f(x)=1/3(4-x)^2 ................

Given:

Annual per capita consumption in earlier years = 496 eggs / year

Annual per capita consumption in recent years = 255 eggs/ year

Solution:

(A) Earlier year had 500 eggs (nearest ten)

(B) More recent years had 260 eggs (nearest ten)

(C) In more recent year, the average person ate :

Hence, the average person in recent years ate 0.52 as many eggs as those consumed in earlier years

Answer: 1 quarter, 3 dimes, 2 nickels, and 2 pennies

Step-by-step explanation:

8 coins.

1 quarters = 25¢

42¢ = 2 pennies and 3 dimes and 2 nickels

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

Answer:

(B) 350 °F.

Step-by-step explanation:

To find the mode of the cooking temperatures, we need to determine which temperature occurs most frequently in the data.

From the given data, we can see that 350 °F occurs 3 times, while all other temperatures occur either once or twice. Therefore, the mode of the cooking temperatures is 350 °F.

Therefore, the answer is (B) 350 °F.

Answer:

3/5

Explanation:

Given the expression:

Change the division sign to multiplication and swap the numerator and denominator of the fraction after the division sign.

Step-by-step explanation:

First we recall the relevant definitions and properties:

An even integer is an integer that is a multiple of 2, that is, an integer that can be written as 2k2k where kk is also an integer.

An abelian group is a set with an operation that is closed in that set, is associative, has an identity element, has inverses, and is commutative.

Addition is already associative and commutative over the set of all integers, and has an identity 00 and an inverse −n−n for each integer nn.

Oh, and multiplication of integers distributes over addition (this is important because we’re dealing with multiples of 2 but also with addition. The distributive property is how multiplication relates to addition).

This means we have to show a few things:

Addition is closed over the even integers. This holds due to the distributive property: if you have even integers 2k2k and 2m2m, then 2k+2m=2(k+m)2k+2m=2(k+m) is also an even integer. The odd integers fail this property: for example, 11 is odd but 1+1=21+1=2, which is not odd.

Addition is associative over the even integers. This holds because addition is already associative over the set of all integers: 2k+(2m+2j)=(2k+2m)+2j2k+(2m+2j)=(2k+2m)+2j. The odd integers do satisfy associativity, since they’re also a subset of the integers.

Addition has an identity element over the even integers. Since we already know that 00 is an identity for the set of all integers and 00 is even, this shows that we have an identity for the even integers: 2k+0=2k2k+0=2k. This doesn’t hold for the set of odd integers, because if nn and kk are odd integers and n+k=nn+k=n then k=0k=0, a contradiction since 00 is not odd.

Addition has inverses over the even integers. We already know that integers have inverses, and if 2k2k is an even integer then −k−k is the inverse of kk, so that 2k+2(−k)=2(k+(−k))=2(0)=02k+2(−k)=2(k+(−k))=2(0)=0. This means the even integer 2(−k)2(−k) is the inverse of 2k2k. The odd numbers do satisfy this property, since they’re also a subset of the integers.

Addition is commutative over the even integers. This holds because addition is already commutative over the set of all integers: 2k

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

-17

Step-by-step explanation:

You have to simplify the expression!

Answer:

-17

Step-by-step explanation:

The evaluated exact value of 6 trigonometric functions concerning an angle θ is
sin(θ) = -√(3)/2
cos(θ) = 1/2
tan(θ) = -√(3)
csc(θ) = -2/√(3)
sec(θ) = 2
cot(θ) = -1/√(3)

Here,
cos(θ) = 1/2 and sin(θ) < 0, we can apply the Pythagorean identity to evaluate sin(θ).
sin²(θ) + cos²(θ) = 1
sin²(θ) + (1/2)² = 1
sin²(θ) = 3/4
sin(θ) = -√(3)/2
Therefore, we have both sin and cos of theta, we can evaluate the other four trigonometric functions:
tan(θ) = sin(θ)/cos(θ)
= (-√(3)/2)/(1/2)
= -√(3)
csc(θ) = 1/sin(θ) = -2/√(3)
sec(θ) = 1/cos(θ) = 2
cot(θ) = 1/tan(θ) = -1/√(3)
Hence , the evaluated six trigonometric functions of θ are
sin(θ) = -√(3)/2
cos(θ) = 1/2
tan(θ) = -√(3)
csc(θ) = -2/√(3)
sec(θ) = 2
cot(θ) = -1/√(3)
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Answer:

Step-by-step explanation:

8x + 4 + 4 (x + 4) + 2 =

8x + 4 + 4x + 16 + 2 =

12x + 4 + 16 + 2 =

12x + 22

Answer:

12x + 22

Step-by-step explanation:

open the brackets:

4(x+4) = 4x + 16

write the sum:

8x + 4 + 4x + 16 + 2

put like terms together:

8x + 4x + 4 + 16 + 2

add the rest:

12x + 20 + 2

answer:

12x + 22

Answer:

The value of y° = 80°

Step-by-step explanation:

Given

m∠A = 20

m∠B = x°

as

x = 100,

so

m∠B = 100

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

Thus, the m∠C of the triangle ABC can be calculated as:

m∠A + m∠B + m∠C = 180°

20° + 100° + m∠C = 180°

                    m∠C = 180° - 120°

                              = 60°

As we know that Vertical angles are always congruent.

