Answer:
The zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=2x^2-2x+13[/tex]
To find the zeros of the function using quadratic formula.
Solution:
Applying quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given function:
[tex]a=2, b=-2\ and\ c=13[/tex]
Thus, we have:
[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(13)}}{2(2)}[/tex]
[tex]x=\frac{2\pm\sqrt{4-104}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{-100}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{100}i}{4}[/tex]
[tex]x=\frac{2\pm10i}{4}[/tex]
[tex]x=\frac{2+10i}{4}[/tex] and [tex]x=\frac{2-10i}{4}[/tex]
[tex]x=\frac{2}{4}+\frac{10i}{4}[/tex] and [tex]x=\frac{2}{4}-\frac{10i}{4}[/tex]
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Thus, the zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Helen, Francesca, and Olivia each took a test that had 25 questions. Helen got 20 questions correct, Francesca answered 3 questions incorrectly, and Olivia got 84% of the questions correct. The three unlabeled marks on the double number line below represent the percent and number of the questions each of the three friends answered correctly. Use the double number line to order Helen, Francesca, and Olivia from least to greatest according to the percentage of questions correct.
Answer:
the order is Helen Olivia Francessca
Step-by-step explanation:
ik im late but i hop this helps C:
The order of percentage of correct questions from least to greatest.
80% < 84% < 88%
Helen < Olivia < Francesca.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of questions in the test = 25.
Helen:
Percentage of the number of questions correct.
= 20/25 x 100
= 80%
Francesca:
Percentage of the number of questions correct.
= 22/25 x 100
= 88%
Olivia:
Percentage of the number of questions correct.
= 84%
Thus,
Arranging the percentage in increasing order.
80% < 84% < 88%
Helen < Olivia < Francesca.
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Please help! I'm stuck on this question.
A puzzle piece in the shape of a triangle has perimeter 25 centimeters. Two sides of the triangle are each twice as long as the shortest side. Find the length of the shortest side.
Answer: the shortest side is 10 centimeters.
The length of each of the other sides is 10 centimeters each.
Step-by-step explanation:
Let x represent the length of the shortest side of the triangle.
Two sides of the triangle are each twice as long as the shortest side. This means that the length of the two sides would be 2x.
The perimeter of a triangle is the sum of each side of the triangle.
The puzzle piece in the shape of a triangle has perimeter 25 centimeters. This means that
x + 2x + 2x = 25
5x = 25
x = 25/5
x = 5
The length of each of the two sides is
2x = 2 × 5 = 10
The length of the shortest side of the triangle is 5 centimeters.
Let's denote the length of the shortest side of the triangle as "x" centimeters. According to the problem, the other two sides are each twice as long as the shortest side. Therefore, the lengths of the other two sides are "2x" centimeters each.
Now, we can use the information given about the perimeter to set up an equation:
Perimeter = Sum of all sides
Given that the perimeter is 25 centimeters:
25 = x + 2x + 2x
Now, combine like terms on the right side:
25 = 5x
To solve for x, divide both sides by 5:
x = 25 / 5
x = 5
So, the length of the shortest side of the triangle is 5 centimeters.
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A road crew must repave a road that is seven eights
miles long. They can repave one fifty six
miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
Answer:
seven eights mean; 8888888
they can repave one fifty six mile per hour; 156/hour
Step-by-step explanation:
To calculate total time to repave
8888888/156 = 56980.02 hours require
Using this equation for Wien’s Law (λ = 2898/T), the wavelength most emitted by the Sun (T = 6000K) is approximately: a. 48.3 µm b. 483 µm c. 0.48 µm
Step-by-step explanation:
By Wien’s Law we have
[tex]\lambda =\frac{2898}{T}[/tex]
where λ is in μm and T is in K
Given that
T = 6000 K
Substituting
[tex]\lambda =\frac{2898}{6000}=0.483\mu m[/tex]
Option C is the correct answer.
