Answer:
[tex]16a^6x^4y^2[/tex]
Step-by-step explanation:
To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])
Using that rule, we get:
[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].
This can be simplified to
[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],
which can be written as:
[tex]16a^6x^4y^2[/tex]
using the commutative property of multiplication.
can someone pls help me i don’t ll get this
Answer: 6
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angles are equal to [tex](13x-6)^{\circ}[/tex].
Since angles in a triangle add to [tex]180^{\circ}[/tex], so:
[tex]36+2(13x-6)=180\\\\2(13x-6)=144\\\\13x-6=72\\\\13x=78\\\\x=6[/tex]
At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s=64t-16t^2
In how many seconds does the object reach its maximum height?
The time it takes the object to attain maximum height is 2 seconds
Time to Attain Maximum HeightTo find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as
t = -b/2a
But let's write and define our quadratic equation with it's variables.
S = 64t - 16t²
To attain maximum height;
t = -b/2a
a = -16, b = 64,c = 0
Substituting the values
t = -64/2(-16)
t = 2
The time is 2 seconds
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The cost to replace a water pump in a sports car was $899. This included $365 for the water pump and $89 per hour for labor. How many hours of labor were required to replace the water pump?
By solving a linear equation we will see that there were 6 hours of labor.
How many hours of labor were required?We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:
c(x) = $365 + x*$89
We know that the total cost is $899, then we can write the linear equation:
$899 = $365 + x*$89
$899 - $365 = x*$89
($899 - $365)/$89 = x = 6
So there were 6 hours of labor.
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#11 i
PROBLEM SOLVING The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp.
Time (seconds), x 0 0.25 0.75 1 1.1
Height (feet), y
22 22.5 17.5 12 9.24
Write a function that models the height of the water-skier over time.
The function y =
Interpret the y-intercept.
B
22
I U
models the height.
T' T₂
When is the water-skier 5 feet above the water? Round your answer to the nearest hundredth.
70°F
Cloudy
The skier is 5 feet above the water after about
second(s).
O Search the web
J
O
L
D
(
1/10000 Word L
The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
A competitive water skier's heights y, x seconds after soaring off a ramp.
For x = 0, y = 22
for x = 0.25, y = 22.5
For x = 0.75, y = 17.5
For x = 1, y = 12
For x = 1.1, y = 9.24
The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]
Putting x = 0 and y = 22 in the equation, we get :
[tex]y = ax^{2} +bx +c[/tex]
c = 22
Now, putting x = 1 and y =12, we get,
12 = a*1 + b*1 + 22
a +b = 12 - 22 = -10 equation (1)
Putting x = 0.25, y = 22.5,
22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22
506.25 a +22.5b = 0.5 equation(2)
Solving equation (1) and equation(2), we get :
a = -16 and b = 6 and c = 22
So, the quadratic equation becomes,
[tex]y = -16x^{2} + 6x +22[/tex]
Now, Time when the skier is 5 feet above the water,
[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]
Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
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Consider the following linear equation.
y=2+34x
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given:
y = 2 + 34x
y = 34x + 2
Compare with y = mx + c, we will get;
m = 34
b = 2
So, the slope is 34 and the y-intercept is 2.
Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
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Can some one please help me do these work sheets before I fail my class♀️
Answer of the given question are respectively,
[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]
Exponent:
A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.
Example:
[tex]2^3[/tex] = 2 × 2 × 2
Combine like term:
1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]
2. Subtract 6w from 8w
8w -6w = 2w
Rule:
[tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]
1.
[tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]
2.
[tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]
Rule:
[tex](x^a)^b = x^{ab}[/tex]
1. [tex](x^2)^3 = x^6[/tex]
2.
[tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]
Rule:
[tex]x^a/x^b = x^{a-b}[/tex]
1.
[tex]27x^5/42x\\\\= 9x^4 /14[/tex]
2.
[tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]
Rule:
[tex]x^{-a}= 1/x^a[/tex]
1.
[tex]-5x^{-2} \\\\= -5/x^2[/tex]
2.
[tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]
Rule:
[tex]x^0 =1[/tex]
1.
[tex]7x^0\\\\= 7[/tex]
2.
[tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]
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I need to know what NM is
The length of NM is 10 units
What are similar triangles?
If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.
Similar triangles are triangles with the same shape but different sizes. Examples of related objects are all equilateral triangles and squares with any side length.
The triangles ONP and LNM are similar triangles.
So, the following is true.
(ON/LN)=(NP)/(NM)
(3.6/6)=(6)/(NM) ( LN=LO+ON=2.4+3.6=6 )
3.6 NM=6*6 =36
NM=36/3.6 = 10
So, the length of NM is 10 units
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What is the image point of (-6, -4) after the transformation T4.-1 ° ry=-x?
(16, 36) is the image point .
What is image point?
The provided point P is "reflected" in the mirror, appearing on the other side of the line at a distance equal to that from it. To see this, move the point P. Conventionally known as P' (pronounced "P prime"), the point P's reflection over the line is also referred to as the point P's "image."Reflecting (-6, -4) in the line y= - x yields the point (4, 6).
Dilating (4, 6) by a factor of 4 gives the point (16, 36).
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There are 1400 students in a school. Out of these 350 students wear glasses. What percentage of students wear glasses
Answer:
25%
Step-by-step explanation:
divide the number by the total then multiply by 100 and add a percent sign
350/1400*100=25%
A poster measuring 150cm by 180cm is enlarged in the ratio 8:5. Find the length and breadth of the enlarged poster
Answer:
240 cm by 288 cm
Step-by-step explanation:
You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.
SolutionThe enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...
(8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm
The Bloomington Times had 8,050 subscribers last year. This year, after the paper was bought out, it had 70% more. How many subscribers were there this year?
plwease help due tommrow
Answer:
13685
Step-by-step explanation:
8050 + .7(8050)
8050 + 5635
13685
The functions r and s are defined as follows.
r(x) = 2x+1
s(x) = -x²
Find the value of r (s (4)).
r(s(4))=
Answer:
[tex]33[/tex]
Step-by-step explanation:
Define functions:
[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]
Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:
[tex]2(-x^2) + 1[/tex]
Solve for value:
[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]
** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.
PLEASE HELP SOLVE!!!
Answer:
positive, positive, zero, zero, negative, negative, positive
Step-by-step explanation:
The derivative is positive when a function is increasing.
The derivative is zero when a function is neither increasing nor decreasing.
The derivative is negative when the function is decreasing.
One year consumers spent an average of $23 on a meal at a restaurant. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $5.
A) What is the probability that a randomly selected person spent more than $25?
B) What is the probability that a randomly selected person spent between $12 and $21?
C) Between what two values, symmetrically distributed around the mean, will the middle 95% of the amounts of cash spent fall?
Using the normal distribution, it is found that:
a) The probability that a randomly selected person spent more than $25 is of 0.3446 = 34.46%.
b) The probability that a randomly selected person spent between $12 and $21 is of 0.3307 = 33.07%.
c) The middle 95% of the amounts are between $13.2 and $32.8.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the costs of the meal are given as follows:
[tex]\mu = 23, \sigma = 5[/tex]
The probability that a randomly selected person spent more than $25 is one subtracted by the p-value of Z when X = 25, hence:
Z = (25 - 23)/5
Z = 0.4
Z = 0.4 has a p-value of 0.6554.
1 - 0.6554 = 0.3446 = 34.46%.
The probability that a randomly selected person spent between $12 and $21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:
X = 21:
Z = (21 - 23)/5
Z = -0.4
Z = -0.4 has a p-value of 0.3446.
X = 12:
Z = (12 - 23)/5
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
0.3446 - 0.0139 = 0.3307 = 33.07%.
The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.-1.96 = (X - 23)/5
X - 23 = -1.96 x 5
X = $13.2
1.96 = (X - 23)/5
X - 23 = 1.96 x 5
X = $32.8
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A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
PLEASE HELP MEEEE!!!!!
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
someone help pls due soon
Answer:
snap to solve
Step-by-step explanation:
u can use snap to solve to get ur answers
Answer:
Step-by-step explanation:
cost price = $640
sell price = $940
percentage = ?
Rate * Base = Amount
Percent * Sell Price = Cost Price
P * 940 = 640
P940 = 640
P940/940 = 640/ 940
P = 0.66666667
Percent = (0.66666667 × 100)/100 = 66.666667
Correct Answer is 66 2/3%
10] Salim walked 1 1/2 miles to school and then 2 1/2 miles to work after school. How far did he walk in all?
Answer:
4
Step-by-step explanation:
Solution by separating parts
Rewriting our equation with parts separated
=1 + 1/2 + 2 + 1/2
Solving the whole number parts
1 + 2 = 3
Solving the fraction parts
1/2 +1/2 = 2/2
Reducing the fraction part, 2/2,
2/2 = 1/1
Simplifying the fraction part, 1/1,
1/1 = 1
Combining the whole and fraction parts
3 + 1 = 4
Answer:
4 miles
Step-by-step explanation:
1 1/2 = 1.5
2 1/2 = 2.5
1.5 + 2.5 = 4 miles
A neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates A(1,−1) , B(1,−2) , and C(2,−1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A′(3,−4) . What are the new coordinates of House B and House C when each house is moved using the same translation?
The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the 3 houses be A , B ,C
The coordinate of House A = A ( 1 , -1 )
The coordinate of House B = B ( 1 , -2 )
The coordinate of House C = C ( 2 , -1 )
Now , the houses are relocated to new coordinates with
The new coordinate of House A = A' ( 3 , -4 )
The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor
So ,
A ( x₁ , y₁ ) to A' ( x₂ , y₂ )
A ( 1 , -1 ) to A' ( 3 , -4 )
x₂ = x₁ + 2
y₂ = y₁ - 3
From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are
x₂ = x₁ + 2
y₂ = y₁ - 3
Therefore ,
B ( x₁ , y₁ ) to B' ( x₂ , y₂ )
B' ( x₂ , y₂ ) = B' ( 3 , -5 )
C ( x₁ , y₁ ) to C' ( x₂ , y₂ )
C' ( x₂ , y₂ ) = C' ( 4 , -4 )
Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
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the area of a square photo frame is 250 cm2 .find the perimeter of photo frame
Answer:
63.2 cm
Step-by-step explanation:
Perimeter formula from Area =
4√Area units.
4√250 =
4 × 15.8 =
63.2 cm
Help on number 1 please!! Thanks.
Answer:
I believe the answer is c
Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy through her employer. Karen is paid weekly.
How much is deducted from her paycheck for life insurance? (Use the table.)
ABC Term Life Insurance Company
Annual premium
Age at issue
Male Female 10-year
per $1000 of coverage
20-24 23-27 $2.50
25-29 28-32 $3.25
30-34 33-37 $3.82
35-39 38-42 $4.55
40-44 43-47 $5.78
45-49 48-52 $7.53
20-year
$3.80
$5.84
$7.93
$10.33
$13.68
$17.56
As Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
As given in the question,
Information given about Karen,
Age = 52- year old
Gender = female
Policy = 20 -year life insurance policy
Annual premium given per $1000 for coverage
Karen policy amount = $75,000
From the table it is given that,
Amount deducted per $1000 for 20year policy in the age limit of 48 -52
= $17.56
⇒ $1000 = $17.56
⇒ $75,000 = $( 17.56 × 75,000)/ 1000
= $1317.
Therefore, as Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
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Un taxi en Myrtle Beach cobra $2 por milla y $1 por cada persona. Si un viaje en taxi para dos personas cuesta $12.
¿Cuánto viajó el taxi?
Respuesta:
5 millas
Explicación paso a paso:
Si hay 2 personas y cuesta 12 dólares primero restarás 2 dolars por cada persona dejándote con 10 dólares. Después de eso, dividirá 10 por 2 para las millas porque cada milla cuesta 2 dólares. que te llevará a 5 millas
GRACIAS
Prizes in a raffle are determined by taking a ball from a bag. There are 15 balls in the bag, 12 of them are green, two of them with black stars. There are two silver balls, one with a black star, and one gold ball. If you draw the green ball, without the black star, you win a small prize. If you get a green ball with the black star, you get a medium prize. If you get the silver ball without the star, you get a large prize. If you get the silver ball with the black star, you get the extra-large prize. If you get the gold ball, you get the super deluxe prize.
If you get a ball, what is the probability of getting the green with the black star?
