0.1116 is the area under the standard normal curve using the given z-score.
What is Z-score?The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed.
Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator.
Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.
So, the area under the standard normal curve will be:
Find the z-scores by looking at the table's intersection of the 0.9 down and 0.07 across columns, which is 0.1660.
Similarly, find -0.5 down and 0.09 across to get 0.2776.
Add them together now: 0.2776 - 0.1660 = 0.1116
Therefore, 0.1116 is the area under the standard normal curve using the given z-score.
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PLEASE HELP WILL GIVE BRAINLIST ! , PLEASE MAKE IT FAST
Answer:
t >28= the temp is warmer than 28
t >29= the table is heavier than 29 kilos
t <29= tony is you get than 29 yrs old
t <28= tia ran the race in under 28 secs
Step-by-step explanation:
hope this helps
Find the product of 2x2(6x + 3)
Answer:
22x
Step-by-step explanation:
2x 2(6x+3)
2x 12x+6x
22x
outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.
Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, the temperature, d, in terms of t. The Equation is :
D = - 11 sin(π/12) + 65
The range is 76 - 54 = 22
so, a = 11
we know that the period is 24 hours
So, 2π/k=24
⇒ 24k = 2π
⇒ k = π/12
So far we have:
D = 11 sin(π/12)(t) + 65
Giving us a range from 76 to 54
But obviously the temp after midnight would decrease, whereas our function has it increasing to 76 when t = 6 (6:00 am)
We could do a phase shift, or more simply, just flip the function to
D = -11sin(π/12)t + 76
Checking some values
t = 0 , D = -11sin0 + 65 = 65
t=6 , (6:00 am) D = -11 sin (π/2) + 65 = 54
t = 12 (noon), D = -11 sin π + 65 = 65
t = 18 , (6:00 pm) , D = -11sin 3π/2 + 65 = 76
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A random number generator is used to create a list of 150 single-digit numbers. of those 150 numbers, 72 are odd and 78 are even. the number 9 was generated 15 times to the nearest whole percent, what is the experimental probability of an odd number other than 9 being generated? o 38% 0 48% o 52% o 79% 20°f sunny 'o
The experimental probability of an odd number other than 9 being generated is 38%.
Explain the term experimental probability?A probability that has been established by a series of tests is called an experimental probability. To ascertain their possibility, a random experiment is initiated and iterated over a number of times; each iteration is referred to as a trial. The goal of the experiment is to predict the likelihood that an event will occur or not.For the stated question-
150 numbers altogether.Odd numbers in total: 72There are 15 nines.Other odd numbers outside nine are as follows: 72 - 15 = 57
Probability = (number of odd numbers except nine)]/(total number)
Probability = 57/150
Probability = 0.38.
Thus, the experimental probability of an odd number other than 9 being generated is 38%.
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An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n=55 C of I students found 11 with brown eyes. Give the numerical value of the statistic p^(P HAT)=
The numerical value of the statistic ^p or sample proportion (p-hat) is 0.2.
^p = X/N where X denotes the number of successes and N denotes the size of the sample. Here, X=55 and N=11.
Sample Proportion (p-hat) of the data:
The sample proportion is a random variable which varies from sample to sample which is not predicted with certainty.Sample proportion is given by the ratio of number of successes in a sample to the size of that sample. It is symbolised as p-hat.the mean of p-hat is exactly (p).Standard Deviation of sample proportion is [tex]\sqrt{[p(1-p)/n]}[/tex].To know more about Sample proportion:
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What is the gradient of the graph shown? Give your answer in its simplest form.
Answer:
gradient = 2
Step-by-step explanation:
calculate the gradient m using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-(-5)}{2-0}[/tex] = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
the profit realized by the sales of a particular item follows a normal distribution with a mean of $0.5 million per quarter and a standard deviation of $0.1 million per quarter. what percent of the quarters can be expected to see a profit of at least $0.5 million?
98% of the quarters can be expected to see a profit of at least $0.5 million.
What is a standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Z score = 0.7-0.5 = 0.2
σ = 0.1
P-value from Z-Table:
P(x<0.5) = 0.97725
≈ 98%
Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.
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David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. determine what amount david must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year for 30 years. round to the nearest cent. a. $783,760.48 b. $979,054.50 c. $1,225,080.50 d. $795,516.88 please select the best answer from the choices provided a b c d
If David wants to withdraw $32,635.15 every year from his account at the end if each year for 30 years, he has to have $783243.6 in the bank account .
Define the term present annuity?The amount of money that would be required today to finance a series consecutive future annuity payments is referred to as the annuity's present value. sum of money received now is worth more than a similar sum at a later time due to the time value of money.We would use the equation for calculating present annuity.
It is written as
PV = R[1 - (1 + r)^- n]
In which.
The investment's present value is represented by PV.R stands for the consistent payments made (also weekly, monthly)The expression r stands for interest rate/interval payments.A total number of repayments is indicated by the number n.Considering the data provided,
r = 1.5/100 = 0.015
n = 30 years
R = $32,635.15
Put the values in the formula,
PV = 32635.15[1 - (1 + 0.015)⁻³⁰]/0.015
PV = 32635.15[1 - (1.015)⁻³⁰]/0.015
PV = 32635.15(1 - 0.64)/0.015
PV = 32635.15 × 24
PV = $783243.6
Thus, amount David must have in the bank presently is $783243.6.
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two brothers each purchased a new pair of hiking boots and two canteens the hiking boots cost $34.00 each and the total of their purchase was $98.00 what was the cost of each canteen
Answer:
Ok this is easy you got this!
Step-by-step explanation:
Ok so, we know their over total is 98.00, we also know that the boots cost $34 each
lets start with 34+34= 68
now we are going to take that from 98
98-68=30
now because they bought two canteens we will divide 30 by 2
30 divided by 2 is 15
the cost of each canteen is $15
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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what is the variance of the number of times a 6 appears when a fair die is rolled 12 times? (enter the final answer in decimal format and round to three decimal places.)
The variance of the number of occasions a 6 appears when a fair die is thrown 12 times is 0.156.
It determines the likelihood of achieving a specific number of successes over a specific number of trials with a consistent success rate using the binomial distribution.
With a 1/6 likelihood of success for each trial, the number of successes in this example is equal to the number of 6s that occur.
The probability of each conceivable value of the quantity of 6s that appear may be calculated using the binomial formula. The likelihood of receiving exactly 0 number of 6s is (12 choose 0) ×[tex](\frac{1}{6})^0[/tex] × [tex](\frac{5}{6}) ^{12}[/tex] = 0.1680. The probability of getting exactly 1 number of 6 is (12 choose 1) × [tex](\frac{1}{6})^1[/tex] × [tex](\frac{5}{6})^{11}[/tex] = 0.4401. The probability of getting exactly 2 numbers of 6s is (12 choose 2) × [tex](\frac{1}{6})^2[/tex] × [tex](\frac{5}{6})^{10}[/tex] = 0.3744. And so on.
The likelihood of receiving 0 6s, for instance, multiplied by the square of the 0's divergence from 2 is 0.1680 × (0 - 2)² = 0.7056. The likelihood of receiving 1 6 when multiplied by the square of the difference between 1 and 2 is 0.4401 × (1 - 2)² = 0.4401. And so on.
To get the anticipated value of the squared departure of the number of 6s that occur from 2, we may finally total up all of these probabilities.
This predicted value is equal to 1.8801 by adding 0.7056, 0.4401, 0.3744, 0.1596, 0.0368, and 0.0036.
The range in the number of 6s that appear after tossing a fair die 12 times is thus 1.8801.
To express the variation in decimal notation, divide the difference by the total number of rolls (12), then round the output to the closest three decimals.
As a consequence, we obtain a variance of 0.1567. The variance in the number of occasions a 6 appears when a fair dice is rolled 12 times is thus 0.1567.
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How many solutions does the equation 5n + 1 = 1 + 4n have
Short Answer:
The given equation has one solution; [tex]n=0[/tex].
Further Explanation:______________________________________________________
"How Can You Determine Whether An Equation Has One Solution, Infinite Solutions, or No Solution?"
One Solution - Some equations have exactly one solution. In these equations, there is only one value for the variable that makes the equation true. You can tell that an equation has one solution if you solve the equation and get a variable equal to a number.Infinite Solutions - Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.No Solution - If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This being said, lets now go back to the given scenario and determine the amount of solutions it has, if any.
1. We are given the following to solve:
[tex]5n+1=1+4n[/tex]2. First, subtract 1 from both sides.
[tex]5n+1-1=1+4n-1[/tex]3. Simplify.
[tex]5n=4n[/tex]4. Move 4n to the left side, leaving us with our final solution.
[tex]n=0[/tex] ← Final Solution____________________________________________________
Hope this helps!
what is the rate of change in y = 2x + 4 and initial value?
Answer: rate of change is 2
Step-by-step explanation:
Pls help
, I really need an answer for this rn
Answer:
Step-by-step explanation:
A health researcher conducted a survey and recorded the percentage of body fat of 20 randomly selected men from two different towns.
Answer: 7 hrs and 15 minutes
Step-by-step explanation: because 15 - 8 = 7 45 - 30 = 15
q4. a rt tomatometer score of 75% is considered fresh. is the mean mcu rt tomatometer score significantly above fresh?
From the given statement the mean mcr rt tomatometer score is significantly above fresh.
What is tomatometer score?
The Tomatometer score represents the percentage of professional critic reviews that are positive for a given film or television show.
To find answer we need to perform hypothesis.
The mean MCU Rotten Tomatoes score is equal to or less than 75%, which is the null hypothesis.
The mean MCU Rotten Tomatoes score is more than 75%, which is the alternative hypothesis. To test this theory, we can use a one-tailed t-test.
The null hypothesis can be rejected if the p-value is less than the significance level, which is typically 0.05, at which point it can be determined that the mean MCU Rotten Tomatoes score significantly exceeds fresh.
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-3-6i divided by 3+2i please help
To divide complex numbers, you multiply by the conjugate of the denominator:
[tex]\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}[/tex]
We do this to turn the denominator into a real number.
[tex]\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}[/tex]
Answer:
[tex]-\dfrac{21}{13}-\dfrac{12}{13}i[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{-3-6i}{3+2i}[/tex]
Multiply the numerator and denominator by the complex conjugate of the denominator:
[tex]\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}[/tex]
Simplify:
[tex]\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}[/tex]
[tex]\implies \dfrac{-9-12i+12i^2}{9-4i^2}[/tex]
Apply the imaginary number rule [tex]i^2=-1[/tex] :
[tex]\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}[/tex]
[tex]\implies \dfrac{-9-12i-12}{9+4}[/tex]
[tex]\implies \dfrac{-21-12i}{13}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:[/tex]
[tex]\implies -\dfrac{21}{13}-\dfrac{12}{13}i[/tex]
a sample of 1200 computer chips revealed that 37% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 34% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.05 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
As per the question the required hypothesis are
Null Hypothesis, H0: p=0.72
Alternate Hypothesis, H1 : p ≠ 0.72
The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample.
Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.
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(8x + 5)^3 find the product
Answer: [tex]512x^3+960x^2+600x+125[/tex]
Step-by-step explanation: Start by spreading the expression out so it turns into (8x + 5)*(8x + 5)*(8x + 5). (* means multiply). Then, foil (multiply the first numbers, outside numbers, inside numbers, and last numbers to form a new expression) the first two expressions to get 64x^2+80x+25*(8x + 5). Foil that again, going through and multiplying each number from both expressions by every number in the other expression to get 512x^3+960x^2+600x+125. Hope that helps.