Final answer:
By using Wien's Law with the given temperature of the Sun (6000K), we calculate the peak emission wavelength as 0.483 micrometers, which corresponds to option c. 0.48 µm.
Explanation:
The student asked about the wavelength most emitted by the Sun as predicted by Wien's Law, given the temperature of 6000K using the equation λ = 2898/T, where λ is the wavelength in micrometers and T is the temperature in Kelvin. According to Wien's displacement law, the temperature and peak wavelength of emission of an object are inversely proportional.
Plugging in the given temperature (T = 6000K) into the equation λ = 2898/T, we calculate the peak emission wavelength to be 2898/6000 = 0.483 µm.
So, the correct answer is c. 0.48 µm.
A forest has 800800800 pine trees, but a disease is introduced that kills \dfrac{1}{4} 4 1 start fraction, 1, divided by, 4, end fraction of the pine trees in the forest every year.
The required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]
Exponential functionThe standard exponential function is expressed as:
[tex]y=ab^x[/tex] where:
a is the initial pine treesb is the growth rate/declinet is the time takenGiven the following parameters:
a = 800
b = 1/4
Substitute into the formula to have;
[tex]y=800(\frac{1}{4} )^t[/tex]
Hence the required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]
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Answer:
It's 800(3/4)^t
Step-by-step explanation:
Can someone please answer this I don’t understand!
Point P is located at (2, 2) and point T is located at (7, 17). What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of partitioning point.
The coordinates of X are (5, 11).
Solution:
Given points of the line segment are P(2, 2) and T(7, 17)
Let X be the point that partitions the directed line segment PT in the ratio 3 : 2
Using section formula, we can find the coordinate of the point that partitions the line segment.
Section formula:
[tex]$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]
Here, [tex]x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17[/tex] and m = 3, n =2
Substitute these in the section formula,
[tex]$X(x, y)=\left(\frac{3 \times 7+2 \times 2}{3+2}, \frac{3 \times 17+2 \times 2}{3+2}\right)[/tex]
[tex]$=\left(\frac{21+4}{5}, \frac{51+4}{5}\right)[/tex]
[tex]$=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]
[tex]=(5, 11)[/tex]
X(x, y) = (5, 11)
The coordinates of X are (5, 11).
Julia has 2 children who are 4 years apart in age. Julia is four times older than her youngest child. The sum of the ages of Julia and her 2 kids is 76 years
Answer: Julia is 48 years
The oldest child is 16 years
The youngest child is 12 years
Step-by-step explanation:
Let x represent the age of the youngest child.
Let y represent the age of the oldest child.
Let x represent Julia's age.
The sum of the ages of Julia and her 2 kids is 76 years. This means that
x + y + z = 76- - - - - - - - - - -1
Julia has 2 children who are 4 years apart in age. This means that
y = x + 4
Julia is four times older than her youngest child. This means that
z = 4x
Substituting z = 4x and y = x + 4 into equation 1, it becomes
x + x + 4 + 4x = 76
6x = 76 - 4 = 72
x = 72/6 = 12
y = x + 4 = 12 + 4
y = 16
z = 4x = 4 × 12
z = 48
Answer:
what?
Step-by-step explanation:
A student translated the phrase below into an algebraic expression, and then evaluated it for g = one-fourth. Is the student's work correct? one-third more than the product of four and a number; evaluate when g = one-fourth The expression is StartFraction 4 Over g EndFraction + one-third; for g = one-fourth. StartFraction 4 Over 1 EndFraction divided by one-fourth + one-third = StartFraction 4 Over 1 EndFraction times StartFraction 4 Over 1 EndFraction + one-third = 16 + one-third = 16 and one-third.
Answer: D
Step-by-step explanation:
it makes the most sense ( do ont know how to explain but I do know it is right. )
Answer:
D.) No, product means multiplication, and the student wrote a division expression.
Step-by-step explanation:
did the assignment. good luck! <3
NEED HELP!!!!
