Answer:
x = 14Angle 1 = 6°Angle 2 = 84°Step-by-step explanation:
from the sign it's a right angle, so 90°
Find x90 = x - 8 + 6x
90 + 8 = 7x
98 = 7x
x = 98 : 7
x = 14
------------------
check
90 = 14 - 8 + 6 * 14 (remember pemdas)
90 = 14 - 8 + 84
90 = 90
the answer is good
Find angle 1
x - 8
14 - 8 =
6°
Find angle 2
6x
6 * 14 = 84°
--------------------
check
84 + 6 = 90°
the answer is good
Answer:
\(\textsf{a)} \quad \textsf{Equation}: \quad \boxed{x-8+6x=90}\)
\(\begin{aligned}\textsf{b)} \quad m \angle 1 & =\boxed{6^{\circ}}\\ m \angle 2 & =\boxed{84^{\circ}}\end{aligned}\)
Step-by-step explanation:
Part (a)From inspection of the given diagram, the sum of the two angles is 90° (indicated by the right angle sign):
\(\implies m \angle 1+m \angle 2=90^{\circ}\)
\(\implies (x - 8)^{\circ} + (6x)^{\circ} = 90^{\circ}\)
\(\implies x-8+6x=90\)
\(\textsf{Equation}: \quad \boxed{x-8+6x=90}\)
Part (b)To find the measure of each angle, solve the equation for x:
\(\implies x-8+6x=90\)
\(\implies x+6x-8=90\)
\(\implies 7x-8=90\)
\(\implies 7x-8+8=90+8\)
\(\implies 7x=98\)
\(\implies \dfrac{7x}{7}=\dfrac{98}{7}\)
\(\implies x=14\)
Substitute the found value of x into the expression for each angle:
\(\implies m \angle 1=(x-8)^{\circ}\)
\(\implies m \angle 1=(14-8)^{\circ}\)
\(\implies m \angle 1=\boxed{6^{\circ}}\)
\(\implies m \angle 2=(6x)^{\circ}\)
\(\implies m \angle 2=(6 \cdot 14)^{\circ}\)
\(\implies m \angle 2=\boxed{84^{\circ}}\)
the statement int grades[ ] = { 100, 90, 99, 80 }; is an example of
Answer:
implicit array sizing
Step-by-step explanation:
The statement "int grades[] = { 100, 90, 99, 80 };" initializes an integer array called "grades" with the values 100, 90, 99, and 80. The given statement is an example of initializing an integer array in C++.
The array is named "grades" and has an unspecified size denoted by the empty square brackets []. The values inside the curly braces { } represent the initial values of the array elements.
In this case, the array "grades" is initialized with four elements: 100, 90, 99, and 80. The first element of the array, grades[0], is assigned the value 100, the second element, grades[1], is assigned 90, the third element, grades[2], is assigned 99, and the fourth element, grades[3], is assigned 80.
The array can be accessed and manipulated using its index values. This type of initialization allows you to assign initial values to an exhibition during its declaration conveniently.
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Please help now please ASAP
Answer:
g = 59⁰
h = 9
(by using opposite sides and angles of a parallelogram are equal.)
1. What is the name of the shape to the left?
Answer:
for me it is a circle
Step-by-step explanation:
Naoya read a book cover to cover in a single session, at a rate of 555555 pages per hour. After reading for 444 hours, he had 330330330 pages left to read. How long is the book? pages how long did it take naoya to read the entire book? hours.
There are 550 pages in the book and Naoya read the entire book in ten hours.
Given that,
Naoya read a book from beginning to end in a single sitting, turning 55 pages per hour. He still had 350 pages to read after four hours. The number of pages to read for P as a function of time t is denoted by P(t), left parenthesis, t, and right parenthesis (measured in hours).
We have to find the function's formula in writing.
We know that,
Naoya consumed 55 pages each hour, or 55T pages, during the course of T hours.
The number of pages Naoya has already read and the number of pages still to be read make up the total number of pages. This can be stated using the formula B=55T+R, where
B is a measure of the book's size.
T stands for time (in hours)
R is the total number of pages to be read at any given moment.
We are aware that Naoya has 330 pages left to read after reading for 44 hours (T=4) (R=330). To determine the value of B, let's enter these values into the equation.
B=55×4+330=550
We get the book is 550 pages long.
We may enter R=0 into the equation and calculate T to determine how long it took Naoya to complete the entire book.
550 =55T + 0
55T = 550
T= 10
Therefore, There are 550 pages in the book and Naoya read the entire book in ten hours.
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What do the coordinates of an undefined slope have in common?
The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.
someone please help,
You drop a water balloon from a height of 50 feet. a. Write a function h that gives the height (in feet) of the water balloon above the ground after t seconds. Interpret each term. How long does it take the water balloon to hit the ground? + b. Find and interpret h(1) - h(1.5).
The time to hit the ground is 1.77 seconds and the interpretation of h(1) - h(1.5) is that the water balloon covered a distance of 22 meters between 1 and 1.5 seconds
How to determine the time to hit the groundThe height of launch is given as:
Launch = 50 feet
The height function can be calculated as
h(t) = -16t² + Launch
So, we have
h(t) = -16t² + 50
When it hits the ground, we have h(t) = 0
This gives
-16t² + 50 = 0
So, we have
-16t² = -50
Divide both sides by -16
t² = 3.125
Take the square roots
t = 1.77
Interpret h(1) - h(1.5)Recall that
h(t) = -16t² + 50
So, we have
h(1) = -16(1)² + 50 = 34
h(1.5) = -16(1.5)² + 50 = 12
So, we have
h(1) - h(1.5) = 34 - 12
Evaluate
h(1) - h(1.5) = 22
This means that the height difference is 22 meters
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A strawberry farmer will receive $33 per bushel of strawberries during the first week of harvesting. Each week after that, the value will drop $0.80 per bushel. The farmer estimates that there are approximately 125 bushels of strawberries in the fields, and that the crop is increasing at a rate of four bushels per week. When should the farmer harvest the strawberries (in weeks) to maximize their value? (Assume that "during the first week of harvesting" here means week 1.) weeks How many bushels of strawberries will yield the maximum value? bushels What is the maximum value of the strawberries (in dollars)? $
To find the week when the farmer should harvest strawberries to maximize their value, we need to use quadratic equations. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. The maximum value occurs at x = 20.625 weeks. Plugging this into the equation, we can find that the maximum value is $527.81. To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, the farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries.
To solve the problem, we need to use quadratic equations because the value of strawberries decreases linearly each week. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. Plugging these values into the formula, we get x = -33/(2*(-0.8)) = 20.625 weeks. This means that the maximum value occurs at week 21 since we started counting from the first week of harvesting.
To find the maximum value, we need to plug x = 20.625 into the equation for the value of strawberries. Therefore, y = -0.8*(20.625)^2 + 33*(20.625) = $527.81. This is the maximum value of the strawberries.
To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, y = 4*(20.625) + 125 = 205 bushels of strawberries.
The farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries. The farmer can use this information to plan their harvesting schedule and maximize their profits.
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what's the solution to the equation x/3 + x/6 = 7/2
Step-by-step explanation:
x/3+x/6=7/2
We simplify the equation to the form, which is simple to understand
x/3+x/6=7/2
Simplifying:
+ 0.333333333333x+x/6=7/2
Simplifying:
+ 0.333333333333x + 0.166666666667x=7/2
Simplifying:
+ 0.333333333333x + 0.166666666667x=+3.5
We move all terms containing x to the left and all other terms to the right.
+ 0.333333333333x + 0.166666666667x=+3.5
We simplify left and right side of the equation.
+ 0.5x=+3.5
We divide both sides of the equation by 0.5 to get x.
x=7
take l.c .m of 3 and 6 then
2x+x/6 = 7/2
3x = 7/2*3
x = 21/2/3
x = 21/2 * 1/3
x = 7/2
The measure of m/JML is 85°. Select all the true statements.
M
(6x + 2)°
K
(4x+3) °
L
A. m/JMK = 10°
B. m/KML = 11°
C. m/JMK = 50°
D. m/KML = 35°
E. m/JMK - m/KML = m/JML
Answer:
C an D are correct
Step-by-step explanation:
we add the two angles so as to find the value of x,
(6x+2)+(4x+3)=85
10x+5=85
10x=80
x=8
m/JMK=6x+2=6(8)+2=48+2=50°
m/KML=4x+3=4(8)+3=32+3=35°
so only C and D are correct
The measure of the angles ∠JMK and ∠KML will be 50° and 35°, respectively. Then the correct options are C and D.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of angle ∠JML is 85°. ∠JMK = 6x + 2 and ∠KML = 4x + 3.
We know that the sum of the angles ∠JMK and ∠KML is equal to the angle ∠JML. Then we have
∠JMK + ∠KML = ∠JML
6x + 2 + 4x + 3 = 85°
10x = 80°
x = 8°
Then the angles will be
∠JMK = 6 × 8 + 2
∠JMK = 48 + 2
∠JMK = 50°
∠KML = 4 × 8 + 3
∠KML = 32 + 3
∠KML = 35°
The measure of the angles ∠JMK and ∠KML will be 50° and 35°, respectively.
Then the correct options are C and D.
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Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4
The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.
The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of
u1, u2 and u3.
The span of
{u1, u2, u3, u4}
will be a subset of the span of
{u1, u2, u3}.
This means that the span of
{u1, u2, u3, u4}
will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of
{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},
as there may be other vectors that are in the span of
{u1, u2, u3, u4}
but not in the span of {u1, u2, u3}. Hence, the statement is false.
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The complete question is
Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.
Name each polynomial by degree and number of terms.
¶ Cσncєptѕ tσ вє uѕєd hєrє :
✦ Degree of a polynomial íѕ thє híghєѕt pσwєr σf α vαríαвlє ín thє gívєn pσlчnσmíαl.
✦ numвєr σf tєrmѕ = díѕtínguíѕhєd tєrmѕ ín α pσlчnσmíαl hαvíng díffєrєnt єхpσnєntíαl pσwєr, αnd ѕєpєrαtєd вч mαthєmαtícαl σpєrαtσrѕ ( + αnd - )
➳ nσtє :
#1. Combine the like terms before performing any operation.
#2. íf thєrє íѕ α multíplícαtíσn σr dívíѕíσn σpєrαtσr ín thє pσlчnσmíαl, wє hαvє tσ fínd thє prσduct fírѕt tσ pєrfσrm αnч σthєr σpєrαtíσn.
✿ lєt'ѕ prσcєєd ~\(\sf \#1 \: \: \: \{-9 {x}^{4} - 3x \}\)
dєgrєє : 4 [ frσm -9х⁴ ]numвєr σf tєrmѕ : 2\(\rule{20cm}{1 mm}\)
\(\sf \#2 \: \: \: \{-2v \}\)
dєgrєє : 1 [ frσm -2v ]numвєr σf tєrmѕ : 1\(\rule{20cm}{1 mm}\)
\( \sf \#3 \: \: \: \{9 {n}^{3} - 6n + 10\}\)
dєgrєє : 3 [ frσm 9n³ ]numвєr σf tєrmѕ : 3\(\rule{20cm}{1 mm}\)
\( \sf \#4 \: \: \: \{3 + 4 p {}^{4} + ( 4{p}^{4} - 5)\}\)
[ cσmвínє thє líkє tєrmѕ ]
\( \sf \#4\: \: \: \{ 8p {}^{4} - 2\}\)
dєgrєє : 4 [ frσm 8p⁴ ]numвєr σf tєrmѕ : 2\(\rule{20cm}{1 mm}\)
\(\sf \#5 \: \: \: \{(8v+6v³) - ( v - 3v {}^{3 }{+ 5 {v}^{2} } )\}\)
[ cσmвínє thє líkє tєrmѕ ]
\(\sf \#5 \: \: \: \{9v³ - 5 {v }^{2} + 7v \}\)
dєgrєє : 3 [ frσm 9v³ ]numвєr σf tєrmѕ : 3\(\rule{20cm}{1 mm}\)
\( \sf \#6 \: \: \: \{(3y + 4)(2y - 6) \}\)
[ pєrfσrm thє multíplícαtíσn ]
\( \sf \#6 \: \: \: \{ 6 {y}^{2} - 10y - 24\}\)
dєgrєє : 2 [ frσm 6y² ]numвєr σf tєrmѕ : 3\(\rule{20cm}{1 mm}\)
Keep learning ~\(\qquad \qquad\huge \dag \: \normalsize \sf \boxed{ \underline{ǤríʍɌεαƿєr}} \: \huge \dag\)
b) 8% of the light bulbs manufactured on an assembly line are defective.
(i) Calculate the probability that the second defective light bulb will be found on the tenth inspection if the light bulbs are inspected one by one.
(Ii) In a random sample of n light bulbs, the probability to get at least one defective light bulb is greater than 0.9. Calculate the smallest possible value of n.
(iii) A random sample of 1800 light bulbs is taken. Calculate the probability that there are at least 152 are defective.
The probability that at least 152 out of 1800 light bulbs are defective is approximately 0.7664 or 76.64%.
(i) To calculate the probability that the second defective light bulb will be found on the tenth inspection, we need to consider the binomial distribution.
The probability of finding a defective light bulb on any given inspection is 8%, which means the probability of not finding a defective bulb is 92% (1 - 0.08).
To find the probability of finding the second defective bulb on the tenth inspection, we need to have 9 successful (non-defective) inspections followed by a successful (defective) inspection on the tenth attempt.
Using the binomial distribution formula, the probability is given by:
P(X = 9) * P(X = 1) = C(10, 9) * (0.92)^9 * (0.08)^1 = 10 * 0.92^9 * 0.08
Calculating this expression, we find:
P(second defective on tenth inspection) ≈ 0.1959 or 19.59%
(ii) In a random sample of n light bulbs, the probability of at least one defective light bulb is given by the complement of the probability of having all non-defective light bulbs.
The probability of a single light bulb being non-defective is 92% (1 - 0.08). Therefore, the probability of all n light bulbs being non-defective is \((0.92)^n.\)
We want the probability of at least one defective light bulb, which is the complement of all non-defective light bulbs:
P(at least one defective) = 1 - P(all non-defective)
P(at least one defective) = \(1 - (0.92)^n\)
Given that the probability of at least one defective light bulb is greater than 0.9, we have:
\(1 - (0.92)^n\)> 0.9
To solve this inequality, we can take the logarithm of both sides:
\(log(1 - (0.92)^n) > log(0.9)\)
Rearranging the inequality and solving for n, we find:
n > log(0.1) / log(0.92)
n > 21.854
Therefore, the smallest possible value of n is 22.
(iii) To calculate the probability that at least 152 out of 1800 light bulbs are defective, we can use the binomial distribution.
The probability of a single light bulb being defective is 8% (0.08). Therefore, the probability of a single light bulb being non-defective is 92% (1 - 0.08).
Using the binomial distribution formula, the probability of having at least 152 defective bulbs out of 1800 is given by:
P(X ≥ 152) = P(X = 152) + P(X = 153) + ... + P(X = 1800)
Calculating this probability involves summing the probabilities for each individual value of X from 152 to 1800. However, this calculation is computationally intensive.
Alternatively, we can use a normal approximation to the binomial distribution for large sample sizes. In this case, both the number of trials (n = 1800) and the probability of success (p = 0.08) are sufficiently large.
Using the normal approximation, we can calculate the mean and standard deviation of the binomial distribution:
mean = n * p = 1800 * 0.08 = 144
standard deviation = sqrt(n * p * (1 - p)) = sqrt(1800 * 0.08 * 0.92) ≈ 10.439
To find the probability of having at least 152 defective bulbs, we can calculate the z-score corresponding to X = 151.5 (using continuity correction):
z = (151.5 - mean) / standard deviation = (151.5 - 144) / 10.439 ≈ 0.721
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 0.721 is approximately 0.7664.
Therefore, the probability that at least 152 out of 1800 light bulbs are defective is approximately 0.7664 or 76.64%.
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Make up two different equations that equal 8.4 x 10^-5
Answer:
assuming that "x" is a multiplication symbol
(4.2*2)10^-5
0.00001 * 8.4
(b) A private club grew by 7 members each week for 56 weeks. What was the total change in the
club's size?
members
the cost of 19/4 m of wire Is Rs.171/2 .The cost of one meter of the wire is ________.
Answer:
.The cost of one meter of the wire is _Rs18_______.
Step-by-step explanation:
the cost of 19/4 m of wire = Rs.171/2
the cost of 1m of wire = Rs.171/2×4/19=Rs18
You can buy 3 pounds of strawberries for 3.99 at Kroger knowing this what is the unit rate per pound of strawberries and how much would 5 pounds cost
Answer:
1.33 per pound6.65 for 5 poundsStep-by-step explanation:
To find cost per pound, divide cost by pounds.
3.99/(3 lb) = 1.33/lb . . . . cost per pound
The cost of 5 pounds will be found by multiplying that by 5:
(1.33/lb)(5 lb) = 6.65 . . . cost of 5 pounds
1/8y= -3/4x-1 in standard form
There are about
3 * 10^11
stars in our galaxy and about 100 billion galaxies in the observable universe. Suppose every galaxy has as many stars as ours. How many stars are in the observable universe? Write in scientific notation.
The number of stars in 100 billion galaxies in scientific notation is
3 x \(10^{22}\).
What is scientific notation?Scientific Notation is the expression of a number in the form a x \(10^{b}\). where a is an integer such that 1 ≤ |a| < 10 and b is an integer too.
We have,
Number of stars in our galaxy = 3 x \(10^{11}\)
Number of galaxies in the observable universe = 100 billion.
1 billion = 1,000,000,000 = \(10^{9}\)
Number of stars in 100 billion galaxies:
= 3 x \(10^{11}\) x 100 x \(10^{9}\)
= 3 x \(10^{11 + 2 + 9}\)
= 3 x \(10^{22}\)
Thus the number of stars in 100 billion galaxies in scientific notation is
3 x \(10^{22}\).
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Factors for x2-2x-2=0
Answer:
Not factor-able
heat can be produced by - two things
we have a study involving 3 different groups that each contain 9 participants (27 total). what two degrees of freedom would we report when we report the results of our study?
Using degree of freedom,
Two degrees of freedom would we report when we report the results of our study is (2,24).
Degree of freedom:
The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.
degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters
DF = N – P
Where:
N = sample size
P = the number of relationships
We given that,
Number of groups , k = 3
Number of total participants, n = 27
Degrees of freedom for F-test is F(k-1,n-k)
= F(3-1 , 27-3)
= F(2,24)
Hence, (2,24,) are required two degrees of freedom.
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2
Select the correct answer
What is the sum of the first 28 terms of this arithmetic sequence?
69, 75, 81, 87, 93, 99,...
A. 2,436
B. 4,200
C. 4,320
D. 4,368
Answer:
B. 4200
Step-by-step explanation:
A suitable calculator can add the terms for you. (See attached)
__
The first term is 69, and the common difference is 75-69 = 6. The general term is ...
an = a1 +d(n -1)
an = 69 +6(n -1)
Then the 28th term is ...
a28 = 69 +6(27) = 231
The average term is (a28 +a1)/2 = (231 +69)/2 = 150.
The sum is the number of terms multiplied by the average term:
sum = 28×150= 4200
____________ is an economic and political doctrine that emphasized free trade and the constitutional guarantee of individual rights such as freedom of speech and religion.
The economic and political doctrine that emphasizes free trade and the constitutional guarantee of individual rights, such as freedom of speech and religion, is called liberalism.
Liberalism is a political and economic ideology that promotes individual freedom, limited government intervention, and free market principles. It emphasizes the importance of protecting individual rights, including civil liberties such as freedom of speech, religion, and assembly. Liberalism advocates for a system of governance that ensures equality under the law and encourages free trade and open markets. Economic liberalism promotes free trade and opposes government restrictions or regulations on business and commerce. It supports the idea of a market economy where prices are determined by supply and demand and individuals have the freedom to engage in economic activities. In the context of politics, liberalism advocates for democratic principles, constitutionalism, and the protection of individual rights as essential components of a just and prosperous society.
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For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
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some people claim they can get relief from migraine headache pain by drinking a large glass of ice water resources plan to enlist several people who suffer from migraines and i test
The correct response variable is the amount of pain relief.
Given that,
A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.
To find : What is the response variable in this experiment.
Explanation :
Response variable or study variable, in general called as dependent variable is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.
For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.
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Which inequality is equivalent to −4≥28?
Answer:
-1 ≥ 7
Step-by-step explanation:
-1 ≥ 7 = -4 ≥ 28
-4 ≥ 28
We simplify both sides by 4 and get -1 ≥ 7
8
Helen thinks of two numbers.
The Highest Common Factor (HCF) of her two numbers is 5
The Lowest Common Multiple (LCM) of her two numbers is a multiple of 12
Write down two possible numbers that Helen could be thinking of.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
what is HCF ?The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one. Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.
given
1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. The smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 and 6 is 12, for instance.
3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
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Please awnser wuicklyyy
The value of c in the following equation F = (9/5)C + 32 will be (5F - 160)/9.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
A formula known as an equation uses the same sign to denote the equality of two expressions.
Given that,
F = (9/5)C + 32
F - 32 = (9/5)C
Multiply both sides by 5/9
5F/9 - 160/9 = C
C = (5F - 160)/9
Hence "The value of c in the following equation F = (9/5)C + 32 will be (5F - 160)/9".
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An American Society of Investors survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability: a. Exactly two of the sampled individuals have used a discount broker
The probability that exactly two of the sampled individuals have used a discount broker is approximately 0.2217 or 22.17%.
To calculate the probability of exactly two individuals in a random sample of nine having used a discount broker, we can use the binomial probability formula.
The binomial probability formula is given by:
\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)x^{2}\)
Where:
- P(X = k) is the probability of exactly k successes,
- n is the total number of trials (sample size),
- p is the probability of success on a single trial (probability of an individual investor using a discount broker), and
- (n choose k) represents the number of combinations of n items taken k at a time.
In this case, n = 9 (sample size) and p = 0.30 (probability of an individual investor using a discount broker).
\(P(X = 2) = (9 choose 2) * (0.30)^2 * (1 - 0.30)^(9 - 2)\)
Using the binomial coefficient formula (n choose k) = n! / (k! * (n - k)!) to calculate (9 choose 2), we can plug in the values:
\(P(X = 2) = (9 choose 2) * (0.30)^2 * (1 - 0.30)^(9 - 2)\)
\(P(X = 2) = (9! / (2! * 7!)) * (0.30)^2 * (0.70)^7\)
\(P(X = 2) = (36 / 2) * (0.30)^2 * (0.70)^7\)
P(X = 2) = 36 * 0.09 * 0.08235456
P(X = 2) ≈ 0.2217
Therefore, the probability that exactly two of the sampled individuals have used a discount broker is approximately 0.2217 or 22.17%.
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