To find the equation of the regression line for the given data, we need to use a statistical software or a calculator. Once we have the equation, we can plot the data on a scatter plot and draw the regression line.
Using the regression equation, we can predict the value of y (girth) for each of the given x-values (length). However, if the x-value is not within the range of the observed data, the prediction may not be meaningful. For example, if x = 140 cm or x = 172 cm are outside the range of the observed lengths, the predicted girth may not be accurate. On the other hand, if x = 164 cm or x = 158 cm are within the range of the observed lengths, the predicted girth may be more reliable.
Overall, regression analysis helps us understand the relationship between two variables and make predictions based on that relationship. In this case, we can use the regression equation to estimate the girth of harbor seals based on their length, but we need to be mindful of the limitations of the data and the prediction.
To learn more about regression line click here : brainly.com/question/7656407
#SPJ11
Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).
Answer:
a= 100.2
Step-by-step explanation:
You solve it like you ate looking for the hypotenuse
Help all of these are confusing me
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (1, - 4 ) and a = 1 , then
y = (x - 1)² - 4 → b
------------------------------------
given 3 sides of a triangle then an angle may be found using the cosine law. → b
if the 3 sides are a, b, c then
cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex] ← allowing ∠ A to be found
--------------------------------------
cosC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{4}{5}[/tex] → a
-----------------------------------------
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{AB}{DE}[/tex] = [tex]\frac{BC}{EF}[/tex] ( substitute values )
[tex]\frac{x}{6}[/tex] = [tex]\frac{10}{4}[/tex] ( cross- multiply )
4x = 6 × 10 = 60 ( divide both sides by 4 )
x = 15 → b
Answer:
bbabStep-by-step explanation:
There are a few algebraic, geometric, and trig relations you are expected to remember. These come into play in this set of questions.
vertex form for equation of a parabola: y = a(x -h)² +k, has vertex at (h, k)Sine Law relates triangle sides and their opposite angles: a/sin(A) = b/sin(B)Cosine Law relates triangle sides and the angle between two of them: c² = a² +b² -2ab·cos(C)SOH CAH TOA reminds you of trig relations in a right trianglerelationships of corresponding sides and angles in congruent and similar triangles: angles are congruent; sides are congruent or proportional.When solving any problem, the first step is to understand what is being asked. The second step is to identify the relevant information and relationships that can help you answer.
1)You are asked for the equation of a parabola with a given vertex. The vertex form equation will be useful. We can assume a scale factor ('a') of 1.
For vertex (h, k) = (1, -4) and a=1, the vertex form equation is ...
y = a(x -h)² +k
y = 1(x -1)² +(-4)
y = (x -1)² -4
2)You are given 3 sides and want to find an angle. The useful relation in this case is the Cosine Law. (If you wanted to use the Sine Law, you would already need to know an angle.)
3)The mnemonic SOA CAH TOA reminds you that the cosine relation is ...
Cos = Adjacent/Hypotenuse
The side adjacent to angle C is marked 4; the hypotenuse is marked 5. The desired ratio is ...
cos(C) = 4/5
4)The measure x is also the measure of side AB. The similarity statement lists those letters as the first two. It also lists the letters DE as the first two. The other given side in ΔABC is BC, corresponding to side EF in the smaller triangle. Corresponding sides are proportional, so we have ...
AB/DE = BC/EF
x/6 = 10/4
We can find the value of x by multiplying this equation by 6:
x = 6(10/4) = 60/4
x = 15
Please note that BC is the shortest side in ΔABC. This means x > 10. There is only one such answer choice. (No math necessary.)
For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8
Answer:
Step-by-step explanation:
The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5
Hello,
We have s0 = 1 and q = -2/3
[tex]S _{n} = S _{0} \times q {}^{n} = 1 \times ( - \frac{2}{3} ) {}^{n} [/tex]
[tex]S _{8} = ( - \frac{2}{3} ) {}^{8} = \frac{2 {}^{8} }{3 {}^{8} } = \frac{256}{6 561} [/tex]
What is the remainder when f(x) = 2x^3 – 12x^2 + 11x + 2 is divided by x – 5? Show your work.
Answer:
7
Step-by-step explanation:
given a polynomial divide by (x - a) then the remainder is f(a)
here f(x) is divided by (x - 5) , so remainder is
f(5) = 2(5)³ - 12(5)² + 11(5) + 2
= 2(125) - 12(25) + 55 + 2
= 250 - 300 + 57
= - 50 + 57
= 7
HELP, WILL GIVE BRAINLEST..
Factor the GCF: -6x³y + 9x²y2 - 12xy³ (5 points)
O 3xy(-2x² + 3xy - 4y²)
O-3xy(2x² + 3xy - 4y²)
O-3xy(2x2-3xy + 4y²)
O-3(2x³y - 3x²y² + 4xy³)
Answer:
[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]
Step-by-step explanation:
[tex]\sf -6x^3y+9x^2y^2-12xy^3[/tex]
To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-
[tex]\boxed{\sf a^{b+c}=a^ba^c}[/tex]
[tex]\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}[/tex]
[tex]\sf -6xx^2y+9xxyy-12xyy^2[/tex]
Rewrite,
-6 as 2 * 39 as 3 * 3-12 as 4 * 3[tex]\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2[/tex]
Now, factor out the common term [tex]\sf -3xy[/tex]:-
[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]__________________________
A chemist wants to make 45 ml of a 17% acid solution by mixing a 13% acid solution and a 19 % acid solution. How many milliliters of each solution should the chemist use?
Answer:
22 millilitres of 13% solution
23 millilitres of 19% solution
Step-by-step explanation:
A + B = 45
13A + 19B = 45 x 17 = 765
-13A - 13B + 13A + 19B = -650 + 765 = 115
5B = 115
B = 23
22 + 23 = 45
A = 22
The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
Lets simplify it,
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
Vertex Form:
f(x) = a(bx - c)² + d
f(x) = -1/3(x + 12)² + 9
Standard Form:
f(x) = -1/3(x + 12)² + 9
f(x) = -1/3(x² + 24x + 144) + 9
f(x) = -1/3x² - 8x - 48 + 9
f(x) = -1/3x² - 8x - 39
Learn more about Quadratic Function on:
https://brainly.com/question/11064204
#SPJ4
A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)
A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex] is [tex]33.6million[/tex].
How can we find the population size ?
The projection of population growth in yeast is given by
[tex]N=N_{0} e^{rt}[/tex]
Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]
[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]
N is population size
Substitute the values
[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]
Learn more about population size here :
https://brainly.com/question/28045705
#SPJ4
A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?
The length of the square pool is 8. 49cm
How to determine the areaNote that the formula for finding the area of a square is given as;
Area = length^2
We have
Area = 72 m²
Substitute into the formula
I^2 = 72
Find the square root of both sides
I= √72
I = 8. 49cm
The length of the square pool given as I is 8. 49cm
Thus, the length of the square pool is 8. 49cm
Learn more about area of a square here:
https://brainly.com/question/486778
#SPJ1
A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?
Answer:
8:35 PM
Step-by-step explanation:
First, subtract 15 from 50.
50-15=35
Add that 15 taken from 50 to 7:45.
7:45 + 0:15 = 8:00
Add 35 to 8:00
8:00 + 0:35 = 8:35
The next movie will start at 8:35 PM.
Hope this helps!
Which triangles are similar to ABC? Explain.
Answer: △JKL & △ MNP
Step-by-step explanation:
△JKL is similar because:
5 x 1.6 = 8
2.5 x 1.6 = 4
3.75 x 1.6 = 6
△MNP is also similar because:
4 x 2 = 8
2 x 2 = 4
3 x 2 = 6
Please please help me. It’s due right now! it would mean a lot :))<3 Pls show work!!!
Answer: 9 triangles.
Step-by-step explanation:
Just make a dot in the middle and make lines and connect each line to an edge or bend.
Select the correct answer.
Which statement correctly compares functions f and g?
Answer:
C
Step-by-step explanation:
Exponential functions have 2 things in common
-They increase infinitely once they approach a certain point
-They don't decrease anymore once they approach a certain point
Someone please help meeeeeee
Answer:
a ≈ 16.5 cm , b ≈ 23.8 cm
Step-by-step explanation:
using the Law of Sines in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
we require to calculate ∠ C
∠ C = 180° - (42 + 75)° = 180° - 117° = 63°
Then to find a
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )
[tex]\frac{a}{sin42}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )
a × sin63° = 22 × sin42° ( divide both sides by sin63° )
a = [tex]\frac{22sin42}{sin63}[/tex] ≈ 16.5 cm ( to the nearest tenth )
similarly to find b
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )
[tex]\frac{b}{sin75}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )
b × sin63° = 22 × sin75° ( divide both sides by sin63° )
b = [tex]\frac{22sin75}{sin63}[/tex] ≈ 23.8 cm ( to the nearest tenth )
Answer:
Step-by-step explanation:
Sine rule of Law of sine:[tex]\sf \boxed{\bf\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}=\dfrac{c}{Sin \ C}}[/tex]
Side 'a' faces ∠A.
Side 'b' faces ∠B.
Side 'c' faces ∠C.
We have to find ∠C using angle sum property of triangle.
∠C + 75 + 42 = 180
∠C +117 = 180
∠C = 180 - 117
∠C = 63°
[tex]\sf \dfrac{a}{Sin \ 42}= \dfrac{22}{Sin \ 63}\\\\ \dfrac{a}{0.67}=\dfrac{22}{0.89}\\\\[/tex]
[tex]\sf a = \dfrac{22}{0.89}*0.67\\\\ \boxed{a = 16.56 \ cm }[/tex]
[tex]\sf \dfrac{b}{Sin \ B} = \dfrac{c}{Sin \ C}\\\\ \dfrac{b}{Sin \ 75}=\dfrac{22}{Sin 63}\\\\ \dfrac{b}{0.97} =\dfrac{22}{0.89}\\\\[/tex]
[tex]\sf b = \dfrac{22}{0.89}*0.97\\\\ \boxed{b =23.98 \ cm }[/tex]
Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
gghhhh
jkkkkk
lllll
vvvvv
dddfff
oooooo
eeeerer
kkkkkk
lllll.ssss
Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Source
StylesFormatFontSize
Answer:
(-2, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]
To solve by substitution, substitute the first equation into the second equation:
[tex]\implies x+4=-2x-2[/tex]
Add 2x to both sides:
[tex]\implies x+4+2x=-2x-2+2x[/tex]
[tex]\implies 3x+4=-2[/tex]
Subtract 4 from both sides:
[tex]\implies 3x+4-4=-2-4[/tex]
[tex]\implies 3x=-6[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=-2+4[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of equations is (-2, 2).
Learn more about systems of equations here:
https://brainly.com/question/27868619
https://brainly.com/question/27868564
Substitute y value from first eqn in second equation
y=-2x-2x+4=-2x-23x=-6x=-2Put in first one
y=-2+4=2(-2,2) is the solution
Question 6
10 pts
Which is a counterexample for the following biconditional: "A figure is a quadrilateral if and only if it
is a polygon"?
Answer:
Trapezium, Rhombus, Kite, etc.
Step-by-step explanation:
A four - sided figure.
The name of a counterexample for the following biconditional: "A figure is a quadrilateral if and only if it is a polygon" is Triangle.
Used the concept of the polygon that states,
In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded by straight sides.
Given the condition is,
"A figure is a quadrilateral if and only if it is a polygon"
Now, we know that;
If a polygon is a quadrilateral, then it has four sides, and if a polygon has four sides, then it is a quadrilateral.
Hence, Triangle is a counterexample for the biconditional "A figure is a quadrilateral if and only if it is a polygon."
To learn more about quadrilaterals visit:
https://brainly.com/question/11037270
#SPJ7
Write y=5x-9 in standard form
Will give brainliest!
Answer:
5x - y = 9
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = 5x - 9 ( subtract 5x from both sides )
- 5x + y = - 9 ( multiply through by - 1 )
5x - y = 9 ← in standard form
Anthony is rowing a boat upstream. The following equation models his speed: f(x) = 3x2 − 6x − 13, where x is the velocity of the boat relative to land. What is the domain of the function?
Which of the following is an equivalent form of the equation of the graph shown in the xyxyx, y-plane above, from which the coordinates of vertex AAA can be identified as constants in the equation
The equivalent form of the equation y=[tex]x^{2} -2x-15[/tex]given is y=(x+3)(x-5).
Given an equation y=[tex]x^{2}[/tex]-2x-15 and we are required to find the equivalent form of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or any other equation depending on the powers of the variable.
To find the equivalent equations we are required to form factors of the equation. Equivalent equation are those equations which when solved gives the same solution as the equation when solved gives.
y=[tex]x^{2}[/tex]-2x-15
y=[tex]x^{2}[/tex]-5x+3x-15
y=x(x-5)+3(x-5)
y=(x+3)(x-5)
Hence the equivalent form of the equation y= [tex]x^{2}[/tex]-2x-15 given is
y=(x+3)(x-5).
Learn more about equation at https://brainly.com/question/2972832
#SPJ4
Question is incomplete as question should includes the equation
y= [tex]x^{2}[/tex]-2x-15.
2+8+32+128…..,n=9
Evaluate each geometric series described
The value of 2+8+32+128…..,n=9 is 174762
How to evaluate the series?The series is given as:
2+8+32+128…..,n=9
Start by calculating the common ratio (r)
r = 8/2
r = 4
The sum of the series is then calculated as:
[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]
This gives
[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]
Evaluate the difference
[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]
Evaluate the quotient
[tex]S_9 = 174762[/tex]
Hence, the value of 2+8+32+128…..,n=9 is 174762
Read more about series at:
https://brainly.com/question/7882626
#SPJ1
Study the illustration. Write the ratio
of flowers to bees. Complete the sentence.
For every 5 flowers there are _______
bees.
Answer: 6 bees
Step-by-step explanation:
The picture has 12 bees and 10 flowers. Thus, the ratio of flowers to bees is 10 to 12, which simplifies to 5 to 6.
Therefore, for every 5 flowers, there are 6 bees.
3\sqrt(6)*6\sqrt(6)
Please quick reply!
Answer: 3
Step-by-step explanation:
Multiply the numerator to get 3 x 6 is 18
Multiply the denominator to get √6 x √6 = 6
Divide 18 by 6 to get the answer is 3
x =_______ y =_______ 12. Find the values of x and y.
Answer:
Below in bold.
Step-by-step explanation:
Opposite angles of a quadrilateral i a circle are supplementary so
x = 180 - 112 = 68 degrees.
y = 180 - 81 = 99 degrees.
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30
The value of the Mean & Standard deviation is 1.30 and 1.18.
According to the statement
we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.
And we have to find the mean and standard deviation from the given data which is related to the probabilities values
So, according to the given data
The formula to compute the mean is:
Mean = summation [x*p(x)]
Compute the mean as follows:
Mean = summation [x*p(x)]
Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]
Mean = 0 +0.05 + 0.64 + 0.21 + 0.28
Mean = 1.18
The mean of the random variable x is 1.18.
And after calculating the variance from the formula get
The value of standard deviation is 1.30
So, The value of the Mean & Standard deviation is 1.30 and 1.18.
Learn more about mean and standard deviation here https://brainly.com/question/14650840
#SPJ4
Let k be a positive integer. In how many ways can one select three distinct numbers from the set {1,2,..., 3k} such that their sum is divisible by 3
Reduce the numbers in the list modulo 3 to get the set
{1, 2, 0, 1, 2, 0, …, 1, 2, 0}
containing [tex]k[/tex] copies each of 1, 2, and 0.
Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:
3 elements each with the same residue, so0 + 0 + 0 ≡ 0 (mod 3)
1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)
2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)
1 element each with different residues, so0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)
There are
[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]
ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence
[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]
ways of choosing any 3 elements with the same residue, and there are
[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]
ways of choosing any 3 elements with distinct residues.
So, the total number of ways of making the selection is
[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]
A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. Her work is shown below. What is Amies error
Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
Learn more about volumes at
https://brainly.com/question/12398192
#SPJ4
For the complete question, refer to the attachment.
10 points please help me!!!
Step-by-step explanation:
16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)Which graph models the pH of this solution?
The graph that models the pH of this solution is graph A.
What is a graph?It should be noted that a graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.
The pH is a measure of how acidic or basic water is. It should be noted that the range goes from 0 - 14, with 7 being neutral. The pHs of less than 7 indicate acidity, while a pH of greater than 7 indicates a base. The pH is really a measure of the relative amount of free hydrogen and hydroxyl ions that are in the water.
In this case, x represents the concentration of the hydrogen ions. The first graph illustrates this.
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
Complete question:
The ph of a particular solution is given by pH=-log(x-2) where x represents the concentration of the hydrogen ions in the solution in moles per liter. Which graph models the ph of this solution?
If 3 square feet of fabric costs $3.75. what would 7 square feet cost?
Answer:
8.75
Step-by-step explanation:
3.75/3=1.25
1.25=1 square feet
1.25(7)=8.75