Use long division or synthetic division to find the quotient of (2x^3 + x^2 + 1)/(x + 1)
Answer: The quotient is 2x² - x + 1
Step-by-step explanation:
We would apply the long division method to find the quotient of
(2x^3 + x^2 + 1)/(x + 1)
The attached photo shows the step by step calculations
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠X.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠X = °
Answer:
Step-by-step explanation:
Triangle VWX is a right angle triangle.
From the given right angle triangle,
VX represents the hypotenuse of the right angle triangle.
With m∠X as the reference angle,
WX represents the adjacent side of the right angle triangle.
VW represents the opposite side of the right angle triangle.
To determine m∠X, we would apply
the tangent trigonometric ratio. It is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan X = 2/1 = 1
m∠X = Tan^-1(1)
m∠X = 45°
A suncatcher has 6 sections. Each section is in the shape of a parallelogram witha base of 12 cm and a height of 8 cm. What is the total area of the sections?
Answer:
576 cm²
Step-by-step explanation:
Given:
Number of sections in a suncatcher (n) = 6
Each section is in the shape of a parallelogram.
Base of parallelogram = 12 cm
Height of parallelogram = 8 cm
Now, area of a parallelogram is given as:
Area of parallelogram = Base × Height
Area of 1 parallelogram = 12 cm × 8 cm = 96 cm²
Now, there are 6 parallelogram shaped sections.
So, area of the sections = area of 1 section × total number of sections
∴ Area of 6 sections = 96 cm² × 6 = 576 cm²
Therefore, the total area of the sections of a suncatcher is 576 cm².
Murphy family has 4 members and they went to 7 games. Chen family has 5 members and they went to 4 games. In total, the two families spent $1200. If the seats cost the same for each person, how much did the Murphy family spend?
The Murphy family spend $ 700
Solution:
Given that,
Murphy family has 4 members and they went to 7 games
Let "x" be the cost of each game
Murphy family cost: [tex]4 \times 7 \times x = 28x[/tex]
Chen family has 5 members and they went to 4 games
Chen family cost: [tex]5 \times 4 \times x = 20x[/tex]
In total, the two families spent $1200
Therefore,
28x + 20x = 1200
48x = 1200
Divide both sides by 48
x = 25
How much did the Murphy family spend?
Murphy family cost = 28x = 28(25) = 700
Thus murphy family spend $ 700
Marisa wants to buy a quality phone for least $200.She has already saved $125 and plans to save an additional $10 each week.Write an inequality that represents this
The inequality representing Marisa's goal to buy a phone costing at least $200, with $125 already saved and a plan to save $10 each week, is 125 + 10w \\geq 200, where w is the number of weeks of additional savings.
Explanation:To write an inequality that represents Marisa's situation, we need to consider the amount she has already saved, the additional amount she plans to save weekly, and the minimum amount she needs for the phone. Marisa wants a phone that costs at least $200 and has saved $125. She plans to save $10 each week. We can use the variable w to represent the number of weeks she will save additional money.
Marisa's current savings plus the additional amount she plans to save for w weeks needs to be at least $200. This situation can be represented by the following inequality:
125 + 10w \\geq 200
Here, 125 represents the amount already saved, 10w represents the additional amount saved after w weeks, and the inequality symbol \\geq (greater than or equal to) establishes that Marisa's total savings must be at least $200.
Find an explicit formula for the geometric sequence -8,-40,-200,-1000
Step-by-step explanation:
The given geometric sequence:
- 8, - 40, - 200, - 1000
Here, first term(a) = - 8, common ration(r) = [tex]\dfrac{-40}{-8}[/tex] = 5
To find, an explicit formula for the given geometric sequence = ?