The probability of getting the green ball with the star is
a.) 0.1333
b.) 0.1133
c.) 0.0123
d.) 0.0333
This is an example of:
a.) a joint event
b.) an elementary event
The probability of winning the small prize is:
a. 0.7666
b. 0.6666
c. 0.6667
d. 0.6777
This is an example of:
a.) a joint event
b.) an elementary event
What is the probability of winning the super deluxe prize?
The probability of winning the super deluxe prize is:
a.) 6.6677
b.) 0.6667
c.) 0.7667
d.) 0.0667
This is an example of:
a.) a joint event
b.) an elementary event
Answer:
a. )
Step-by-step explanation:
There are 15 balls ...... two are green with a star
2 out of 15 = 2/15 = .1333
78 children attended a trip to the fair. 60 of them were girls. Find the ratio of the number of girls to boys.
Do not put in simplest form.
Answer:
First, find the number of boys: [tex]78-60=18[/tex]
The ratio of the number of girls to boys would be 60 : 18.
A nursing administrator went through a sample of hospital records and found that, out of 500 randomly selected records, 217 of the patients had been admitted for heart issues. What is the sample statistic?
The sample statistic when the nursing administrator went through a sample of hospital records is 217.
What is statistic?A statistic is a metric used to describe a sample. Estimation or hypothesis testing can be used to determine how likely it is that a sample statistic differs from the population parameter.
A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
A sample statistic is a piece of statistical data derived from a small number of items. A sample is merely a subset of a population. Therefore, the 217 of the patients had been admitted for heart issues is the sample.
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Atudent mark tardy 5 different times in 40 days what percentage was he tardy
The percentage is the indicating hundredth is 12.5%.
What is the percentage?A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.
Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A student was marked tardy five different times in a 40-day period.
Percentage of 5 among 40
= (5/40) x 100
= 12.5%
Hence, The percentage of times the students marked will be 12.5%".
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30 POINTS AND BRAINLIEST!! PLEASE HURRY I HAVE 20 MIN LEFT. <3 tysm (:
25. doubled
26. doubled
27. increases 4 times
28. remains unchanged
29. increases 6 times
Rewrite the equation in vertex form. (Include fractions in final answer).
y=-3x^2 -7x+4
For the given equation y = 3x² -7x + 4 the vertex form is given by
( 7/6, -1/12).
As given in the question,
Equation is given by :
y = 3x² -7x + 4
Standard form of the equation to get the vertex form is given by :
y = a ( x - h )² + k
Where ( h, k ) represents the vertex of the equation,
Now,
Simplify the given equation y = 3x² -7x + 4 into standard form to get vertex form,
y = 3x² -7x + 4
⇒ y = 3 [x² -2×(7/6)] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4
⇒ y = 3 [x - (7/6)]² - (49/12) + 4
⇒ y = 3[x - (7/6)]² - (1/12)
Compare it with standard form ,
a = 3, h = (7/6) , k = -(1 /12)
Vertex form ( h, k) = ( 7/6 , -1/12 )
Therefore, for the given equation y = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).
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Read the problem below on the picture. It's Geometry by the way. Also if u can answer my other one its in my profile.
Answer:
x = 18. y = 54
Step-by-step explanation:
first we we figure out the degrees of the spot where N is.
(I know N references the line but ill be using it to call the spot)
72 + N = 90
subtract 72 from both sides
N = 18
So since opposite angles are the same
2x + N = 3x
2x + 18 = 3x
subtract 2x from both sides
18 = 1x
divide by 1 both sides
18 = x
______
now we add all the angles from the left sides to make 180
2x + N + 72 + y = 180
we know x is equal to 18 and N is also 18
2(18) + 18 + 72 + y = 180
simplify
36 + 18 + 72 + y = 180
add
126 + y = 180
subtract both sides by 126
y = 54
The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.
Answer:
[tex]\hat{y}=-0.29x+5.67[/tex]
Step-by-step explanation:
Given points on the scatter plot:
(1, 5.4)(2, 5)(3, 4.6)(4, 4.9)(5, 4.1)(6, 3.9)(7, 3.6)(8, 3.3)Plot the given points and draw a line of best fit (see attachment).
As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.
From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.
Therefore, the equation that is appropriate for the line of best fit is:
[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]
Answer:
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
Step-by-step explanation:
i took the test :)