What is the equation for a straight line that would allow you to predict the value of Y from a given value of X. That is, calculate the value of "a" and the value of "b" and then substitute the 2 values into the generic equation (Y = a + bX) for a straight line. (Hint: calculate "b" first)
Answers
Answer:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Step-by-step explanation:
We have the following data:
X: 3,3,2,1,7
Y:6,7,8,9,5
We want to find an equationinf the following form:
[tex] y= bX +a[/tex]
[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]
[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]
[tex]\sum_{i=1}^n x^2_i =72[/tex]
[tex]\sum_{i=1}^n y^2_i =255[/tex]
[tex]\sum_{i=1}^n x_i y_i =99[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]
And the slope would be:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Related Questions
Sreya bought shoes for $37.57 and x pairs of socks for $1.95 each. Which expression shows the total money spent? (1 point) 37.57x + 1.95 37.57x + 1.95x 37.57 + 1.95 + x 37.57 + 1.95x
Answers
Answer:
37.57 + 1.95x
Step-by-step explanation:
The cost of the shoes is a constant, and we don't know how many socks she bought, but we know that for every pair of socks she bought, they cost would be 1.95. Since we haven't been given the total cost of the purchase, meaning how much the total was, this will be an expression. We will multiply an x against the amount (1.95), which will calculate the price for how many socks were purchased. This means the answer will be 37.57 + 1.95x.
I will clarify a little bit more on why the other answers are incorrect. The first option is 37.57x + 1.95. This is incorrect because the question is not asking how many shoes were bought, but it is questioning how many socks were bought. Option number two states 37.57x + 1.95x. This means that the number of socks and shoes are both unknown, and the question does not state that. Also, another point to make would be that we could also add these variables together, and we do not want that. Option number three states 37.57 + 1.95 + x. X cannot be a separate variable, because by stating that, it means that there would be one more object that was bought that is unknown. I hope this helps you understand my explanation a bit more.
Have a great day, and best of luck for your math problem!
12
y= x2 + x-2
x+ y=1
If (x, y) is a solution of the system of equations
above, which of the following is a possible value of
xy?
A) 7
B 1
C) -1
D) -12
Answers
Answer:
D,xy=-12
Step-by-step explanation:
y=x²+x-2
x+y=1
or x+x²+x-2=1
x²+2x-3=0
x²+3x-x-3=0
x(x+3)-1(x+3)=0
(x+3)(x-1)=0
either x=-3
or x=1
when x=-3
x+y=1
-3+y=1
y=1+3=4
one solution is (-3,4)
xy=-3×4=-12
if x=1
1+y=1
y=0
second solution is (1,0)
xy=1×0=0
Hey everyone, can you please help me with this question? THANKS!
Answers
Answer:
6 granite, 3 marble, 14 sandstone, 1 slate
ratio of sandstone to marble
how many sandstone does she have .....14
how many marble does she have......3
so the ratio would be 14:3
Answer:
C. 14:3
Step-by-step explanation:
Dana has 14 pieces of sandstone.
Dana has 3 pieces of marble.
The ratio of pieces of sandstone to pieces of marble is 14:3.
The ratio cannot be simplified further.
Which statement is true about the ranges for the box plots? A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix.
Answers
*The box plots are shown in the attachment
Answer/Step-by-step explanation:
Range is the difference between the largest value of a data set and the lowest value in that data set.
In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.
For Crackers, the range = 100-70 = 30
For Cookies, the range = 115-70 = 45
Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).
Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
The population of Oregon is about 4,000,000 what is the order of magnitude of this number? A) 6 B) 4 C) 3 D) 7
Answers
Answer:
A
Step-by-step explanation:
Here, we are tasked with finding the order of magnitude.
What we are basically asked here is to write the number in powers of ten.
Thus
4,000,000 = 4 * 10^6
We can see that 10 is raised to the power of six here and thus we can say that the order of magnitude here is simply 6
Which of the following statements could be used in the proof?