We know that,
The explicit formula for the geometric sequence
[tex]a_{n} =ar^{n-1}[/tex]
∴ An explicit formula for the given geometric sequence
[tex]a_{n} =(-8)(5)^{n-1}[/tex]
[tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]
∴ An explicit formula for the given geometric sequence, [tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]
Answer:
what the guy above me said
Step-by-step explanation:
Samantha and her children went into a movie theater and will buy bags of popcorn and candies. Each bag of popcorn costs $6 and each candy costs $3.25. Samantha has a total of $50 to spend on bags of popcorn and candies. Write an inequality that would represent the possible values for the number of bags of popcorn purchased, bb, and the number of candies purchased, c.c.
Multiply the price of popcorn by the number of bags so 6b.
Multiply the price of candy by the number bought, so 3.25c
Add those together to get total :
6b + 3.25c
Now the most she can spend is 50 so set the equation to less than it equal to what she can spend:
6b + 3.25c <= 50
Final answer:
The inequality representing Samantha's budget for purchasing popcorn and candies is 6b + 3.25c ≤ 50.
Explanation:
To formulate the inequality representing the possible values for the number of bags of popcorn (b) and the number of candies (c) Samantha can purchase without exceeding her $50 budget, we can set up an expression based on the given prices for each item.
The cost of the popcorn bags is $6, and the cost of each candy is $3.25.
The inequality that represents this scenario would be:
6b + 3.25c ≤ 50
This inequality denotes that the total cost of b popcorn bags and c candies, which is the sum of $6 times the number of popcorn bags plus $3.25 times the number of candies, should be less than or equal to $50.
Samantha must choose combinations of b and c that satisfy this inequality to stay within her budget.
When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
B) We are interpolating. There are no concerns about interpolation.
C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.
D) We are extrapolating. There are no concerns about extrapolation.
Answer:
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
Step-by-step explanation:
When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
B) We are interpolating. There are no concerns about interpolation.
C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.
D) We are extrapolating. There are no concerns about extrapolation.
The answer is A
assuming we are looking for the value of y within the range of x, we are interpolating. Take for instance, the range of xi between 60 and 65, what is the value of y at point 62.5. This is interpolation.
But then we have the data sets of temperature of a particular place within 1 to 15 days in a month. if we are asked to look for its temperature on the 31st of that particular month, we are extrapolating, which might take a different pattern from the line of best bit
Using a least-squares line to predict y values for x values beyond the range of the data is called extrapolation. This process is risky because the pattern of data may change outside of the existing range, leading to inaccurate predictions.
Explanation:When using a least-squares line to predict y values for x values beyond the range of x values found in the data, we are extrapolating. This is because we are making predictions outside of the range of the existing data set. However, extrapolation comes with certain risks. The pattern of the data may not remain constant beyond the data we have, leading to inaccurate predictions.
Therefore, answer A is the most accurate: 'We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.'
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Am I correct for the second part?
Answer:yes
Step-by-step explanation:
Answer:
should be the 3rd choice
Step-by-step explanation:
even though the 2nd choice is technically correct for a rhombus, but this property does not explain the first part of this 2 part question.
We are looking for an answer that supports pert 1 of the question.
by definition, a rhombus is a parallelogram with 4 sides of equal length, which means 2 adjacent sides will have the same length, which explains the answer in the first part because JK and KL are adjacent sides
The temperature is 71 °F at 2:00 in the afternoon. If the temperature drops 8 °F every hour after that, what is the temperature at 6:00 in the evening?
Answer:
39 °F
Step-by-step explanation:
There's 4 hours difference between given times so the change in the temperature would be 4 × 8 = 32° F if the temperature drops 8 °F every hour therefore the temperature would be 71 - 32 = 39 °F
A hypothesis test is to be conducted using LaTeX: \alphaα = 0.05. This means:_________.
a) there is a 5 percent chance that a Type II error has been committed.
b) there is a 5 percent chance that the alternative hypothesis is true.
c) there is a maximum 5 percent chance that a true null hypothesis will be rejected.
d) there is a 5 percent chance that the null hypothesis is true.
