The next step in the construction of a regular hexagon is A. Use a compass and straightedge to continue drawing an equilateral
A circle with the required radius must first be drawn in order to make a regular hexagon. Draw a second circle whose centre is one of the spots on the first circle using the same radius. These two circles' intersection points will form the vertices of an equilateral triangle. Three of these equilateral triangles, with their vertices on the circle, must be drawn inside a circle. At the circle's centre, these three triangles will have a common vertex.
Drawing three more equilateral triangles, each of which shares a side with one of the previously drawn triangles, is necessary to finish the building of a regular hexagon. Drawing equilateral triangles keeps on until there are six of them, each of which has a side in common with a preceding triangle.
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Please help here is screenshot!! QUCIK! Algbera
Answer:
Right three
Step-by-step explanation:
Because the translation is applied inside the parentheses, we are shifting the function left/right. To determine whether it is shifted left or right, note that shifting right will have a negative number and shifting left will have a positive number. Since we have a negative number -3, it is shifted right.
Answer:
Step-by-step explanation:
Here if we put [tex]x=3[/tex] then then equation will give 0. Hence it will shift right side three unit .
Final answer: right 3
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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If ✓(x+iy) =a+ib, then find ✓(x-iy) and x^2+y^2.
The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² = (a + ib)²(a - ib)²
Calculating the complex expressionsFrom the question, we have the following parameters that can be used in our computation:
✓(x + iy) = a + ib
Changing the signs, we have
✓(x - iy) = a - ib
Multiply both expressions
This gives
✓(x + iy) * ✓(x - iy) = (a + ib)(a - ib)
Square both sides
So, we have
(x + iy) * (x - iy) = (a + ib)²(a - ib)²
This gives
x² + y² = (a + ib)²(a - ib)²
Hence, the values of ✓(x - iy) is a - ib and x² + y² is (a + ib)²(a - ib)²
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A bag contains 2 red marbles, 4 white marbles, and 8 blue marbles. You pick a marble without looking. Find the probability of drawing a white marble.
Answer:
28.57% chance
Step-by-step explanation:
add them all up which is 14, and if there are 4 white marbles that means its 4/14, which is 28.57 as a percent (2:7 as ratio)
factoring
ax²+bx+c
after factoring
out a moromial
The presence of the coefficient "a" in ax^2 + bx + c requires that we look for numbers that have a product of ac
Here we have to determine the difference
From the question, we have the following parameters that can be used in our computation:
ax^2 + bx +c and x^2 + bx +c
The presence of the coefficient "a" in the first expression makes a difference in the factoring process.
When factoring x^2 + bx + c, we are looking for two numbers that multiply to give c and add up to b.
For ax^2 + bx +c , we look for the product of ac and sum of b
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Help me pls because I need for tomorrow
Answer:
Step-by-step explanation:
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
D(1,-3,1)
y'' + 2y' - y = x.exp(x)
The solution of the differential equation y'' + 2y' - y = xe is found to be [tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]
To solve the differential equation y'' + 2y' - y = xeˣ, we first find the complementary solution by solving the characteristic equation,
r² + 2r - 1 = 0
Using the quadratic formula, we get,
r = (-2 ± √(2² + 4(1)(1))) / 2
r = (-2 ± √6) / 2
So the roots are,
r₁ = -1 - √6/2
r₂ = -1 + √6/2
Therefore, the complementary solution is:
[tex]y_c = Ce^{r_{1}t} + C'e^{r_{2}t}\\y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t}[/tex]
To find the particular solution, we use the method of undetermined coefficients. We assume a particular solution of the form,
y_p = Ax²eˣ + Bxeˣ + Ceˣ
Taking the first and second derivatives, we get,
y'_p = (2Ax + B + A)x eˣ + Beˣ + Ceˣ
y''_p = (4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ
Substituting these expressions into the differential equation, we get,
(4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ + 2[(2Ax + B + A)x eˣ + Beˣ + Ceˣ] - (Ax²eˣ + Bxeˣ + Ceˣ) = xeˣ
Simplifying, we get,
(3Ax² + 4Ax + B)x eˣ = xeˣ
Equating coefficients, we get,
3A = 1
4A + B = 0
Solving for A and B, we get,
A = 1/3
B = -4/3
Substituting these values into the assumed particular solution, we get,
y_p = (1/3)x²eˣ - (4/3)xeˣ + Ceˣ
Taking the first and second derivatives, we get,
y'_p = (2/3)x eˣ - 4/3eˣ + Ceˣ
y''_p = (2/3)eˣ + Ceˣ
Substituting the particular solution and its derivatives into the differential equation and simplifying, We get,
(2/3)xeˣ = xeˣ
This equation is true for all x, so there is no restriction on C. Therefore, the general solution is,
y = y_c + y_p
[tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]
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Complete question - y'' + 2y' - y = xeˣ solve the differential equation.
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1. The product of the matrix MG would be [tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36\\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]
2. The values of k₁ = -9; k₂ = -9; t₁ = 0; t₂ = -1
How do we solve for the Matrix product of MG?
The values of the matrix M and G are;
M = [1, 4, 5; G = [2, k₁, -19;
t₁, 3, -1; 1, -4, k₂;
1, t₂, 1] -1, 5, 11]
The product MG will be row 1
1×2 + 4×1 + 5×-1 1k₁+4×-4+ 5×5 1×-19+4k₂+5×11 ⇒1 k₁+9 4k₂+36
Row 2
t₁×2+3×1+-1×-1 t₁k₁+3×-4+-1×5 t₁×-19+3k₂+-1×11 ⇒ 2t₁ k₁t₁-17 3k₂-19t₁-11
Row 3
1×2+t₂×1+1×-1 1k₁+t₂×-4+-1×5 1×-19+t₂k₂+1×11 ⇒ t₂+1 k₁-4t₂+5 k₂t₂-8
Therefore MG =
1 k₁+9 4k₂+36
2t₁ k₁t₁-17 3k₂-19t₁-11
t₂+1 k₁-4t₂+5 k₂t₂-8
G = M⁻¹ should be an identity matrix which looks like
IM = [ 1 0 0
0 1 0
0 0 1 ]
MG and I to find the values of t₁, t₂, k₁, and k₂:
1 = 1, k₁+9 = 0, 4k₂+36 = 0
2t₁ = 0 k₁t₁-17 = 1 3k₂-19t₁-11 = 0
t₂+1 = 0 k₁-4t₂+5 = 0 k₂t₂-8 = 1
k₁+9 = 0 ⇒k₁ = -9
4k₂+36 = 0 ⇒ k₂ = -9
2t₁ = 0 ⇒ t₁ = 0
t₂+1 = 0 ⇒ t₂ = -1
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9
Look at the functions f (x) and g(x):
ƒ (x) = x²
g(x) = 2² +3
Which transformation of f (x) makes f(x) < g(x)?
The value of transformation of f (x) makes f(x) < g(x) is,
⇒ shifts the function 3 units upward.
We know that;
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, We have;
Functions are,
f (x) = x²
g(x) = x² +3
Hence, The value of transformation of f (x) makes f(x) < g(x) is,
⇒ shifts the function 3 units upward.
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The points A, B and C are the vertices of a triangle. The coordinates of the
points are A(5,3), B(5,6) and C(x,3). Find two values for x so the points
form a right triangle.
The two values for x so the points form a right triangle are x = -4 and x = 10
Finding two values for x so the points form a right triangle.From the question, we have the following parameters that can be used in our computation:
The coordinates of the points are A(5,3), B(5,6) and C(x,3).
The third point is given as
C(x,3)
The value of x can be any real value apart from 5
This is because if x = 5, then it would be the same as point A
So, we can use the following values for x
x = -4 and x = 10
Note that all real values work for x
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Someone please help and show work
Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.
11+13+14+16+17+18+20+20+21+24+25+29 = 228
There are 12 numbers, so divide by 12.
228/12 = 19. The mean is 19.
Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.
(Side note: yes, median and mean can be the same.)
Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.
Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.
HELP ASAP PLEASE! Mrs. Smith has 6 activity tables she wants to place side by side in her classroom.
(a) In how many ways can she arrange all 6 tables? Show your work.
(b) If she only wants to have 4 of the tables set up, in how many ways can she choose the tables she wishes to have set up? Show your work.
The total number of ways to arrange all 6 tables is 720
There are 15 ways to choose 4 tables out of 6.
(a) There are 6 options for the first table, 5 options left for the second table, 4 options left for the third table, and so on.
Therefore, the total number of ways to arrange all 6 tables is:
6 x 5 x 4 x 3 x 2 x 1 = 720
(b) To choose 4 tables out of 6, we can use the combination formula:
C(6,4) = 6! / (4! x 2!)
= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)
= 15
Therefore, there are 15 ways to choose 4 tables out of 6.
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A random sample of 250 students from ASU with a total population of 7,500 students is surveyed about their college majors. In the sample, 75 students said that they are majoring in Art. Based on these results, predict how many students in the total population are Art majors
We can predict that there are approximately 2,250 Art majors in the total population of 7,500 students at ASU based on the sample data.
We have,
We can use the formula for estimating population proportion:
Population proportion = sample proportion x population size
where the sample proportion is the fraction of students in the sample who are Art majors, and the population size is the total number of students in the population.
From the sample of 250 students, 75 said that they are majoring in Art, so the sample proportion of Art majors.
sample proportion = 75/250 = 0.3
The population size is 7,500 students.
Using the formula above, we can estimate the number of Art majors in the total population:
population proportion = sample proportion x population size
population proportion = 0.3 x 7,500
population proportion = 2,250
Therefore,
We can predict that there are approximately 2,250 Art majors in the total population of 7,500 ASU students based on the sample of 250 students surveyed.
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a farmer has two types of milk, one that is 28% butterfat and another that is 16% butterfat. how many gallons of each should be combined to create a 60-gallon mixture that is 22.5% butterfat?
30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.
Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,
⇒ x + y = 60 ⇒ x = 60 - y ----(1),
Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,
⇒ 28% of x + 16% of y = 22% of 60
⇒ 0.28x + 0.16y = 0.22 × 60
⇒ 0.28x + 0.16y = 13.2
⇒ 28x + 16y = 1320
⇒ 14x + 8y = 660
From equation (1),
14(60-y) + 8y = 660
840 - 14y + 8y = 660
6y = 180
y = 30
Again from equation (1),
x = 60 - y
= 60 - 30
= 30
Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%
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FInd the value of x such that l ⊥ m.
A) 46
B) 48
C) 16
D) 10.7
Answer:
C) 16
Step-by-step explanation:
(3x + 5) + 37 = 90
3x = 90 - 5 - 37
3x = 48
x = 48/3 = 16
Answer:
x = 16°
Step-by-step explanation:
It is 90° angle so their sum must be 90°( complement) .
3x + 5° + 37° = 90°
3x + 42° = 90° ... simplify the like term
3x = 90° - 42°
3x = 48°
3x/3 = 48°/3
x = 16°
So the answer is C, 16
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Answer:
Part a)
[tex]MG = \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]
Part b)
[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]
Step-by-step explanation:
a) Computing MG
We have
[tex]M = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}[/tex]
[tex]G = \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]
[tex]MG = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}\times \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]
[tex]= \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]
I am using a matrix calculator to compute the product rather than going through the rather cumbersome multiplication exercise by hand
Essentially we multiply each row of M by each row of G and simplify
b) One property of matrices is that if M is a matrix and M⁻¹ is its inverse
M x M⁻¹ is the identity matrix which has a 1 along the primary diagonal (top left - bottom right) and zeros everywhere
Here we are given G = M⁻¹ so M x G is an identity matrix
For a 3 x 3 matrix, the identity matrix is of the form[tex]MG(1, 2) \\= k_1 + 9 = 0\\= > k_1 = -9\\\\MG(1, 3)\; is\\ 4k_2 + 36 = 0\\k_2 = -36/4 = -9\\\\MG(2, 1) = 2t_1 + 4 = 0\\\implies t_1 = -4/2 = -2\\\\MG(3, 1) = t_2 + 1\\t_2 + 1 = 0\\t_2 = -1\\[/tex]
So the values of the variables are
[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]
To check if these are correct, you can plug in these values into the product matrix MG. You will see that all elements except the diagonal elements are 0; diagonal elements are 1
m < B = 32°, m < C = 38° and a = 22. Find the length of b
Using the law of sines, the length of b, to the nearest tenth, is: 21.4.
What is the Law of Sines?The Law of Sines is a mathematical equation that relates the lengths of the sides of a triangle to the sines of its angles. It states that for any triangle with sides of length a, b, and c and angles A, B, and C (where C is the largest angle), the following relationship holds:
[tex]\sf \dfrac{a}{sin(A)}= \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]
This equation allows you to solve for the unknown sides or angles of a triangle if you know the lengths of its sides and the measure of at least one of its angles. It is often used in geometry and trigonometry to find the unknown parts of a triangle when you have limited information about it.
Given that triangle ABC has the following measures:
[tex]\sf m\angle B = 32^\circ[/tex]
[tex]\sf m\angle C = 38^\circ[/tex]
[tex]\sf a = 22[/tex]
[tex]\sf m\angle A = 180 - 32 - 38 = 110^\circ \ \ [triangle \ sum \ theorem][/tex]
Applying the law of sines, we have:
[tex]\sf \dfrac{38}{sin \ 110} =\dfrac{b}{sin \ 32}[/tex]
Cross multiply:
[tex]\sf (sin \ 110)(b) = (sin \ 32)(38)[/tex]
[tex]\sf b = \dfrac{(sin \ 32 \times38)}{(sin \ 110)}[/tex]
[tex]\sf b = 21.4 \ \ (nearest \ tenth)[/tex].
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Use the function f(x) = 2x2 − 5x + 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
The quadratic function f(x) = 2x² - 5x + 3, it is found :
a. The factored function is, f(x) = 2(x - 1)(x - 1.5).
b. The x-intercepts of the function are: x = 1, x = 1.5.
c. The end behavior of the graph is:
As x -> -∞, f(x) -> -∞.
As x -> ∞, f(x) -> ∞.
The quadratic function is :
f(x) = 2x² - 5x + 3.
Hence the coefficients are:
a = 2, b = -5, c = 3.
Using a calculator with these coefficients, the x-intercepts are:
x = 1.
x = 1.5.
Then the factored form of the function;
f(x) = 2(x - 1)(x - 1.5).
Let the leading coefficient of 2 and the x-intercepts.
This is a concave-up parabola, it goes to positive infinity to the left and to the right of the graph.
Hence the end behavior is;
As x -> -∞, f(x) -> -∞.
As x -> ∞, f(x) -> ∞.
To determine the graph, the axis of symmetry is:
x = -b/2a = 5/(2(2)) = 1.25.
The y-coordinate at this point, that is the turning point of the function, is:
f(1.25) = 2(1.25)² - 5(1.25) + 3 = -0.125.
The y-intercept of the function
f(0) = 2(0)² - 5(0) + 3 = 3.
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Guys I’m in 7th grade taking pre ap class for math so for STAAR I’m taking 8th grade math do you guys have any tips? Any Advice for me too remember everything?
Anything would help my test is on Wednesday
To memorize knowledge there are several tips that can help us. Some are: Repeat some knowledge from time to time to memorize them.
How to memorize knowledge?To memorize knowledge there are several methods that can be useful when we need to learn something difficult. In this case, we must use some methods that can help us such as:
Practice Spaced Repetition: Spaced repetition is a memorization technique that involves repeating information at specific intervals.Create associations: Try to associate the information you are trying to memorize with something you already know.Use visualization: Visualization is a technique that consists of creating mental images of the information that you are trying to memorize.Learn more about memorization in: https://brainly.com/question/762011
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solev the following equation
a, 2m+8=15
b 10x-3=45
form equation and solve them
a}Ashley thinks of a number if i double my number and add 6 the anser is 40
Answer:
2m=7. m=7/2. 10x =48. x = 4.8
Step-by-step explanation:
2m
Answer:
a) 7/2 or 3.5
b) 4.8
form equation and solve them
a}n = 17
Step-by-step explanation:
a) 2m + 8 = 15
Subtract 8 from both sides: 2m + 8 - 8 = 15 - 8
Simplify: 2m = 7
Divide both sides by 2: (2m)/2 = 7/2
Simplify: m = 7/2 or 3.5
b) 10x - 3 = 45
Add 3 to both sides: 10x - 3 + 3 = 45 + 3
Simplify: 10x = 48
Divide both sides by 10: (10x)/10 = 48/10
Simplify: x = 4.8
To form and solve an equation for Ashley’s problem, we need to translate the words into mathematical expressions. Here are the steps and solution:
a) Ashley thinks of a number if i double my number and add 6 the answer is 40
Let n be Ashley’s number.
If we double the number, we get 2n.
If we add 6 to the doubled number, we get 2n + 6.
The answer is equal to 40, so we can write an equation: 2n + 6 = 40
To solve for n, we need to isolate it on one side of the equation by using inverse operations.