Answers
Answer:
Option (3)
Step-by-step explanation:
To prove ΔULV ≅ ΔKLY,
Statements Reasons
1). VL ≅ LY 1). Radii of a circle are equal
2). UL ≅ KL 2). Radii of a circle are equal
3). ∠ULV ≅ ∠KLY 3). Vertical angles are equal
4). ΔULV ≅ ΔKLY 4). SAS property of congruence
Therefore, property (3) given in the options will be used to prove the triangles congruent.
find the height of a tree whose shadow is 42m long when the shadow of a man 1.8m tall is 2.4m long
Answers
Answer:
The ratio 1.8 : 2.4 can be rewritten as 3 : 4. We have to solve:
3 : 4 = x : 42
3 * 42 = 4x
x = 3 * 42 / 4 = 31.5
Gwendolyn shot a coin with a sling shot up into the air from the top of a building. The graph below represents the height of the coin after
x seconds.
Answers
Answer: A
Step-by-step explanation:
Which statements are true regarding the diagram? Check all that apply.
The side opposite the 60° angle has a length of
The side opposite the 60° angle has a length of .
sin(60°) =
sin(60°) =
The other acute angle of the triangle is 30°.
Answers
Answer:
A. The side opposite the 60° angle has a length of √3/2
C.Sin(60°)=√3/2
E.The other acute angle of the triangle is 30°
Step-by-step explanation:
The diagram has been attached to the answer
A. The side opposite the 60° angle has a length of
B. The side opposite the 60° angle has a length of .
C. sin(60°) =
D. sin(60°) =
E. The other acute angle of the triangle is 30°.
Answer
The side opposite the 60° angle has a length of the square root of 3/2
Opposite side of the 60° angle has a length of √3/2
sin(60°) = the square root of 3/2
Sin(60°)=√3/2
The other acute angle of the triangle is 30°
Proof:
Total angle in a triangle=180°
180°-60°-90°
=30°
Answer:
A, D, E
Step-by-step explanation:
I do is big smart
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
Answers
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
Polynomial function in standard form with zeros 5,-4,1
Answers
Answer:
[tex]\boxed{\sf \ \ \ x^3-2x^2-19x+20 \ \ \ }[/tex]
Step-by-step explanation:
hello,
by definition we can write
[tex](x-5)(x+4)(x-1)[/tex]
as 5,-4,1 are the zeroes
now we have to write it in the standard form, let's do it
[tex](x-5)(x+4)(x-1)=(x^2+4x-5x-20)(x-1)\\=(x^2-x-20)(x-1)=x^3-x^2-20x-x^2+x+20\\=x^3-2x^2-19x+20[/tex]
hope this helps
expand the following 4 (x - 1)
Answers
Answer:
4x - 4
Step-by-step explanation:
4 × x = 4x
4 × -1 = -4
4x - 4
Answer:
4x-4
Step-by-step explanation:
4(x-1) 4*x-1*44x-4The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5million. In which year is the maximum salary reached
Answers
In the 5th year
Step-by-step explanation:For the first year, the salary is 1.2million = 1,200,000
For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000
.
.
.
For the last year, the salary is 1.5million = 1,500,000
This gives the following sequence...
1,200,000 1,275,000 . . . 1,500,000
This follows an arithmetic progression with an increment of 75,000.
Remember that,
The last term, L, of an arithmetic progression is given by;
L = a + (n - 1)d ---------------(i)
Where;
a = first term of the sequence
n = number of terms in the sequence (which is the number of years)
d = the common difference or increment of the sequence
From the given sequence,
a = 1,200,000 [which is the first salary]
d = 75,000 [which is the increment in salary]
L = 1,500,000 [which is the maximum salary]
Substitute these values into equation (i) as follows;
1,500,000 = 1,200,00 + (n - 1) 75,000
1,500,000 - 1,200,000 = 75,000(n-1)
300,000 = 75,000(n - 1)
[tex]\frac{300,000}{75,000} = n - 1[/tex]
4 = n - 1
n = 5
Therefore, in the 5th year the maximum salary will be reached.
find the value of x in the isoscleles triangle sqrt45 and altitude 3
Answers
Answer:
[tex]c.\hspace{3}x=12[/tex]
Step-by-step explanation:
Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.
You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached. As you can see:
[tex]x=2a[/tex]
And we can find a easily using pythagorean theorem:
[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]
Solving for a:
[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]
[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]
Therefore:
[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]
What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. Negative 1 and one-fourth + one-half A number line going from negative 3 to 0 in increments of one-fourth. Negative 1 and three-fourths Negative 1 and one-half Negative three-fourths Negative one-half
Answers
Answer:
C. Negative three-fourths
Step-by-step explanation:
Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:
-1 1/4 + 1/2
Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:
-5/4 + 1/2
Taking the LCM of the expression
= (-5+2)/4
= -3/4
Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths
Answer:
-3/4
Step-by-step explanation:
-1 1/4 +1/2
-5/4 + 2/4
-3/4
Anybody pls solve this question and explanation btw.
Answers
Answer:
[tex]Vol=883.6875\,\, cm^3\\[/tex]
Step-by-step explanation:
Recall that the volume of a whole sphere is given by the formula:
[tex]Vol_{sphere}=\frac{4}{3} \pi\,R^3[/tex]
then, the volume of a semi-sphere would be half of the formula above:
[tex]Vol=\frac{2}{3}\, \pi\,R^3[/tex]
Now, the radius R is given by half of the semi-sphere diameter: 15/2 = 7.5 cm.
which makes our calculation:
[tex]Vol=\frac{2}{3}\, \pi\,R^3=\frac{2}{3}\, \pi\,(7.5\,cm)^3=883.6875\,\, cm^3\\[/tex]
Five times sum of a number, x,and nine is ten. What is the number?
Answers
Answer:
[tex]-7[/tex]
Step-by-step explanation:
[tex]5(x+9) = 10[/tex]
[tex]5x+45=10[/tex]
[tex]5x = -35[/tex]
[tex]x=-7[/tex]
Hope this helps.
Answer:
-7
Step-by-step explanation:
5(x + 9) = 10
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
...and is your order of operation.
First, divide 5 from both sides:
(5(x + 9))/5 = (10)/5
x + 9 = 10/5
x + 9 = 2
Next, isolate the variable x, by subtracting 9 from both sides:
x + 9 (-9) = 2 (-9)
x = 2 - 9
x = -7
x = -7 is your answer.
~
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answers
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!
The perimeter of a triangular field is 84 m, if the ratio of its sides are 13: 14:15, Find the area of the field. *
Answers
Answer:
[tex]Area = 336\ m^2[/tex]
Step-by-step explanation:
If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.
Then, if the perimeter is 84 m, we have:
[tex]P = 13x + 14x + 15x = 84[/tex]
[tex]42x = 84[/tex]
[tex]x = 2[/tex]
The length of each side is:
[tex]13x = 26\ m[/tex]
[tex]14x = 28\ m[/tex]
[tex]15x = 30\ m[/tex]
Now, to find the area of the field, we can use the following formula:
[tex]Area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides and p is the semi perimeter:
[tex]p = P/2 = 42\ m[/tex]
So we have that:
[tex]Area = \sqrt{42(42-26)(42-28)(42-30)}[/tex]
[tex]Area = 336\ m^2[/tex]
check all the answers of a present the same level precision. A) 22.543 B) 98.4 C) 0.264 D) 1.04
Answers
Answer:
A,and C
Step-by-step explanation:
A and C have the same level precision , they have three significant digit
What is the speed of a plane that goes 15000 miles per hour in per seconds?
Answers
Answer:
There are 60 * 60 = 3600 seconds in one hour so the plane goes 15000 / 3600 = 4 and 1/6 miles per second.
Answer:
[tex]4 \frac{1}{6} \: miles \: per \: seconds[/tex]Step-by-step explanation:
[tex]1500 \: miles \: \: per \: hour[/tex]
[tex] = \frac{15000}{60 \times 60} [/tex]
[tex] = \frac{15000}{3600} [/tex]
[tex] = \frac{25}{6} [/tex]
[tex] = 4 \frac{1}{6} \: miles \: per \: second[/tex]
Hope this helps...
Good luck on your assignment...
Study the following figure, where two concentric circles share center C.
Segment AB is a diameter of the larger circle.
Segment AB intersects a chord of the smaller circle, PQ, at a right angle at point Z.
Segment AB intersects a chord of the larger circle, MN, at a right angle at point 0.
If MO=7x-4, and NO=6x, what is the length of MN
Answers
Answer:
Length of MN = 48 units
Step-by-step explanation:
AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).