Answer:
c)
Step-by-step explanation:
α also known as type I error depicts the probability of rejecting the true null hypothesis. So, when α=0.05 then it means that there is 5% probability or chance of rejecting the true null hypothesis.
So, in hypothesis testing α=0.05 means that there is a maximum 5 percent chance that a true null hypothesis will be rejected.
Yesterday Allen's heart beat 100,000 times. On average, how many times did it beat in a six-hour period yesterday?
Answer:
100
Step-by-step explanation:
Answer:
25,000
Step-by-step explanation:
In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. There are 75 total red and yellow flowers. How many red flowers are in Sakura's garden?
Answer: there are 25 red flowers in Sakura's garden.
Step-by-step explanation:
In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. This means that if there are 10 red flowers, there would be 20 yellow flowers. if there are 20 red flowers, there would be 40 yellow flowers. Therefore, the ratio of red flowers to yellow flowers in the garden is
5/10 = 10/20 £= 20/40 = 1/2 = 1:2
Total ratio = 2 + 1 = 3
If there are 75 total red and yellow flowers, then the total number of red flowers are in Sakura's garden would be
1/3 × 75 = 25
Answer:
25
Step-by-step explanation:
Step-by-step explanation: Understand it as a ratio. 5:10. Add both ratios together, 15. Make an expression, 15x=75. x=5, Then multiply 10 and 5 by 5 and that will give you the ratio of 25:50 red to yellow flowers.
Taco Bell prepared 88 tacos for a meeting at Smith Elementry. If the tacos will be separaded equally among 4 trays, how many tacos will be on each tray?
Answer:
The answer is:
22 tacos per tray
Step-by-step explanation:
Number of trays:
Pretend 1,2,3, and 4 are the traysIf there's 4 traysand there's 88 tacosdivide 88 by 4Number of Tacos is 88:
88 ÷ 4 = 22Put 22 Taco's in each tray:
Tray 1. 22 Tacos
Tray 2. 22 Tacos
Tray 3. 22 Tacos
Tray 4. 22 Tacos
Dividing is Separating So your separating the tacos into 4 trays
Example of dividing:
John takes 5 cookies from the cookie jar, there are 20 cookies total. He goes out to his friends and wants to share his cookies, but his mom said "no more cookies after you take 5 cookies." He had 3 friends with him that day. John keeps 1 cookie for himself and gives 1 cookie to each friend his friends. Now they are left with 1 cookie, they divide the cookie into 4 pieces, splitting it into half, they now have 2 halves, they split those 2 into 2 pieces. This example is showing how John and his friends shared by dividing the cookies among each other.All 4 trays Add up to 88 tacos total
I hope this helped! <3
Samantha and Luke got married. They received $4,500 in gift money and deposited it into a savings account that pays 2.85% simple interest. How much will they have in savings after 3 years?
Group of answer choices
$384.75
$4,884.75
$9,000.00
$38,475.75
Answer: $4,884.75
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the duration of the savings in years.
From the given information,
P = 4500
R = 2.85
T = 3 years
I = (4500 × 2.85 × 3)/100 = $384.75
The total amount that they will have in savings after 3 years is
4500 + 384.75 = $4884.75
PLZ HURRY IT'S URGENT!!
Which fraction represents the ratio 35:42 in simplest form?
7/5
6/5
6/7
5/6
Answer:
5/6
Step-by-step explanation:
The ratio 35:42 represents the fraction:
[tex]\dfrac{35}{42}[/tex]
Now we have to cancel this fraction - we will divide numerator and denominator by 7:
35/7 = 5
42/7 = 6
Therefore,
[tex]\dfrac{35}{42} = \dfrac{7\cdot 5}{7\cdot 6} =\dfrac{5}{6}[/tex]
The manager at a concert venue keeps track of the number of adult tickets and student tickets sold each day and the total money received. On Wednesday, a total of 74 tickets were sold, and the money collected was $994. If adult tickets are sold for $15 and student tickets are sold for $11, how many adult tickets and student tickets were sold? Give your answer as an ordered pair (x,y), where x is the number of adult tickets and y is the number of student tickets.
