The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees

Answer:

b. Exactly two outcomes are possible on each trial.

Step-by-step explanation:

The correct answer is option B: Exactly two outcomes are possible on each trial.

We can define the binomial probability in any binomial experiment, as the probability of getting exactly x successes for n repeated trials, that can have 2 possible outcomes.

The binomial probability distribution is applicable when an experiment has exactly two outcomes. These trials are independent and the probabilities of the outcomes remain the same for each trial, referred to as Bernoulli trials. Using this distribution, we can calculate mean and standard deviation for the function.

The characteristic of an experiment where the binomial probability distribution is applicable is when exactly two outcomes are possible on each trial, referred to as 'success' and 'failure.' These are termed as Bernoulli trials for which binomial distribution is observed. In this situation, 'p' denotes the probability of a success on one trial, while 'q' represents the failure likelihood. The trials are independent, which means the outcome of one trial does not affect the results of subsequent trials. Moreover, the probabilities of the outcomes remain constant for every trial. The random variable X signifies the number of successes in these 'n' independent trials. The mean and standard deviation can be calculated using the formulas µ = np and √npq, respectively.

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The real zeroes of given function is [tex]-\frac{3}{2},-1, \text { and } 2[/tex]

Given that, [tex]f(x)=2 x^{3}+x^{2}-7 x-6[/tex]

We have to find the real and imaginary zeroes

This can be found out by equating the function to zero and finding the roots "x"

Now, let us use trail and error method.

So put x = 1 in f(x)

f(1) = 2 + 1 – 7 – 6 = - 10  

1 is not a root.  Since f(1) is not equal to 0

Now put x = -1

f(-1) = -2 + 1 + 7 – 6 = 0  

-1 is a root.  Since f(-1) is equal to 0

So, one of the roots is -1. Let the other roots be a, b.

[tex]\text { Sum of roots }=\frac{-x^{2} \text { coefficient }}{x^{3} \text { coefficient }}[/tex]

[tex]\begin{array}{l}{a+b+(-1)=\frac{-1}{2}} \\\\ {a+b=1-\frac{1}{2}} \\\\ {a+b=\frac{1}{2} \rightarrow(1)}\end{array}[/tex]

[tex]\begin{array}{l}{\text {Product of roots }=\frac{-\text {constant}}{x^{3} \text {coefficient}}} \\\\ {a b(-1)=\frac{-(-6)}{2}} \\\\ {a b(-1)=3} \\\\ {a b=-3 \rightarrow(2)}\end{array}[/tex]

Now, we know that, algebraic identity,

[tex]\begin{array}{l}{(a-b)^{2}=(a+b)^{2}-4 a b} \\\\ {(a-b)^2=\left(\frac{1}{2}\right)^{2}-4(-3)} \\\\ {(a-b)^2=\frac{1}{4}+12} \\\\ {(a-b)^2=\frac{49}{4}} \\\\ {a-b=\frac{7}{2} \rightarrow(3)}\end{array}[/tex]

Add (1) and (3)

[tex]\begin{array}{l}{2 a=\frac{7+1}{2} \rightarrow 2 a=4 \rightarrow a=2} \\\\ {\text { Then, from }(2) \rightarrow b=-\frac{3}{2}}\end{array}[/tex]

Hence, the roots of the given equation are [tex]-\frac{3}{2},-1, \text { and } 2[/tex]

Answer:

C

Step-by-step explanation:

2x²-4x=0

2x(x-2)=0

either x=0

or x-2=0

x=2

so x=0,2

Answer:each pound of jelly beans cost $2.5

Each pound of trailmix cost $1.25

Step-by-step explanation:

Let x represent the cost of one pound of jelly bean.

Let y represent the cost of one pound of trail mix.

A stores having a sale on jelly beans and trail mix for 8 pounds of jelly beans and 4 pounds of trail mix the total cost is $25. This means that

8x + 4y = 25 - - - - - - -1

For 3 pounds of jelly beans and 2 pounds of trailmix the total cost is $10. This means that

3x + 2y = 10 - - - - - - - - 2

Multiplying equation 1 by 3 and equation 2 by 8, it becomes

24x + 12y = 75

24x + 16y = 80

Subtracting,

- 4y = -5

y = - 5/ -4 = 1.25

Substituting y = 1.25 into equation 2, it becomes

3x + 2×1.25 = 10

3x + 2.5 = 10

3x = 10 - 2.5 = 7.5

x = 7.5/3 = 2.5

To find the athlete's salary for year 7 of the contract, apply a 4% annual increase to the previous year's salary starting from year 2. The athlete's salary for year 7 is approximately $3,836,192.

To find the athlete's salary for year 7 of the contract, we need to calculate the annual increase for each year from year 2 to year 7 and apply it to the starting salary of $3,000,000 for year 1.

In year 2, the salary is 1.04 times the previous year's salary, so the salary for year 2 is $3,000,000 * 1.04 = $3,120,000.

In year 3, the salary is 1.04 times the previous year's salary, so the salary for year 3 is $3,120,000 * 1.04 = $3,244,800.

Following the same pattern, we can calculate the salaries for years 4, 5, 6, and 7:

In year 4: $3,244,800 * 1.04 = $3,379,392

In year 5: $3,379,392 * 1.04 = $3,523,027.68

In year 6: $3,523,027.68 * 1.04 = $3,675,348.11

In year 7: $3,675,348.11 * 1.04 = $3,836,191.72

Therefore, the athlete's salary for year 7 of the contract is approximately $3,836,192.

The athlete's salary for year 7 of the contract is $3,822,736.

To calculate the athlete's salary for year 7, we use the formula for compound interest, which is also applicable to salaries that increase annually at a fixed percentage. The formula is:

[tex]\[ A = P(1 + r)^n \][/tex]

Given that the initial salary (principal amount P is $3,000,000 and the annual increase rate r is 4% (or 0.04 as a decimal), we can calculate the salary for year 7 as follows:

[tex]\[ A = 3,000,000(1 + 0.04)^{7-1} \] \[ A = 3,000,000(1.04)^6 \] \\[ A = 3,000,000 \times 1.26530612 ](after calculating ( 1.04^6 \)) \\\\[A = 3,822,736 \][/tex]

(after rounding to the nearest dollar)

Therefore, the athlete's salary for year 7 of the contract, rounded to the nearest dollar, is $3,822,736.

Answer:

B

Step-by-step explanation:

There is a vertical asymptote at x=3. It is not defined and therefore not included in the domain.

All other numbers are included in the domain.

Answer:

The hikers are 5.9 miles apart.

Step-by-step explanation:

Let O represents the base camp,

Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in the line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras theorem,

[tex]BD^2 = BD'^2 + DD'^2[/tex]

[tex]BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9[/tex]

Hence, the hikers are 5.9 miles apart.

The speed is 66.33 miles per hour

Step-by-step explanation:

Given

Total distance = 325 miles

They still have 126 miles to go. In order to find the distance they have covered, we will subtract the remaining miles from the total

So,

[tex]Distance\ covered=325-126=199\ miles[/tex]

the car has been driving for 3 hours

So,

t= 3 hours

d = 199 miles

[tex]Speed=\frac{d}{t}\\=\frac{199}{3}\\=66.33\ miles\ per\ hour[/tex]

The speed is 66.33 miles per hour

Keywords: Speed, Distance

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Answer:

0.273

Step-by-step explanation:

Let the number of insured pieces of luggage be i and u be the number of uninsured pieces of luggage, therefore,

i + u = 27

Now,

probability that exactly one of the damaged pieces of luggage is insured = (iC1)(uC3)/(27C4)

probability that none of the damaged pieces are insured = (uC4)/(27C4)

and,

(iC1)(uC3)/(27C4) = 2 (uC4)/(27C4)

=> u − 2i = 3

By solving, i + u = 27 and  u − 2i = 3

i = 8 and u = 19

and,

(8C2)(19C2)/(27C4) = 0.273

Answer:

Step-by-step explanation:

Answer:

he age of girl 3 [tex]\frac{1}{2}[/tex] years ago is 8.5 years  .