Theorem says,
"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."
Therefore, MO ≅ ON
m(MO) = m(ON)
7x - 4 = 6x
7x - 6x = 4
x = 4
m(MN) = m(MO) + m(ON)
= (7x - 4) + (6x)
= 13x - 4
= (13 × 4) - 4
= 52 - 4
= 48
Length of chord MN will be 48 units.
A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel?
Answers
Answer: 240 seconds OR 4 minutes
Step-by-step explanation:
Length of the train = 1 km
Length of the tunnel = 1 km
Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km
= 2000 m
Speed of the train = 30 km/hr = 8.333 metres per second
Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.
= 240 seconds = 4 minutes
One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?
Answers
Answer:
29
Step-by-step explanation:
Let the smaller integer be x.
The other integer is 1 greater than 3 times x, or 3x + 1.
The product is 154.
x(3x + 1) = 154
3x^2 + x - 154 = 0
157 = 2 * 7 * 11
14 * 11 = 154
22 * 7 = 154
(3x + 22)(x - 7) = 0
3x + 22 = 0 or x - 7 = 0
3x = -22 or x = 7
x = -22/3 or x = 7
-22/3 is not a positive integer, so we discard that solution.
The smaller integer is 7.
3x + 1 = 3(7) + 1 = 22
The greater integer is 22.
The sum of the integers is 7 + 22 = 29
Answer: 29
Step-by-step explanation:
Help !!!! Match the written mathematical operation to the equivalent symbolic form
Answers
Answer:
The matched pairs are:
(A, 4), (B, 1), (C, 2) and (D, 3)
Step-by-step explanation:
The complete question is:
Match each description of an algebraic expression with the symbolic form of that expression :
A. 2 terms; variables = x and y
B. 3 terms; variables = x and y; constant = 3
C. 2 terms; variable = x; constant = 4.5
D. 3 terms; variables = x and y; constant = 2
1. x - 2y + 3
2. 4.5 - 2x
3. 4.5x + 2 - 3y
4. 4.5y - 2x
Solution:
A. 2 terms; variables = x and y ⇒ 4. 4.5y - 2x
B. 3 terms; variables = x and y; constant = 3 ⇒ 1. x - 2y + 3
C. 2 terms; variable = x; constant = 4.5 ⇒ 2. 4.5 - 2x
D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y
two factors of -48 have a difference of 19. the factor with a greater absolute value is positive. what is the sum of the factors? -19, -13 13 or 16
Answers
Answer:
-19
Step-by-step explanation:
-19 is the absolute value of 19
hope this helps
Answer:
sum = +13
Step-by-step explanation:
The possible factors of 48 are
{1,2,3,4,6,8,12,16,24,48}
Of these, the pair 3,16 gives a sum of 19 and a product of 48.
We are given that 16 (greater absolute value) is positive, so 3 is negative.
The sum of the two is therefore 16-3 = 13
a group of girls bought 72 rainbow hairbands ,144 brown and black hairbands and 216 bright colored hairbands .what is the largest possible number of girls in the group
Answers
Answer:
72
Step-by-step explanation:
We are assuming that all girls in the group bought the same number of items.
Therefore, we need to find the highest common factor of 72, 144 and 216.
HCF
72 = 2 * 2 * 2 * 3 * 3
144 = 2 * 2 * 2 * 2 * 3 * 3
216 = 2 * 2 * 2 * 3 * 3 * 3
The product of the emboldened numbers is the highest common factor.
That is:
2 * 2 * 2 * 3 * 3 = 72
Therefore, the largest possible number of girls in the group is 72.
Which of the following are solutions to the quadratic equation? Check all that
apply.
2x2 + 7x- 14 = x2 + 4
Answers
Answer:
[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]
hope this helps
what is two plus two
Answers
Answer:
4 is the answer to your question
Step-by-step explanation:
Find the area of this triangle..
Answers
Answer:
39.936 ( not rounded )
Step-by-step explanation:
Use Pythagorean theorem
a^2 + 6.4^2 = 9^2
height = 6.24 (rounded to nearest hundredth)
1/2 * base * height = area
1/2 * 12.8 * 6.24
= 39.936 ( not rounded )