Exit ticket for geometry

Using an inverse trigonometric function, we will find that the solution is:

θ = 1.047

Here we want to solve the equation:

1 - cos(θ) = 1/2

Such that θ ∈  [0,2pi)

Now let's return to our equation:

1 - cos(θ) = 1/2

1 - 1/2 = cos(θ)

1/2 = cos(θ)

Now we could apply the inverse cosine function to both sides, then we will get:

Acos(1/2) = Acos(cos(θ))

1.047 = θ

That is the solution.

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Answer:

2.5

Step-by-step explanation:

the radius is half of a diameter so

radius = 5/2 = 2.5 inches

Answer:

2.3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

In order to find the answer to the equation, you must substitute the given values into the equation.

A^3 - C + B

We know that A = 3, B = 6, and C = 8

(3)^3 - (8) + (6)

9 - 8 + 6

1 + 6

7

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

CL congruent with CM

WX congruent with YZ

32 = 32

Answer:

127

Step-by-step explanation:

PR is straight line with the measure of 180 degrees

to find PQT we need to subtract 53 from 180

180 - 53 = 127

Answer:

Step-by-step explanation:

3:12 7:28

The means are the second and third terms in the proportion.

The extremes are the two outside terms.

12 and 7 are the means.

(3 and 28 are the extremes.)

So thre answer is D.  12 and 7.

Answer: 4,096

Step-by-step explanation:

There are 12650 ways for pick 4 paintings.

Given:

He has 25 to choose.

No. of ways he can pick 4 in 25 = 25 C 4.

             [tex]\frac{25!}{4!(25-4)!} =\frac{25}{4!\times2!} =12650\\[/tex]

Therefore, 12650 ways for pick 4 paintings.

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Answer:

0.0228 = 2.28% probability that the mean lifespan from the sample exceeds 10 days.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8, standard deviation of 6, sample of 36:

This means that [tex]\mu = 8, \sigma = 6, n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]

What is the probability that the mean lifespan from the sample exceeds 10 days?

This is 1 subtracted by the pvalue of Z when X = 10. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{10 - 8}{1}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the mean lifespan from the sample exceeds 10 days.

Answer:Please see answer in explanation column

Step-by-step explanation:

A

The sum of a number and 7 is not more than 10

Given answer: x + 7 < 10  , This is false

Reason :Not more than 10 means at most 10, less than or equal to 10 , " or " not greater than 10 "and therefore the correct inequality  is written as

x + 7  ≤ 10

B

The product of a number and 4 is at least 20

Given answer: 4X > 20  ---- False

Reason :At least 20  means at no less than 20 " or " greater than or equal to 20  therefore the correct inequality  is written as

4X ≥ 20

C

The difference between a 15 and a number is at most 12

Given answer: 15-x>12----False

Reason :At most 12  means  " no more than 12 , "  " less than or equal to 12 , " or " not greater than 12"therefore the correct inequality  is written as

15-x  ≤  12

D

The quotient of a number and 8 is greater than or equal to

Given answer 8x <3 --False

Reason : It clearly stated greater than or equal to 3. Therefore the correct inequality is  8x  ≥ 3

Answer:

6. 3.14 7. 172.03 8. 78.54 9. 380.13 10. 19.63 11.28.27

Examining the polynomial function g(x) as given in the table the end behavior is

The end behavior of function typically says the characteristics of the function at the ends

The given table when examined shows that there was three zeros hence the graph is that of odd function

The end behavior of an odd function with positive leading coefficient is

x ⇒ ∞ f(x) ⇒ ∞: as x tends to positive infinity the function tends to positive infinity

x ⇒ -∞ f(x) ⇒ -∞: as x tends to negative infinity the function tends to negative infinity

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Answer:

See joint picture.

Step-by-step explanation:

The study lasts 6 days. Since the amount of plant food decreased an equal amount each day, and since the whole 72 millimeters were used, it means that plants consumed 72/6 = 12 millimeters daily.

All the results given come from this justification.

The required consumption of each day is 12 mm.

Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information

The statistic is the study of mathematics which deal with relations between comprehensive data.

Since
observation run for 6 days and have 72 mm of food  has been fed each day.
at the end of 6 day food remains 0 mm i.e.
Rate at which food has been fed for each day is given by
= 72/6 = 12
12 mm of food has been fed every day for to the 6 days.

At day 0 we have 72 mm of food
At day 1 we have  60 mm of food
similary for
At  day 6 we have 0 mm of food

Thus the graph has been attached below for the values of x

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Answer:

Eva has $127.31 after 2 years.