Answer:
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Perfect Cube Formula}\\\\$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$\\\end{minipage}}[/tex]
To find the product of the given expression, use the perfect cube formula.
Given expression:
[tex](8x + 5)^3[/tex]
Therefore:
a = 8xb = 5Apply the perfect cube method:
[tex]\begin{aligned}(8x+5)^3&=(8x)^3+3(8x)^2(5)+3(8x)(5)^2+5^3\\&=8^3 \cdot x^3+3 \cdot 64x^2\cdot5+3\cdot 8x\cdot 25+125\\&=512x^3+960x^2+600x+125\end{aligned}[/tex]
A house on the market was valued at 376,000. After several years, the value decreased by 9%. By how much did the house value decrease in dollars. What is the current value of the house?
Answer:
Step-by-step explanation:
The price decreases by $288,000*(0.19)=$54,720
The current value is then $233,280.
which of the following statements are true for a frequentist definition for the probability of an event g
The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.
What is frequentist probability?Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.
Frequentist probability is different from Bayesian probability in following points,
Frequentist is objective and Bayesian is subjectiveFrequentist based on observed data and Bayesian based on degree of beliefFrequentist need large sample and Bayesian not necessary need large sampleFrequentist reject the prior assumption or knowledge and Bayesian need prior assumption or knowledge for parameterThus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.
Your question is incomplete, but it is general information about the frequentist definition of probability.
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Charolette earns 3,595 per month at her job. She will receive a 7% raise. How much more money will Charolette earn each year after her raise?
The increase in the salary for Charolette will be $251.65.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.
This will be illustrated thus:
= Percentage × Salary
= 7% × $3595
= $251.65
The value of $251.65 will the increase in the salary.
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Matt and Jasmine are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Matt sold 7 packages of white chocolate chip cookie dough and 13 packages of gingerbread cookie dough for a total of $366. Jasmine sold 6 packages of white chocolate chip cookie dough and 15 packages of gingerbread cookie dough for a total of $387. Find the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough.
Answer:
i found something that might help you
Step-by-step explanation:
Find the values of x and y that make k || j and m || n. x = ° y = °
The values of x and y are x = 80° and y = 130°.
What is conservative interior angles?
When a line, referred to as the transversal line, crosses two other lines, two angles are created that are known as consecutive interior angles. Consecutive interior angles, or co-interior angles for short, are the angles formed on the inside of the two lines and on the same side of the transversal line.
Consecutive interior angle CONVERSE is another name for the same side interior angle CONVERSE.
Line line n || m
if (x - 30) + (x + 50) = 180.
x - 30 + x + 50 = 180
2x + 20 = 180
subtract 20 from both sides
2x = 160
divide both sides by 2
x = 80
IF (x - 30) + y = 180, then k || j.
(80 - 30) + y = 180
50 + y = 180
subtract 50 from both sides
y = 130
Hence, the values of x and y are x = 80° and y = 130°.
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Complete question:
Complete question is attached below,
6 yellow balls and 8 red balls are placed in an urn. two balls are then drawn in succession without replacement. what is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?
The probability that the first ball drawn is a red is 8/14
the probability that the first ball drawn is a yellow is 6/13
Let A = getting a red ball
B= getting a yellow ball given that first was red ball
P( A ) = 8/14
P( B ) = 6/ 13 (since 1 red ball is out)
A(A ∩ B)= 6/13 x 8/14 =
48/182
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
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write the general antiderivative. (use c for the constant of integration. remember to use absolute values where appropriate.) 1 8 x 1 8x 1 8 x dx
The general antiderivative is; (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C
Given,
f (x) = x/8 + 1/8x + (1/8)ˣ
We have to find the antiderivative;
Antiderivative;-
In calculus, a differentiable perform F whose spinoff is sufficient to the initial perform f could be an antiderivative, inverse derivative, primitive perform, primitive integral, or integral of a perform f. Symbolically, this could be expressed as F' = f.
Here,
To find antiderivative, we have to integrate the function first;
Then,
∫ f(x) + g(x) dx = ∫ f(x) dx + g(x) dx
∫ f(x/8) dx = x² / 16
∫ f(1/8 x) dx = 1/8 ln |x|
∫ f(1/8ˣ) dx = -1/ (3 ln × 2 × 8ˣ)
That is,
∫ x/8 + 1/8x + 1/8ˣ dx = (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C
Therefore,
(x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C will be the antiderivative.
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Myesha has a coin collection. She keeps 4 of the coins in her box, which is 5% of the collection. How many total coins are in her collection? Multiply/scale up to solve.
Answer:
There are 80 coins in her collection.
Step-by-step explanation:
We can find out how many coins are in her coin collection by first converting 5% into a fraction by moving the decimal place to the left twice. Which then we get 0.05. Then, we can set up this equation:
4 ÷ 0.05 = 80
Now, let's check our answer:
0.05 x 80 = 4.
Yep! It checks out!
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 2 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Graph each function and identify its domain, range, intercepts, asymptotes, and holes.
Thank you! :)
Answer:
Domain: real numbers except {-4, -3, 0}Range: real numbers except {2}Intercepts: (-1, 0); no y-intercept (see Holes)Asymptotes: horizontal, y = 2; vertical, x = -3Holes: (-4, 6), (0, 2/3)Step-by-step explanation:
You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).
SimplifiedThe given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.
[tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]
DomainThe function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.
RangeThe function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.
InterceptsThe x-intercept is found where the numerator of the simplified function is zero: x = -1
The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)
AsymptotesThe function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.
The vertical asymptote is at the uncanceled denominator zero, x = -3.
HolesThe holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.
The holes are (-4, 6) and (0, 2/3).
Select all of the relations that ARE functions.
Select 2 correct answer(s)
Answer:
the first one at the top . but can you put up a better picture ?
Step-by-step explanation:
design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The box's dimensions that reduce the overall cost of the materials are as follows:
L = W = 16 cm
H = 32 cm
Given,
What is the dimensions of the rectangle?
A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.
Here,
We've got
Volume = 512 cm3 L* W * H
Sides of the box cost = 1 cent/cm²
Top and bottom cost 2 cent/cm²
Then,
Box dimensions that reduce the overall cost of materials used
We are aware of
L× W × H = 512 cm³
Where,
L stands for length, W for width, and H for height.
So, when we reduce the cost function
C(L, W, H) = (1) 1 H + (2) 1 (L + W)
Thus insert H.
Replacing H with 512/LW yields,
C(L, W) = 512(1/L, 1/W), plus 2LW
So
When both partial derivatives are 0, there will be a minimum cost.
512/L2 - 2W = dC/dL = 0
So
512/W2 - 2L = 0 for dC/dW.
L = 256/W²
Now
The answer to the aforementioned equation is
L = W = (256)⁻³ = 16cm
And
H = 512/16 = 32
H = 32 cm
Consequently, the box's measurements that reduce the overall cost of the materials utilized are:
L = W = 16 cm
H = 32 cm
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(d) is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.
No, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.
What is a curve on the graph?A smooth-drawn figure or line with a bend or turn is referred to as a curve.
A circle is an illustration of a curved shape.
The path, also known as the topological arc, is the name of the curve (or just arc).
If a curve is the continuous injective image of an interval or a circle, it is considered simple.
If a curve is determined by a continuous function, in other words.
So, it possible for the curve to have a horizontal tangent:
On the curve, horizontal tangents appear where:
x = -1 and y ≠ -1
y = 0 where the curve crosses the x-axis.
-1² + 2(-1) + 0⁴ + 4.0 ≠ 5
No, the point where the curve crosses the x-axis cannot have a horizontal tangent.
Therefore, no, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.
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Complete question:
Consider the closed curve in the xy-plane given by : x²+2x+y⁴=4y = 5
Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.