Step-by-step explanation:

Given as :

The present age of seventh grader girl = 12 years

Let The age of her 3 [tex]\frac{1}{2}[/tex] years ago = x years

So The age of girl [tex]\frac{7}{2}[/tex] years ago = x years

Now, According to question

The age of girl 3.5 years ago = 12 - 3.5

Or,  The age of girl 3.5 years ago = 8.5 years

Hence The age of girl 3 [tex]\frac{1}{2}[/tex] years ago is 8.5 years  . Answer

Answer:

A. 960

Step-by-step explanation:

Multiply each heart rate by 24 (hours in a day)

Subtract the human's daily heart rate from the elephant's.

30 x 24 = 720

70 x 24 = 1680

1680 - 720 = 960

Answer:

It’s A

Step-by-step explanation:

Answer:

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000

Step-by-step explanation:

The total number of alphabet's = 26

The total number of digits  = 10 (0 - 9)

The number plate contains 3 letters followed by 2 digits.

The number of ways the license plates contain no repeated letters and no repeated digits.

The number of ways first letter can be filled in 26 ways.

The number of ways second letter can be filled in 25 ways.

The number of ways third letter can be filled in 24 ways.

The number of ways the first digit can be in 10 ways

The number of ways the second digit can be in 9 ways.

The number of ways the license plates contain no repeated letters and no repeated digits = 26 × 25 × 24 × 1 0 × 9

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000

Answer:

  -tan(73°)

Step-by-step explanation:

The reference angle is the smallest angle between the terminal ray and the x-axis. Here, the terminal ray is in the 4th quadrant, so the reference angle will be ...

  ref∠ = 360° -287° = 73°

In the 4th quadrant, the tangent is negative, so we have ...

  tan(287°) = -tan(73°)

The coffee's temperature after 15 minutes in the freezer, using Newton's Law of Cooling with a cooling constant [tex]\( k \approx 0.0816 \),[/tex] is approximately [tex]\( 45.57^\circ F \).[/tex]

Newton's Law of Cooling is given by the equation:

[tex]\[ T(t) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

Where:

[tex]\( T(t) \)[/tex]= temperature of the object at time \( t \)

[tex]\( T_0 \)[/tex] = initial temperature of the object

[tex]\( T_a \)[/tex] = ambient temperature

[tex]\( k \)[/tex] = cooling constant

[tex]\( t \)[/tex] = time

Given:

[tex]\( T_0 = 155^\circ F \)[/tex] (initial temperature)

[tex]\( T_a = 0^\circ F \)[/tex] (ambient temperature)

[tex]\( T(5) = 103^\circ F \)[/tex](temperature after 5 minutes)

We need to find the coffee's temperature[tex](\( T(15) \))[/tex] after 15 minutes. First, we need to determine the cooling constant [tex]\( k \)[/tex].

Using the given information, let's rearrange Newton's Law of Cooling to solve for [tex]\( k \)[/tex]:

[tex]\[ T(t) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ T(t) - T_a = (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ \frac{T(t) - T_a}{T_0 - T_a} = e^{-kt} \][/tex]

[tex]\[ -kt = \ln\left(\frac{T(t) - T_a}{T_0 - T_a}\right) \][/tex]

[tex]\[ k = -\frac{1}{t} \cdot \ln\left(\frac{T(t) - T_a}{T_0 - T_a}\right) \][/tex]

Given [tex]\( T(5) = 103^\circ F \)[/tex]:

[tex]\[ k = -\frac{1}{5} \cdot \ln\left(\frac{103 - 0}{155 - 0}\right) \][/tex]

[tex]\[ k = -\frac{1}{5} \cdot \ln\left(\frac{103}{155}\right) \][/tex]

[tex]\[ k \approx -\frac{1}{5} \cdot \ln(0.6645) \][/tex]

[tex]\[ k \approx -\frac{1}{5} \cdot (-0.4081) \][/tex]

[tex]\[ k \approx 0.0816 \][/tex]

Now that we have the cooling constant [tex]\( k \)[/tex], we can find [tex]\( T(15) \)[/tex]:

[tex]\[ T(15) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ T(15) = 0 + (155 - 0) \cdot e^{-0.0816 \cdot 15} \][/tex]

[tex]\[ T(15) = 155 \cdot e^{-1.224} \][/tex]

[tex]\[ T(15) \approx 155 \cdot 0.294 \][/tex]

[tex]\[ T(15) \approx 45.57^\circ F \][/tex]

Therefore, the coffee's temperature after 15 minutes in the freezer is approximately [tex]\( 45.57^\circ F \)[/tex].

Answer:the cost of renting one movie is $1.5

the cost of renting one video game is $5.2

Step-by-step explanation:

Let x represent the cost of renting one movie.

Let y represent the cost of renting one video game. One month melissa rented 12 movies and 2 video games for a total of $29. This means that

12x + 2y = 29 - - - - - - -1

The next month she rented 3 movies and 5 video games for a total of 32$. This means that

3x + 5y = 32 - - - - - - - - 2

Multiplying equation 1 by 5 and equation 2 by 2, it becomes

60x + 10y = 145

6x + 10y = 64

Subtracting,

54x = 81

x = 81/54 = 1.5

Substituting x = 1.5 into equation 2, it becomes

3x + 5y = 32

3×2 + 5y = 32

5y = 32 - 6 = 26

y = 26/5 = 5.2

Answer:

See the answers bellow

Step-by-step explanation:

For 51:

Using the definition of funcion, given f(x) we know that different x MUST give us different images. If we have two different values of x that arrive to the same f(x) this is not a function. So, the pair (-4, 1) will lead to something that is not a funcion as this would imply that the image of -4 is 1, it is, f(-4)=1 but as we see in the table f(-4)=2. So, as the same x, -4, gives us tw different images, this is not a function.

For 52:

Here we select the three equations that include a y value that are 1, 3 and 4. The other values do not have a y value, so if we operate we will have the value of x equal to a number but not in relation to y.

For 53:

As he will spend $10 dollars on shipping, so he has $110 for buying bulbs. As every bulb costs $20 and he cannot buy parts of a bulb (this is saying you that the domain is in integers) he will, at maximum, buy 5 bulbs at a cost of $100, with $10 resting. He can not buy 6 bulbs and with this $10 is impossible to buy 0.5 bulbs. So, the domain is in integers from 1 <= n <= 5. Option 4.

For 54:

As the u values are integers from 8 to 12, having only 5 possible values, the domain of the function will also have only five integers values, With this we can eliminate options 1 and 2 as they are in real numbers. Option C is the set of values for u but not the domain of c(u). Finally, we have that 4 is correct, those are the values you have if you replace the integer values from 8 to 12 in c(u). Option 4.

Answer:

f(x) = ln(x^3 + e^4x) answer is explain in attachment .

Step-by-step explanation:

f(x) = ln(x^3 + e^4x) =(2x+3e³ˣ) 1/x² + e³ˣ

Answer: m<YSH = 35°  

               m<YIH = 20°

              m<SAI =  71°

               m<PAY = 8°

                    PY =  i don' t know

and P.S these answers may all be wrong sorry but hope it helps. :)

Answer:

Step-by-step explanation:

Answer:

C. 2x^2-7x+7

Step-by-step explanation:

(3x^2-2x+2)-(x^2+5x-5)     Given

From the given you will subtract like terms from both parenthesis.

3x^2-x^2=2x^2

-2x-5x=-7x

2-(-5)=7                      

To simplify the given expression, distribute the negative sign through the second parentheses, combine like-terms, which results in 2x^2 - 7x + 7, corresponding to option (c).

To simplify the expression (3x2−2x+2)−(x2+5x−5), you'd start by distributing the negative sign through the second parentheses.

Doing so gives us 3x^2 - 2x + 2 - x^2 - 5x + 5.

Upon combining like-terms, the expression becomes 2x^2 - 7x + 7.

So, the simplified form of the original expression is 2x^2 - 7x + 7.

In the given options,

c) 2x²-7x+7 is right

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The [tex]a_n[/tex] reprsents the nth term where n is some positive whole number {1,2,3,...}

The [tex]a_{n-1}[/tex] represents the term just before the nth term. For example, if n = 22 then [tex]a_{n} = a_{22}[/tex] and [tex]a_{n-1} = a_{21}[/tex]

The +5 at the end means we add 5 to the previous term just before the nth term to get the nth term. In other words, the rule is "add 5 to each term to get the next term".

To get the 9th term [tex]a_{9}[/tex], we need to find the terms before this one because the recursive sequence builds up. The 9th term depends on the 8th term, which depends on the 7th term, and so on. The countdown stops until you reach the first term.

-------

[tex]a_{1} = 3[/tex] (given)

[tex]a_{2} = 8[/tex] (given)

[tex]a_{3} = 13[/tex] (given)

[tex]a_{4} = 18[/tex] (given)

[tex]a_{5} = 23[/tex] (given)

[tex]a_{6} = a_{5}+5 = 23+5 = 28[/tex] (add 5 to the prior term)

[tex]a_{7} = a_{6}+5 = 28+5 = 33[/tex]

[tex]a_{8} = a_{7}+5 = 33+5 = 38[/tex]

[tex]a_{9} = a_{8}+5 = 38+5 = 43[/tex]

So the 9th term is [tex]a_{9} = 43[/tex]

Answer:

There were 333 seniors in 1990

153 seniors had jobs in 2010.

Step-by-step explanation:

Let the number of high school seniors in 1990 = x

75% of x had jobs in 1990

In 2010 there were 50 more seniors. That is, the number of seniors is x+50.

40% of (x+50) had jobs in 2010.

Total number of jobs in both years = 403.

\[0.75 * x + 0.4 * (x + 50) = 403\]

\[0.75 * x + 0.4 * x  + 20 = 403\]

=> \[1.15 * x  = 403 - 20\]

=> \[1.15 * x  = 383\]

=> \[x  = 383/1.15\]

=> \[x  = 333\]

Number of seniors having job in 2010 = 0.4 * (333 + 50) = 0.4 * 383 = 153.2 = 153(approx)

Answer:

a) 0.3277

b) 0.0128

Step-by-step explanation:

We are given the following information in the question:

N(2750, 560).

Mean, μ = 2750

Standard Deviation, σ = 560

We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P (less than 2500 grams)

P(x < 2500)

[tex]P( x < 2500) = P( z < \displaystyle\frac{2500 - 2750}{560}) = P(z < -0.4464)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 2500) = P(z < -0.4464) = 0.3277 = 32.77\%[/tex]

b) P ((less than 1500 grams)

P(x < 1500)

[tex]P( x < 1500) = P( z < \displaystyle\frac{1500 - 2750}{560}) = P(z < -2.2321)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 1500) = P(z < -2.2321) = 0.0128 = 1.28\%[/tex]

Final answer:

The probability of a late-preterm baby having a low birth weight (< 2500 grams) is approximately 32.74%, and the probability of a very low birth weight (< 1500 grams) is about 1.29%.

Explanation:

To answer the given questions, we will use the properties of the normal distribution, where the mean birth weight (μ) for late-preterm babies is 2750 grams, and the standard deviation (σ) is 560 grams. The distribution of birth weights is assumed to be normal (N(2750, 560)).

1. Probability of a Low Birth Weight (< 2500 grams)

To find the probability of a baby having a low birth weight (less than 2500 grams), we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (2500 grams). Plugging in the values gives us Z = (2500 - 2750) / 560 = -0.4464. Using a Z-table or a normal distribution calculator, we find the probability corresponding to Z = -0.4464, which is approximately 0.3274. Therefore, the probability of a late-preterm baby having a low birth weight is about 0.3274 or 32.74%.

2. Probability of a Very Low Birth Weight (< 1500 grams)

To calculate the probability of a very low birth weight (less than 1500 grams), again we calculate the Z-score: Z = (1500 - 2750) / 560 = -2.2321. The probability of Z = -2.2321, referring to the Z-table or calculator, is extremely low, approximately 0.0129 or 1.29%. This indicates that the chances of a late-preterm baby having a very low birth weight is about 1.29%.

Answer:

c

Step-by-step explanation:

Answer:

(m) +  2 (m)  - 7 = 32 is the needed expression.

Points scored by  Pittsburgh Steelers =  13

Points scored by New Orleans Saints = 19

Step-by-step explanation:

Let us assume the points scored by  Pittsburgh Steelers = m

So, the Points scored by New Orleans Saints

 = 2 (Points scored by Pittsburgh Steelers ) - 7

 = 2 (m)  - 7

Also,the total points scored by both teams = 32

So the points scored by( New Orleans Saints + Pittsburgh Steelers) = 32

⇒ (m) +  2 (m)  - 7 = 32

or, 3 m =  32 + 7 =  39

⇒ m = 39/ 3 = 13, or m = 13

So, the points cored by Pittsburgh Steelers = m =  13

and the points scored by  New Orleans Saints  = 2m - 17

                                                                              = 2(13) - 7 = 19

Answer:

  1

Step-by-step explanation:

(f+g)(1) = f(1) +g(1) = -1 + 2 = 1

__

The pair (1, -1) in the definition of f tells you f(1) = -1.

The pair (1, 2) in the definition of g tells you g(1) = 2.

Answer:

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.

Step-by-step explanation:

We are given the following information in the question:

Probability that a randomly selected person has high blood pressure = 0.4

[tex]P(H) = 0.4[/tex]

Probability that a randomly selected person is a runner = 0.4

[tex]P(R) = 0.4[/tex]

Probability that a randomly selected person has high blood pressure and is a runner = 0.1

[tex]P(H \cap R) = 0.1[/tex]

If the events of selecting a person with high blood pressure and person who is a runner are independent then we can write:

[tex]P(H \cup R) = P(H) + P(R)-P(H\cap R)[/tex]

Probability that a randomly selected person either has high blood pressure or is a runner or both =

[tex]P(H \cup R) = P(H) + P(R)-P(H\cap R)\\P(H \cup R) = 0.4 + 0.4 -0.1 = 0.7[/tex]

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.

Final answer:

The probability that a randomly selected person either has high blood pressure or is a runner or both is 0.7.

Explanation:

To find the probability that a randomly selected person either has high blood pressure or is a runner or both, we use the formula for the probability of either event A or event B occurring, which is:

P(A or B) = P(A) + P(B) - P(A and B).

Given:

P(H) = probability of high blood pressure = 0.4

P(R) = probability of being a runner = 0.4

P(H and R) = probability of both high blood pressure and being a runner = 0.1

Using the formula, we plug in the given probabilities:

P(H or R) = 0.4 + 0.4 - 0.1 = 0.7.

So, the probability that a randomly selected person either has high blood pressure, is a runner, or both events occur is 0.7.

Answer:

The answer to your question is letter A. [tex]\frac{8}{17}[/tex]

Step-by-step explanation:

Sin C = [tex]\frac{opposite side }{hypotenuse}[/tex]

Opposite side = 8

hypotenuse = 17

Substitution and result

sin C= [tex]\frac{8}{17}[/tex]

Answer:

The answer to your question is: Burger = $4.45, Pizza = $2.2

Step-by-step explanation:

Jason = $15.5 for 3 slices of pizza + 2 burgers

Susan = $20 for 1 slice of pizza + 4 burgers

Pizza = p

burger = b

System of equations

Jason                                   3p + 2b = 15.5        (I)

Susan                                     p + 4b = 20           (II)

Solve system by elimination

Multiply (II) by -3

                                          3p + 2b = 15.5

                                        -3p - 12b = -60

                                              -10b = -44.5

                                                   b = -44.5/-10

                                                  b = $4.45

                                             p + 4(4.45) = 20

                                             p + 17.8 = 20

                                             p = 20 - 17.8

                                                 p = 2.2

One slice of pizza costs $2.2 and one burger cost $4.45

Answer:

Step-by-step explanation:

The population P of a certain city can be modeled by

P=19000e0.0215t

where T represent the number of years since 2000.

When t=1 the year is 2001

when t =2 the year is 2002. This means that

When t=0 the year is 2000

To determine the year when the population will be 40,000 , we will substitute P = 40,000 and solve for t. It becomes

40000 = 19000e^0.0215t

40000 / 19000 = e^0.0215t

2.105 = e^0.0215t

Take ln of both sides

0.7443 = 0.0215t

t = 0.7443/0.0215

t = 34.62

Approximately 35 years

So the year will be 2035