Answer: the number of adult and student tickets sold are (45, 29)
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of student tickets that were sold.
On Wednesday, a total of 74 tickets were sold. This means that
x + y = 74
x = 74 - y- - - - - - - - - - - - - - 1
If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that
15x + 11y = 994- - - - - - - - - - - - - - 2
Substituting equation 1 into equation 2, it becomes
15(74 - y) + 11y = 994
1110 - 15y + 11y = 994
- 15y + 11y = 994 - 1110
- 4y = - 116
y = - 116/ - 4
y = 29
Substituting y = 29 into equation 1, it becomes
x = 74 - 29 = 45
The number of adult tickets and student tickets sold is (x, y) = (45, 29)
To determine the number of adult tickets x and student tickets y sold, we need to solve the system of equations given by the following conditions:
1. The total number of tickets sold is 74:
x + y = 74
2. The total revenue from the tickets is $994, with adult tickets sold for $15 each and student tickets sold for $11 each:
15x + 11y = 994
We can solve this system of equations using the substitution or elimination method. Here, we will use the elimination method.
First, let's write the two equations clearly:
x + y = 74
15x + 11y = 994
To eliminate one of the variables, we can multiply the first equation by 11, so the coefficients of y in both equations will be the same:
[tex]\[ 11(x + y) = 11 \cdot 74 \][/tex]
11x + 11y = 814
Now we have:
11x + 11y = 814
15x + 11y = 994
Next, we subtract the first modified equation from the second equation to eliminate y
(15x + 11y) - (11x + 11y) = 994 - 814
15x + 11y - 11x - 11y = 180
4x = 180
x = 45
Now, substitute x = 45 back into the first original equation to find y
x + y = 74
45 + y = 74
y = 29
Therefore, the number of adult tickets and student tickets sold is:
(x, y) = (45, 29)
Which relationships would most likely be causal? Select two options. a negative correlation between the temperature and the amount of snow still on the ground a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left a positive correlation between the length of the side of a pool and its depth a positive correlation between the height of a woman and the height of her brother a negative correlation between the volume of water in a pot and the amount of time that the water takes to boil
Answer:
a negative correlation between the temperature and the amount of snow still on the ground
a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
Explanation:
When it comes to "correlations," a negative one refers to an "inverse" relationship between two variables. So, this means that as one variable increases, the other decreases and vice-versa.
The question is asking for two options that are "casual" (common) when it comes to "negative correlation." So, the answers are:
a negative correlation between the temperature and the amount of snow still on the ground
This is a casual example of negative correlation because as temperature increases, the amount of remaining snow on the ground decreasesa negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
This is a casual example of negative correlation because as the number of digital photos uploaded to a website increases, the amount of storage space left decreases.
Answer:
A negative correlation between the temperature and the amount of snow still on the ground.A negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left.Step-by-step explanation:
These are the two relationships that are most likely to be causal. Causal relationships are those in which one aspect is the cause of the second one being described. Moreover, a negative correlation is one in which one aspect of the relationship increases while the other one decreases. In the first example, as the temperature goes up, this causes the amount of snow on the ground to go down. In the second example, as you upload more pictures to a website, there is less storage space.
Please Help!!!
What is a polynomial function in standard form with zeroes 1, 2, -3, and -1 ?
Answer:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
Step-by-step explanation:
The polynomial function has zeros
x=1, x=2,x=-3,x=-1
This means the factored form of the polynomial is
[tex]p(x) = (x - 1)(x + 1)(x + 3)(x - 2)[/tex]
We expand to get:
[tex]p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)[/tex]
We expand further to get:
[tex]p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)[/tex]
[tex]p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6[/tex]
This simplifies to:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
This is the standard form of the polynomial since it is written in descending powers of x.
Name 3 of the 4 features listed below for the function g (x) = log2 (x + 4) - 1 and include a description of how you found those answers using complete sentences. 1) Vertical Asymptote 2) Domain 3) X and Y Intercepts 4) Transformations compared to its parent function f (x) = log2 x
(1) Vertical asymptote: [tex]x=-4[/tex]
(2) Domain: [tex]x>-4[/tex]
(3) X intercept: [tex](-2,0)[/tex] and Y intercept : [tex](0,1)[/tex]
(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.
Explanation:
The parent function is [tex]f(x)=\log _{2} x[/tex]
The transformed function is [tex]g(x)=\log _{2}(x+4)-1[/tex]
(1) Vertical asymptote:
The vertical asymptote of a function can be determined by equating
[tex]x+4=0[/tex]
Thus, [tex]x=-4[/tex]
The vertical asymptote is [tex]x=-4[/tex]
(2) Domain:
The domain of a function is the set of all independent x-values.
[tex]x+4>0[/tex]
Thus, [tex]x>-4[/tex]
The domain of a function is [tex]x>-4[/tex]
(3) X and Y intercepts:
To determine the x intercept, let us substitute y=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]
[tex]\begin{equation}\begin{aligned}\log _{2}(x+4)-1 &=0 \\\log _{2}(x+4) &=1 \\x+4 &=2^{1} \\x &=-2\end{aligned}[/tex]
Thus, the x intercept is [tex](-2,0)[/tex]
To determine the y intercept, let us substitute x=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]
[tex]\begin{equation}\begin{aligned}y &=\log _{2}(0+4)-1 \\&=\log _{2} 4-1 \\&=2-1 \\&=1\end{aligned}[/tex]
Thus, the y intercept is [tex](0,1)[/tex]
(4) To determine the transformation:
The transformed function [tex]g(x)=\log _{2}(x+4)-1[/tex] is shifted 4 units to the left and shifted 1 unit downwards.
Ethan decides to type up some documents while waiting for the meeting to start he can type two pages every 1/8 hour if the meeting starts 3/4 hour later than the scheduled time how many pages can he typed before the meeting starts
Answer:
Ethan can type 12 pages before the meeting starts.
Step-by-step explanation:
Given:
Number of pages he can type =2
Number of hours he can type 2 pages = [tex]\frac{1}8\ hrs[/tex]
We need to find number of pages he can type in [tex]\frac34\ hrs[/tex]
Solution:
Now first we will find number of pages in 1 hour
So we can say;
In [tex]\frac{1}8\ hrs[/tex] = 2 pages
In 1 hour = number of pages he can type in 1 hour
By Using Unitary method we get;
number of pages he can type in 1 hour = [tex]\frac{2}{\frac18} =\frac{2\times8}{1}=16\ pages[/tex]
Now we can say that;
In 1 hour = 16 pages
So [tex]\frac34\ hrs[/tex] = number of pages he can type in [tex]\frac34\ hrs[/tex]
Again By using Unitary method we get;
number of pages he can type in [tex]\frac34\ hrs[/tex] = [tex]16\times \frac34 = 12\ pages[/tex]
Hence Ethan can type 12 pages before the meeting starts.
Final answer:
Ethan has 3/4 hours to type and can complete two pages every 1/8 hour, resulting in a total of 12 pages typed before the meeting starts.
Explanation:
Ethan can type two pages every 1/8 hour. To find out how many pages he can type before the start of the meeting, we need to calculate the total pages he can type in the waiting time of 3/4 hours. Here's the step-by-step calculation:
Calculate the number of 1/8 hour intervals in 3/4 hours by dividing: (3/4) ÷ (1/8) = (3/4) × (8/1) = 6.
Since he types two pages every 1/8 hour, we find the total number of pages by multiplying the number of intervals by 2: 6 × 2 = 12 pages.
Therefore, Ethan can type a total of 12 pages before the meeting starts.