Answer:
a) mean= 158.4 , standard deviation = 3.394
b) Best option : B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.
c) P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188
Step-by-step explanation:
1) Notation
n = sample size = 8
[tex] \mu [/tex] = population mean = 19.8
[tex] \sigma [/tex] = population standard deviation = 1.2
2) Definition of the variable of interest
Part a
The variable that we are interested is [tex] \sum x_i [/tex] and the mean and the deviation for this variable are given by :
E([tex] \sum x_i [/tex]) = [tex] \sum E(x_i) [/tex] = n [tex] \mu [/tex] = 8x19.8 = 158.4
Var([tex] \sum x_i [/tex]) = [tex] \sum Var(x_i) [/tex] = n [tex] \sigma^2 [/tex]
Sd([tex] \sum x_i [/tex]) = [tex] \sqrt{n \sigma^2} [/tex] = [tex] \sqrt(8) [/tex] x 1.2 = 3.394
Part b
For this case the populations are normal, then the distribution for the sample ([tex] \sum x_i [/tex]) is normal too.
Based on this the distribution for the variable X would be normal, so the best option should be:
B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.
Part c
From part a we know that the mean = 158.4 and the deviation = 3.394
The z score is defined as
Z = (X -mean)/ deviation = (160-158.4)/ 3.394 = 0.471
Then we can find the probability P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188
Find f ′(x) for f(x) = ln(x^3 + e^4x).
SHOW WORK
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
In 1990, 75% of all high school seniors had jobs. In 2010, 40% of all seniors had jobs. If there were 50 more seniors in 2010 than 1990 and there were a total of 403 jobs between both years, how many seniors were there in 1990? How many seniors had jobs in 2010
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)
How much difference do a couple of weeks make for birth weight? Late-preterm babies are born with 34 to 36 completed weeks of gestation. The distribution of birth weights (in grams) for late-preterm babies is approximately N(2750, 560).
1. What is the probability that a randomly chosen late-preterm baby would have a low birth weight (less than 2500 grams)? Round your answer to 4 decimal places.
2. What is the probability that a randomly chosen late-preterm baby would have a very low birth weight (less than 1500 grams)? Round your answer to 4 decimal places.
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%.
The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomly selected person either has high blood pressure or is a runner or both.
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.
From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the nearest tenth of a mile how far apart are the hikers
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.
Is anyone wanna help me?
If you help me you will earn 8+ pts.
( i need all questions answer )
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.
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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:
Omar and Mackenzie want to build a pulley system by attaching one end of a rope to their 8-foot-tall tree house and anchoring the other end to the ground 28 feet away from the base of the treehouse. How long, to the nearest foot, does the piece of rope need to be?
a. 26ft
b. 27ft
c. 28ft
d. 29ft
Answer:
d. 29ft
Step-by-step explanation:
Using pythagoras theorem which states that
a^2 + b^2 = c^2
where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side
From the attached image, Let the length of the rope be x
[tex]x^{2} = 8^{2}+ 28^{2} \\[/tex]
[tex]x^{2} = 64 + 784[/tex]
[tex]x^{2} = 848[/tex]
[tex]x =\sqrt{848}[/tex]
[tex]x = 29.12[/tex]
x≈29
Suppose A is n x n matrix and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In. By Theorem 7, this shows that A must be Invertible.)
Theorem 7: An n x n matrix A is invertible if and only if A is row equivalent to In, and in this case, any sequence of elementary row operations that reduces A to In also transfrms In into A-1.
Answer:
Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
A cup of coffee with temperature 155degreesF is placed in a freezer with temperature 0degreesF. After 5 minutes, the temperature of the coffee is 103degreesF. Use Newton's Law of Cooling to find the coffee's temperature after 15 minutes.
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].
Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?a. The experiment has at least two possible outcomes.b. Exactly two outcomes are possible on each trial.c. The trials are dependent on each other.d. The probabilities of the outcomes changes from one trial.
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.
Explanation: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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How am I supposed to solve this? I know how to do the equations but I don't know why there are only 2 places to put an answer for X and Y when there are 2 equations. Both equations have an X and a Y so that means there are 4 X and Y answers.
Answer:
x = 1
y = -4
Step-by-step explanation:
We will multiply the 2nd equation by 4 first:
4 * [-x + y = -5]
-4x + 4y = -20
Now we will add this equation with 1st equation given. Shown below:
4x + 3y = -8
-4x + 4y = -20
---------------------
7y = -28
Now, we can solve for y easily:
7y = -28
y = -28/7
y = -4
Now, we take this value of y and put it in 1st original equation and solve for x:
4x + 3y = -8
4x + 3(-4) = -8
4x - 12 = -8
4x = -8 + 12
4x = 4
x = 4/4
x = 1
So, this is the only solution to this problem ( 1 intersection point at x = 1 and y = -4)
ASAP PLZ!!! Select the correct answer. Solve for x. 2x2 − 4x = 0 A. 0, -4 B. 0, -2 C. 0, 2 D. 2, 4
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
Find the formula for the nth term in this arithmetic sequence: 8,4,0,-4
Suppose a seventh graders birthday is today, and she is 12 years old. How old was she 3 1/2 years ago? Write an equation, and use a number line to model your answer
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
A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.
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.
Explanation: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.
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. For 3 pounds of jelly beans and 2 pounds of trailmix the total cost is $10. Find the cost for each pound of jelly beans and each pound of trailmix
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
What is the value of sin C ?
A. 8/17
B. 15/8
C. 15/17
D. 8/15
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]
One month melissa rented 12 movies and 2 video games for a total of $29.The next month she rented 3 movies and 5 video games for a total of 32$. Find the cost for each movie and each video game.
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
How many different license plates are possible if each contains 3 letters (out of the alphabet's 26 letters) followed by 2 digits (from 0 to 9)? How many of these license plates contain no repeated letters and no repeated digits?
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
f(x) = x2 + 1 g(x) = 5 – x
(f – g)(x) =
A. x2 + x – 4
B. x2 + x + 4
C. x2 – x + 6
D. x2 + x + 6
Answer:
c
Step-by-step explanation:
NO ONE KNOWS THIS ANSWER?
how does the graph f(x) =(x-8)^3+4 compare to the paren function g(x)=x^3?
Not multiple choice.
Answer:
Their intercepts are unique.
Explanation:
[tex]\displaystyle x^3 - 24x^2 + 192x - 508 = (x - 8)^3 + 4[/tex]
This graph's x-intercept is located at approximately [6,41259894, 0], and the y-intercept located at [0, −508].
[tex]\displaystyle g(x) = x^3[/tex]
The parent graph here, has both an x-intercept and y-intercept located at the origin.
I am joyous to assist you anytime.
A park ticket is $42 per person. For groups with up to 8 people, the cost per ticket goes down $3. Molly's ticket cost $30. How many people are in Molly's group?
There are 4 people in Molly's group.
Step-by-step explanation:
Let,
x be the number of people.
Individual ticket price = $42
Price after discount = $30
Discount per ticket = $3
Discount for x people = 3x
According to given statement;
42-3x=30
Subtracting 42 from both sides
[tex]42-42-3x=30-42\\-3x=-12\\[/tex]
Dividing both sides by -3
[tex]\frac{-3x}{-3}=\frac{-12}{-3}\\x=4[/tex]
There are 4 people in Molly's group.
Keywords: Subtraction, division
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Given f(x)=2x^3+x^2-7x-6. Find all real and imaginary zeroes. Show your work.
The real zeroes of given function is [tex]-\frac{3}{2},-1, \text { and } 2[/tex]
Solution: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]
The New Orleans Saints scored 7 fewer points than twice the points scored by the Pittsburgh Steelers. The two teams together scored a total of 32 points. Write and solve an equation to show how many points each team scored.
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
Consider the following functions:
f = {( -4, 2), (1, -1)} and g= {(0, 3), (1,2), (-3,-2), (-4,2)}
(f+g)(1)= ?
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.
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 based in yhis model in what year will the population reach 40,000
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
Simplify.
(3x2−2x+2)−(x2+5x−5)
a.4x^2+3x−3
b.2x^2+3x−3
c.2x^2−7x+7
d.2x^2−3x−3
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).
Explanation: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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Jason paid $15.50 for 3 slices of pizza and 2 burgers. Susan paid $20 for 1 slice of pizza and 4 burgers. Write a system of equation and then determine the cost of each slice of pizza and the cost of each burger.
Each slice of pizza costs $
Each burger costs $
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
On a trip over Thanksgiving Break Jenn's family has to drive a total of 325 miles.. If there are 126 miles to go and the car has been driving for 3 hours, What is the speed? Explain how this relates to slope?
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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