Step-by-step explanation:

Here is the formula for compound interest

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the initial amount, [tex]r[/tex] is the interest rate as a decimal, [tex]n[/tex] is the number of times the interest applied per time period, and [tex]t[/tex] is the number of time periods.

We are given

[tex]P=120\\r=0.03\\n=1\\t=2[/tex]

Substitute our numbers into the equation

[tex]A=120(1+\frac{0.03}{1})^{1*2}[/tex]

[tex]A=120(1.03)^{2}[/tex]

[tex]A=120*1.03^{2}[/tex]

[tex]A=120*1.0609[/tex]

[tex]A=127.308[/tex]

Answer: atleast alot

Step-by-step explanation:

Answers:

There are infinitely many possible ways to answer the third part.

===========================================================

Explanation:

The midline is the horizontal line that goes through the center of the sine curve. Visually we can see that is y = 0. Another way we can see this is to note how y = 0 is the midpoint of y = 1.5 and y = -1.5, which are the max and min respectively.

---------

The amplitude is the vertical distance from y = 0 to y = 1.5, and it's also the vertical distance from y = 0 to y = -1.5; in short, it's the vertical distance from center to either the peak or valley.

---------

The general format of a sine curve is

y = A*sin(B(x-C)) + D

where,

In this case, we found so far that

The only thing we're missing is the value of C, which is the phase shift.

Note the point (pi/2, 1.5) is one of the max points on this curve. Also, recall that sin(x) maxes out at 1 when x = pi/2

This must mean that the stuff inside the sine, the B(x-C) portion, must be equal to pi/2 in order to lead sin(B(x-C)) = 1.

So,

B(x-C) = pi/2

0.5(pi/2-C) = pi/2

pi/4 - C/2 = pi/2

4*( pi/4 - C/2 ) = 4*(pi/2)

pi - 2C = 2pi

-2C = 2pi - pi

-2C = pi

C = pi/(-2)

C = -pi/2

This allows us to update the function to get g(x) = 1.5*sin(0.5(x+pi/2)) which is the same as g(x) = 1.5sin(0.5x + pi/4)

This is one possible answer because we could have infinitely many possible values for C, due to sin(x) = 1 having infinitely many solutions.

Also, you could use cosine instead of sine. Cosine is just a phase shifted version and of sine, and vice versa.

The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin. Option C

We can say that a relationship  is proportional when the relation does lead to a straight line graph and the graph would have to be able to pass through the origin.

Hence, even if we have a straight line graph but the graph does not pass through the origin of the graph then we can not say that the relationship that is existing between the coordinates that have been shown is proportional.

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The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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Answer:

no solutions

Step-by-step explanation:

you have to divide the whole first equation by 2 and you would get

2x+y=5

2x+y=-3

That is not true the same thing can’t have different outcomes.
it is no solution

Answer:

All Sides are equal to their corresponding ones [SK = BG and so on...]

All angles are equal to thei corresponding angles [angle(T) = angle(I) and so on..]

(C.P.C.T)

Step-by-step explanation:

From the given figure, ignoring the fact that she rotated it, we can prove that the two triangles are congruent by RHS congruence criterion.

After proving so, we can use C.P.C.T to find the relations.

Hope it helps. Thank you :)

Answer:

About 47% of books were nonfiction.

The actual percentage includes decimals and it would be this:

%47.0588235294

Just so you know, there's no diagram

A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.

If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.

In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).

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Answer:

dogwater literally free so freeee!!!!

Step-by-step explanation:

The remainder of the given division 5884/ 94 is 56 and hence the complete sentence is 5884/94 = 62 + 56/94.

The amount that remains after division is complete is known as a remnant. Simply divide the number by another number that is one of its multiples to obtain the remainder.

The division of any number can be written as follows:

a/n = q + r/n

where, a is the dividend, n is the divisor, r is the remainder and q is the quotient.

When we divide the number 5884 by 94 using the long division method the quotient is 62 and the remainder is 56.

Hence, the complete sentence is 5884/94 = 62 + 56/94.

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Answer:

Not a function

Step-by-step explanation:

A function is when every input(x) has only one output (y).  The input 1 has two outputs (0 and 1) so it is not a function.

Answer:

0.16 or 0.2 if rounded

Step-by-step explanation:

4 gallons divided by 25 chairs equals 0.16 gallons for each chair

hope this helps <3

Answer:

5x+2

Step-by-step explanation: