The value of the threshold t that gives a false rejection rate of 0.05 is found to be 5.991. The corresponding probability of false acceptance, or type II error, is computed using the power function of the test and found to be approximately 0.1485.
This is the probability of failing to reject the null hypothesis when the alternative hypothesis is true and the variance is 25.
To determine the value of t that gives a probability of false rejection of 0.05, we need to find the distribution of the test statistic under the null hypothesis H0: σ^2 = 16. The test statistic is:
T = (X1 - μ)² + (X2 - μ)² + (X3 - μ)² / (nσ²)
Under the null hypothesis, T follows a chi-squared distribution with 2 degrees of freedom (n-1). We can use this distribution to find the value of t such that the probability of false rejection is 0.05.
From the tables of the chi-squared distribution, we find that the critical value of T for a false rejection rate of 0.05 is 5.991.
Thus, we reject the null hypothesis if T > 5.991.
The probability of false acceptance, also known as type II error, is the probability of failing to reject the null hypothesis when it is actually false (i.e., when H1: σ^2 = 25 is true). This probability depends on the value of σ^2 and the threshold t.
To find the probability of false acceptance, we need to compute the power of the test, which is the probability of rejecting the null hypothesis when it is false. The power function is given by:
β(σ²) = P(T > t | σ² = 25)
The distribution of T under H1 is also a chi-squared distribution with 2 degrees of freedom, but with a different scale parameter:
T ~ χ^2(2, nσ^2/25)
Using the non-central chi-squared distribution, we can compute the power function:
β(σ²) = Q(√(n/25)(t - 3.2), 2, δ)
where Q is the complementary cumulative distribution function (CCDF) of the non-central chi-squared distribution, δ = √(n)(20-25)/5, and t is the threshold value.
For t = 5.991, we have:
[tex]δ = √(3)(20-25)/5 = -1.3416\\\\β(16) = Q(√(3/25)(5.991 - 3.2), 2, -1.3416) ≈ 0.1485\\β(25) = Q(√(3/25)(5.991 - 3.2), 2, 0) ≈ 0.4259[/tex]
Therefore, the probability of false acceptance is
P(accept H1 | H1 is false) = β(16) ≈ 0.1485
Note that this is the probability of failing to reject H0 when H1 is true and σ^2 = 25. It is not the probability of accepting H1 when H0 is true and σ^2 = 16, which is 1 - the probability of false rejection.
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PLease help me with this I can't understand it it is easy
What is the surface area of the triangular prism?
Use the net to help you. Surface area of triangular prism = triangle base + triangle base + rectangle face + rectangle face + rectangle face
Blue Rectangle
Orange Rectangle
Red Rectangle
One Green Triangle
Total Surface area
_______________
The total surface area of the triangular prism is 200 square inches.
What is a triangular prism?A triangular prism is a three-dimensional geometric shape that consists of two parallel triangular bases connected by three rectangular faces.
To find the surface area of the triangular prism using the net provided, we need to find the area of each face and then add them together.
Using formulas,
Area of rectangle= [tex]length\times width[/tex] square unit.
Area of triangle = [tex]\frac{1}{2}\times Base \times Height[/tex] square unit.
The blue rectangle has a length of 5 inches and a width of 4 inches, so its area is
=> 5 x 4 = 20 square inches.
The orange rectangle has a length of 12 inches and a width of 4 inches, so its area is
=> 12 x 4 = 48 square inches.
The red rectangle has a length of 13 inches and a width of 4 inches, so its area is
=> 13 x 4 = 52 square inches.
The green triangles have a base of 12 inches and a height of 5 inches, so each triangle's area is
=> [tex]\frac{1}{2}\times12\times5[/tex]= 30 square inches.
To find the total surface area, we add the area of each face:
=> 20 + 20 + 48 + 52 + 30 + 30 = 200 square inches.
Therefore, the surface area of the triangular prism is 200 square inches.
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Find the area of the figure below composed of a square and four Semicircles rounded to the nearest tenths place 
The required area of the shape is 2014.88 sq units.
What is Area?Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.
According to question:Given shape consist of a square and four half circles.
Radius of circle = 14 units, side length of the square is 28 units
Area of the shape = are of square + area of four half circles
= 28×28 + 4(π(14)²)/2
= 784 + 2π(14)²
= 784 + 1230.88
= 2014.88 sq units
Thus, required area of the shape is 2014.88 sq units.
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If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'
If a point's preimage is P(x, y), then its image after a dilation with a scale factor of k and centered at the origin (0, 0) is P'(kx, ky).
What is Pre picture of a point?The set of all points in a function's domain that correspond to a given point in the range is known as the preimage of a point in mathematics.
Formally, let f be a function that goes from a set A to a set B, and let y be a point in B. The preimage of y is the set of all points x in A where f(x) = y, or the set of all points in the domain that the function maps to the given point in the range.
If the preimage of the point P has facilitates (x, y), and the expansion focused at the beginning with a scale component of k is applied, then the directions of the picture point P' can be tracked down utilizing the accompanying recipe:
The x- and y-coordinates of P' are determined by multiplying the corresponding coordinates of the preimage point P by the scale factor k; consequently, the coordinates of the image point P' following the dilation with the origin centered on k would be (kx, ky).
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Complete question: If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'.
What are the coordinates of point P'?
If p is inversely proportional to the square of q, and p is 8 when q is 9, determine p when q is equal to 2.
Answer:
the value for p will be 162
PLS PLS PLS help me I'm reposting this question bc no one helped me
Determine whether line segment AB is a diameter of the circle.
O Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
O Yes, The endpoints of line segment AB lie on the circle, so line segment AB is a diameter by the definition of a diameter.
O No, because line segment AB does not bisect line segment CD, line segment AB cannot be a diameter
O No, line segment AB is not perpendicular to line segment CD, so the Perpendicular Chord Bisector Theorem cannot be used to conclude that line segment AB is a diameter
Answer:
Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
Answer:
1st option
Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
(Trig word problems)
From a hot-air balloon, Enola measures a 22° angle of depression to a landmark that’s 310 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Step-by-step explanation:
See image
Find the volume of the sphere.
Use 3.14 for T. Round your
answer to the nearest tenth.
Enter your answer in cm³ (type in
the number only without units).
7.2 cm
Answer:
I think it will help u (:
Step-by-step explanation:
Assuming the given measurement is the diameter of the sphere, we can find the radius as follows:Radius (r) = Diameter / 2 = 7.2 / 2 = 3.6 cmThe formula for the volume of a sphere is:V = (4/3) * π * r³Substituting the values, we get:V = (4/3) * 3.14 * (3.6)³
V = 4.19 * 46.656
V = 195.4 cm³Rounding this to the nearest tenth, we get:V ≈ 195.4 cm³Therefore, the volume of the sphere is approximately 195.4 cm³.
The circle graph shows how a family budgets its annual income. If the total annual income is $125,000, what amount is budgeted for Clothing?
Answer:
Step-by-step explanation:
125,000 x 16% = $20,000
(23%) 28,750 + (8%) 10,000 + (9%) 11,250 + (12%) 15,000 + (16%) 20,000 + (19%) 23,750 + (13%) 16,250 = $125,000
What coordinates would it be? How would I do it?
Answer:
In the images
Hope this helps!
Step-by-step explanation:
Clockwise is the direction the arrow is pointing, counter-clockwise is the other direction.
ramanujan and hardy played a game where they both picked a complex number. if the product of their numbers was $32-8i$, and hardy picked $5+3i$, what number did ramanujan pick?
Let Ramanujan pick a complex number $a+bi$, where $a$ and $b$ are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:
(
�
+
�
�
)
(
5
+
3
�
)
=
5
�
+
3
�
�
+
5
�
�
+
3
�
�
2
=
(
5
�
+
3
�
)
+
(
5
�
+
3
�
)
�
−
3
�
(a+bi)(5+3i)=5a+3ai+5bi+3bi
2
=(5a+3b)+(5b+3a)i−3b
We want this product to be equal to $32-8i$. Equating the real and imaginary parts gives us two equations:
5
�
+
3
�
=
32
(1)
5a+3b=32(1)
5
�
+
3
�
=
−
8
(2)
5b+3a=−8(2)
We can solve this system of equations to find $a$ and $b$. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:
15
�
+
9
�
−
25
�
−
15
�
=
−
96
15a+9b−25b−15a=−96
Simplifying:
−
16
�
=
−
96
−16b=−96
Therefore, $b=6$. Substituting $b=6$ into equation (1) gives:
5
�
+
18
=
32
5a+18=32
Therefore, $a=2$. Thus, Ramanujan picked the complex number $2+6i$.
Based on the given conditions and informations provided, the complex number that was picked by thr Ramanujan is calculated to be 2+6i.
Let Ramanujan pick a complex number a+bi, where a and b are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:
(a+bi)(5+3i) = 5a+3ai+5bi+3bi² = (5a+3b)+(5b+3a)i-3b
We want this product to be equal to 32-8i. Equating the real and imaginary parts gives us two equations:
5a+3b=32 (1)
5b+3a=-8 (2)
We can solve this system of equations to find a and b. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:
15a+9b-25b-15a=-96
Simplifying:
-16b=-96
Therefore, b=6. Substituting b=6 into equation (1) gives:
5a+18=32
Therefore, a=2. Thus, Ramanujan picked the complex number 2+6i.
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how many revolutions will a car wheel of diameter 24 in. make as the car travels a distance of one mile? (round your answer to the nearest whole number.)
The car wheel will make approximately 840 revolutions as the car travels a distance of one mile.
To calculate the number of revolutions that a car wheel of diameter 24 in. will make as the car travels a distance of one mile, we need to use the formula:
number of revolutions = distance traveled / distance per revolution
The distance traveled is given in miles, and we need to convert the diameter of the wheel, given in inches, to the distance per revolution in miles.
The diameter of the wheel is 24 in., which means the radius is 12 in. The distance per revolution is equal to the circumference of the wheel, which is given by the formula:
circumference = 2 * pi * radius
Substituting the values, we get:
circumference = 2 * pi * 12 in. = 75.4 in.
To convert this to miles, we divide by 63,360 inches per mile:
distance per revolution = 75.4 in. / 63,360 in./mi = 0.00119 mi/rev
Now, we can calculate the number of revolutions as:
number of revolutions = 1 mi / 0.00119 mi/rev ≈ 840 revolutions
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Give 1 example of a binomial of degree 35, and a monomial of degree 100.
Answer:
For the binomial with a degree of 35 it would be 2x35+4
For the monomial with a degree of 100 would be 5y100
Step-by-step explanation:
what is 9 25/100 simplified?
Answer:
It is 9 1/4
Step-by-step explanation:
This is because 9 stays the same as the whole number, and 25 divided by 100 is 4. To check our work we can multiply 25 by 4 to get 100. Now we know we have the right answer.
"The beautiful part of learning is that no one can take it away from you" (:
a couple has two children. one is a son. what is the probability that the other child is a daughter?
Answer:
1/2 it’s like flipping a coin it can either come up heads or tails.
Step-by-step explanation:
The probability that the other child is a daughter is 1/2 or 50%.
The gender of each child is independent, and there are two equally likely outcomes for each child (male or female). Therefore, the probability of having a son is 1/2 and the probability of having a daughter is also 1/2. Since one child is already known to be a son, that does not affect the probability of the other child being a daughter. Thus, the probability of having a daughter as the other child is also 1/2 or 50%.
Therefore, the answer to the question is that the probability that the other child is a daughter is 1/2 or 50%
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if nevada has 4 elected members in congress (4 in the house of representatives and 2 senators), how many electoral votes does the state of nevada have in the electoral college?
The number of electoral votes does the state of nevada have in the electoral college is 6 electoral votes.
Nevada will be having a total of 6 electoral votes in the electoral college. The number of electoral votes for each state is equal to the total number of its members in Congress, which will be including its representatives in the House of Representatives and its two senators.
Therefore, since Nevada has 4 members in the House of Representatives and 2 senators, the state has a total of 6 members in Congress, and hence it can be concluded that a total of 6 electoral votes will be there in the Electoral College.
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helppp please, do all the tasks from a to b.
Thank u very much
the task is in the photo
a) 1) x=0 or x=-2 , 2) x=0 or x=2 3) x=0 or x=-2 4) x=0 or x=-2
b) 1) x=0 or x=-5/3 2)x=0 or x=5/3 3) x=0 or x=5/3 4) x=0 or x=-5/3 .this equations can be solved by factorization and simplification.
what is factorization?
Factorization is the process of expressing a given number or algebraic expression as a product of two or more factors. The factors are the numbers or expressions that when multiplied together result in the original number or expression.
In the given question,
a) x²+2x=0:
x(x+2)=0
x=0 or x=-2
x²-2x=0:
x(x-2)=0
x=0 or x=2
x²+2x=0:
x(x+2)=0
x=0 or x=-2
-x²-2x=0:
-x(x+2)=0
x=0 or x=-2
b)
3x²+5x=0:
x(3x+5)=0
x=0 or x=-5/3
3x²-5x=0:
x(3x-5)=0
x=0 or x=5/3
-3x²+5x=0:
x(-3x+5)=0
x=0 or x=5/3
-3x²-5x=0:
x(-3x-5)=0
x=0 or x=-5/3
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Given the function ƒ(x) = x^2 - 4x - 5
1. Identify the zeros using factorization.
2. Draw a graph of the function. Its vertex is at (2, -9).
Step-by-step explanation & Answer
f(x) = x² - 4x -5, factored is simply f(x) = (x - 5)(x + 1).
If you zero out f(x), namely 0=(x-5)(x+1), that simply gives you the zeros of 5 and -1.
Now, from ----- -1------0---------------------------------5,
Notice from -1 to 5, there are 6 units, and half of 6 is 3, so, the half-way is 3 units away from either zero.
We can get to the half-way point by -1 + 3, or 2, x = 2, that's where the vertex is at, but you already knew that, and of course the y-coordinate is at f(2) = (2)² - 4(2) - 5, which is -9, so the vertex is indeed at (2, -9).
Well, surely you can, simply use the zeros location, -1 and 5, and draw a bowl between them, with the bottom of the bowl at 2, -9.
PLEASE HELP ME!!
Marcus got a job through an employment agency that charges a fee equal to 35% of the first four weeks' pay. The job pays $545 per week. How much does Marcus have to pay the employment agency?
A)$190.75
B)$763
C)$2,180
D)$1,144.50
GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
Answer:
the area of the trapezoid is (3/2)x^2 + 2x square units.
Step-by-step explanation:
Let's use "x" to represent the height of the trapezoid. According to the problem, one base measures 5 feet more than the height, so we can use "x + 5" to represent the length of that base. The other base is one foot less than twice the height, so we can use "2x - 1" to represent the length of that base.
The area of a trapezoid is given by the formula:
Area = (1/2)(sum of the bases)(height)
Substituting the expressions for the bases and the height, we get:
Area = (1/2)(x + 5 + 2x - 1)(x)
Simplifying the expression inside the parentheses, we get:
Area = (1/2)(3x + 4)(x)
Expanding the expression, we get:
Area = (3/2)x^2 + 2x
the area of the trapezoid is (3/2)x^2 + 2x square units.
Which set of side lengths form a right triangle?
Responses
7 cm, 8 cm, 10 cm
7 cm, 8 cm, 10 cm
3 ft, 6 ft, 5 ft
3 ft, 6 ft, 5 ft
10 in., 41 in., 40 in.
10 in., 41 in., 40 in.
15 m, 20 m, 25 m
Answer:
Here is the correct answer:
15 m, 20 m, 25 m
what is 33=32x-31 i need help with this problem
Answer:
x=2
Step-by-step explanation:
33=32x-31
64=32x
2=x
Answer: [tex]x = 2[/tex]
what is called the 90 degree angle?
Answer:
right angles
Step-by-step explanation:
The distance from here to the beach at Little Boar’s Head is 10 miles. If you walked there at 4 mph and returned jogging at 8 mph, how much time would the round trip take? What would your overall average speed be?
Triangle PQR is a right triangle. P(-6,9) Q(-1,-1) R(-9,5) what is the area of triangle PQR
The area of triangle PQR is 25/2 * √(5).
Describe Triangle?In geometry, a triangle is a two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has many important properties and applications.
The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles sum to 360 degrees. The three sides of a triangle can be classified according to their lengths and their angles.
To find the area of triangle PQR, we can use the formula:
Area = (1/2) * base * height
where the base and height are the lengths of two sides of the right triangle that meet at a 90-degree angle.
We can use the distance formula to find the lengths of the sides of triangle PQR:
PQ = √[(x_Q - x_P)² + (y_Q - y_P)²] = √[(-1 - (-6))² + ((-1) - 9)²] = √[25 + 100] = 5√(5)
PR = √[(x_R - x_P)² + (y_R - y_P)²] = √[(-9 - (-6))² + (5 - 9)²] = √[9 + 16] = 5
QR = √[(x_R - x_Q)² + (y_R - y_Q)²] = √[(-9 - (-1))² + (5 - (-1))²] = √[64 + 36] = 2√20) = 4√(5)
Since triangle PQR is a right triangle, the base and height are PQ and PR, respectively. Therefore, the area of triangle PQR is:
Area = (1/2) * PQ * PR = (1/2) * 5√(5) * 5 = 25/2 * √(5)
So the area of triangle PQR is 25/2 * √(5).
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2
Ɔ
Question 9 Qn ID 10030368
Miko bought a laptop at $2675, inclusive of 7% GST.
How much is the price of the laptop without GST?
SA
Check Answer
< Previous Qn
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After answering the presented question, we can conclude that As a expression result, the laptop costs $2500 without GST.
what is expression ?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To get the laptop's price without GST, divide the inclusive price by (1 + GST rate as a decimal).
As a result, the laptop's price without GST can be estimated as follows:
Price excluding GST = Price including GST / (1 + GST rate as a decimal)
Price excluding GST = 2675 / (1 + 0.07)
Without GST, the price is $2500.
As a result, the laptop costs $2500 without GST.
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a
=
900
rounded to the nearest 10
b
=
90.7
rounded to 1 DP
Find the minimum of
axb
The minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. It is expressed as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The given values are:
A = 900 rounded to the nearest 10 = 900
B = 90.7 rounded to 1 decimal place = 90.7
We need to find the minimum value of AxB.
Multiplying A and B directly, we get:
AxB = 900 x 90.7 = 81,630
To find the minimum value of AxB, we can use the concept of AM-GM inequality which states that for two positive real numbers a and b, their arithmetic mean (AM) is greater than or equal to their geometric mean (GM):
AM ≥ GM
or
(a+b)/2 ≥ √(ab)
Applying this to our values of A and B, we get:
(A+B)/2 ≥ √(AxB)
Substituting the given values of A and B, we get:
(900 + 90.7)/2 ≥ √(AxB)
Simplifying this, we get:
495.35 ≥ √(AxB)
Squaring both sides, we get:
245,376.72 ≥ AxB
Therefore, the minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).
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Complete question:
A = 900 rounded to the nearest 10
b = 90.7 rounded to 1 DP
Find the minimum of a x b
Complete the equation so it has infinitely many solutions. 4(x-4)= 4x +
guys how do i do this
Answer: To have infinitely many solutions, the equation must simplify to a true statement, such as 0=0.
So, let's simplify the given equation:
4(x-4) = 4x + ?
We need to choose a value for the constant on the right-hand side so that the equation simplifies to a true statement.
We can start by distributing the 4 on the left-hand side:
4x - 16 = 4x + ?
Now we can see that the 4x terms cancel out, leaving:
-16 = ?
We can choose any value for the constant on the right-hand side, and the equation will be true. For example:
-16 = -16
So the complete equation with infinitely many solutions is:
4(x-4) = 4x - 16
Step-by-step explanation:
Factor completely 3x − 12.
a. 3(x − 4)
b. 3(x + 4)
c. 3x(−12)
d. Prime
Answer:
Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?
ask every tenth student she sees ac a concert
ask every fifth student entering her school in the morning
ask every third student she encounters at the mall
ask every student at a local movie theater
Step-by-step explanation:
What question can be answered by finding 10 divided by 2 11/20
The question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".
What is mixed number?A mixed number is a representation of both a whole integer and a legal fraction. In most cases, it denotes an integer that falls between any two whole numbers. Look at the illustration; it shows a fraction that is larger than 1 but less than 2 (see the given image). Therefore, it is a composite number.
The expression "10 divided by 2 11/20" can be simplified as a mixed number or fraction as follows:
10 divided by 2 11/20 = 10 ÷ (2 + 11/20)
= 10 ÷ (40/20 + 11/20)
= 10 ÷ (51/20)
= 10 × (20/51)
= 400/51
= 7 43/51 (in mixed number form)
Therefore, the question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".
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Reflect coordinate ( -12, 16) over the x-axis.
Answer:
(- 12, - 16 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
(- 12, 16 ) → (- 12, - 16 )