In other words, m∠C is common in both triangles ΔABC and ΔCDE

m∠C = 60°

m∠E is also given.

i.e. m∠E = 40°

as

m∠D = y°

So, we have to determine m∠D in order to determine y°.

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

Thus, using the values of the angles ΔCDE

i.e.

m∠C + m∠D + m∠E = 180°

60° + y° + 40° = 180°

y° = 180° - 100°

y° = 80°

Therefore, the value of y° = 80°

The given sequence is

\(z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)\)

First, we need to simplify the expression inside the log. The term \({i*cos(π/2) - i*sin(π/2)}\) can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.

Therefore, the expression inside the log becomes \((1 + (\theta/\alpha)^n)\).

Now, we need to find the limit of this sequence as n approaches ∞.

If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.

If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.

If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).

Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).

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Answer:

9261

Step-by-step explanation:

V=6A3/2

36=6·26463/2

36=9261

Answer:

c

Step-by-step explanation:

Answer:

The answer is B I think.

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

The likelihood that you regain your wallet if you lost a wallet by it being turned in or you being located, is likely.

Based on the information provided, the likelihood that you would regain your lost wallet is 89%, assuming that the survey results are representative of the population of the United States.

When a probability is likely, then it means that the probability is greater than 66 %. Very likely means greater than 90 %. This means that it is likely you get your lost wallet back.

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The question is:

What is the likelihood of regaining your wallet ?

Answer:

2.3 x 10^11

Step-by-step explanation:

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

a =  m

Step-by-step explanation:

i searched it...
i dont give shet if its wrong...

The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

An experiment in probability is a process or activity that involves observing or measuring an outcome or event, in order to determine the likelihood or probability of certain outcomes.

In probability, an outcome refers to a possible result that can occur from an experiment or event. It is one of the possible outcomes that can happen, and it may be a single result or a set of results.

In probability, a trial is a single repetition of an experiment or event. It is the process of observing or measuring the outcome of an event or experiment once.

Here we have

At a sports event, a fair coin is flipped to determine which team has possession of the ball.

The coin has two sides, heads, (H), and tails, (T).  

From the given options correct answers are

a. The experiment identifying whether a head or tail is flipped is correct because the experiment is to determine which side of the coin will be facing up after the coin is flipped, either heads (H) or tails (T).

b. The experiment is flipping the coin is correct because the experiment involves physically flipping the coin.

d. A trial is one flip of the coin is correct as a trial is defined as a single performance of an experiment, in this case, flipping the coin once.  

Therefore,

The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

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Answer:

A and D

Step-by-step explanation:

Hope this helps!

Answer:

To factor a quadratic polynomial use the equation

Step-by-step explanation:

F(x) = k{x2 - (sum of zeroes)x + (product of zeroes)}

Julie studied for a total of 5/6 hours each day.

Given that

Time = 3 1/4 hours

Number of days = 4

To find the number of hours per day Julie studied, we need to divide the total number of hours she studied by the number of days she studied.

So, we have

Total number of hours = 3 1/3 hours = 10/3 hours

Number of days = 4

The daily rate is then calculated as

Number of hours per day = Total number of hours / Number of days

i.e.

Number of hours per day = (10/3) / 4

So, we have

Number of hours per day = 5/6 i.e 50 minutes

Hence, Julie studied for 5/6 hours, or 50 minutes, each day.

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Answer:

1. Given

2. Vertical Angles Theorem (1st Occurrence)

3. Vertical Angles Theorem (1st Occurrence)

4. Transitive Property of Congruence

5. Converse of the Alternate Interior Angles Theorem

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Congruence

If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.

Converse of the Alternate Interior Angles Theorem

If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

\(\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}\)

From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles.  Therefore, the Vertical Angles Theorem applies.

According to the Transitive Property of Congruence,  if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.

The two lines a and b are intersected by transversal \(\ell\) so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel.  This is the Converse of the Alternate Interior Angles Theorem.

Answer:

9 pints

Step-by-step explanation:

there are two cups in a pint, so we need to divide 16 by 2 to convert the cups to pints.

16 ÷ 2 = 8

9 is greater than 8, so 9 pints.

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Answer:

The number is 500.

Step-by-step explanation:

Let n be the number

Convert percent to decimal

20% = 0.20

0.20n = 100

Divide both sides of the equation by 0.20

0.20n/0.20 = 100/0.20

n = 500

He will have $217,043.56 in the account when he retires.

We have,

Monthly deposit = $400

Interest rate = 3.2% / 12 = 0.002667 per month

Number of year = 63 year - 35 year = 28 year

Number of period = 28 × 12 month = 336 month

So, Amount = 400 [ (1+0.002667)³³⁶-1] / 0.002667

= 400 [ (1.002667)³³⁶-1] / 0.002667

= 400 (1.44713794)/ (0.002667)

= 400 (542.608901)

= 217,043.56

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Answer:i would say C ADHAKFFA

Step-by-step explanation: