 4 parts out of 5 total parts, while 5/6 represents 5 parts out of 6 total parts. 2/3 represents 2 parts out of 3 total parts. To check if two fractions are equivalent, you need to see if they simplify to the same fraction. For example, 4/5 simplifies to 8/10 and 5/6 simplifies to 5/6, but neither of them simplifies to 2/3. Hence, 4/5 and 5/6 are not equivalent to 2/3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tree is .0564 meters

Answer:

Step-by-step explanation:

de chill de chill

If Mo and Beth split £48 in the ratio 3.5, Beth gets £10.67.

Let's call the amount that Beth gets "x". Then, the amount that Mo gets is 3.5x.

We know that the total amount they split is £48, so we can set up the following equation:

x + 3.5x = £48

Next, we'll simplify the left side of the equation by combining like terms:

4.5x = £48

Finally, we'll solve for x by dividing both sides of the equation by 4.5:

x = £48 / 4.5 = £10.67

So Beth gets £10.67.

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Answer:

see below

Step-by-step explanation:

(1+20%) * (1-20%) =1.2 *0.8 = 0.96

so it's the same as 1- 4% = 0.96

no

Answer:

mark score is minus 14

7multiply minus 2

Answer:

14

Step-by-step explanation:

Answer:

2793.75

Step-by-step explanation:

1350 - 175 = 1175

1175 / 4 = 293.75

By solving linear equations we will see that they will have the same amount after 6 weeks.

We know that Lauren has $400 in her savings account and spends $20 each week, then the amount that she has after x weeks is modeled by the linear equation below:

y = 400 - 20x

And Lydia has $250 in her account and saves $5 each week, then her equation is:

y = 250 + 5x

They we have the same amount of money when:

400 - 20x = 250 + 5x

400 - 250 = 5x + 20x

150 = 25x

150/25 = x

6 = x

After 6 weeks they will have the same amount of money.

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If at least one of the rolls is a 1, then there is a 1/12 chance that the total of the two dice roll will be less than 4.

idiom, informal, used to indicate that a situation could result in either a good or negative outcome. It's always a gamble to open a new restaurant. Whether we succeed or fail is up to chance.

Probability is calculated as follows: 3 out of 36 potential outcomes x desired outcomes = 0.0833. 8.33 percent is the calculated percentage. 7 is also the most frequent outcome when two dice are used. There are also six different ways to do it. The chance in this situation is 6 x 36 = 0.167, or 16.7%.

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