Subtract 6 from both sides: 2n + 6 - 6 = 40 - 6
Simplify: 2n = 34
Divide both sides by 2: (2n)/2 = 34/2
Simplify: n = 17
Please help me with this question
The results of each iteration are given as follows:
[tex]x_2 = 4.359[/tex][tex]x_3 = 5.466[/tex][tex]x_4 = 6.233[/tex]How to solve the iterative formula?The iterative formula in the context of this problem is defined as follows:
[tex]x_{n + 1} = \sqrt{8x_n - 5}[/tex]
The first value is given as follows:
[tex]x_1 = 3[/tex]
Hence each value is obtained applying the previous value to the iterative formula.
The second value is given as follows:
[tex]x_2 = \sqrt{8 \times 3 - 5}[/tex]
[tex]x_2 = \sqrt{19}[/tex]
[tex]x_2 = 4.359[/tex]
The third value is then given as follows:
[tex]x_3 = \sqrt{8 \times 4.359 - 5}[/tex]
[tex]x_3 = \sqrt{29.872}[/tex]
[tex]x_3 = 5.466[/tex]
The fourth value is then given as follows:
[tex]x_4 = \sqrt{8 \times 5.466 - 5}[/tex]
[tex]x_4 = \sqrt{38.728}[/tex]
[tex]x_4 = 6.233[/tex]
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a software developers current annual gross wage is 93400 for retirement the developer wants to have enough saved to live off 80% of the current annual gross wage and draw 4% the first year. what is the total amount the developer will need
What is the surface area of the image below I’ll give b brainliest
Answer:
50(5π + 6) cm²
Step-by-step explanation:
TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle
= 1/2 of 2πr(h+r) + 20*15
= πr(h+r) + 300
= 10π(15+10) + 300
= 250π + 300 cm²
or 50(5π + 6) cm²
Emily is spending money at a constant rate. Suppose she initially has $1100, and after 5 months, she has $800.
Which of these expresses the rate at which Emily's amount of money is changing?
________________________________
= 1,100 - 800= 300= 300 ÷ 5= $60Emily Is Spending $60 a Month________________________________
2/5(10x-15)>10 solve
The solution set of the inequality (2/5)*(10x - 15) ≥ 10 is:
[4, ∞)
How to solve the inequality?Here we want to solve the inequality:
(2/5)*(10x - 15) ≥ 10
To solve this we need to isolate the variable x, to do so, we can start multiplying both sides by 5/2
(10x - 15) ≥ 10*(5/2)
10x - 15 ≥ 25
Now add 15 in both sides:
10x ≥ 25 + 15
Now divide both sides by 10.
x ≥ 40/10
x ≥ 4
So the solution set is the set of all real numbers equal or larger than 4.
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The probability that a student guesses the correct answer to a four-choice multiple choice question is P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 68 four-choice multiple choice questions?
We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.
Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.
We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).
The expected value of a binomial distribution is given by the formula:
E(X) = n * p
So, in this case, the expected number of correct answers that a student should guess on the test is:
E(X) = 68 * 0.25 = 17
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In the figure, m<1= (3x+12)°, m<2= (3x+18)° and m<3= (7x+10)°. What is m<3?
The m<3 is approximately equal to 85.39 degrees.
The sum of the measures of the angles of a triangle is 180 degrees. So, we have:
m<1 + m<2 + m<3 = 180
So, (3x + 12) + (3x + 18) + (7x + 10) = 180
Simplifying and solving for x, we get:
13x + 40 = 180
13x = 140
x = 10.77
Now, we can find m<3 by substituting x in the expression for m<3:
m<3 = 7x + 10
m<3 = 7(10.77) + 10
m<3 = 85.39
Therefore, m<3 is approximately equal to 85.39 degrees.
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STORAGE A cylindrical tank is placed along a wall.
A cylindrical PVC pipe will be hidden in the corner
behind the tank. See the side view diagram below.
The radius of the tank is r inches and the radius of the
PVC pipe is s inches.
Wall-
Pipe
Tank
Floor
a. Use the Pythagorean Theorem to write an equation
for the relationship between the two radii. Simplify
your equation so that there is a zero on one side of
the equals sign.
Step-by-step explanation:
In the side view diagram, we can see that the tank, the wall, and the floor form a right triangle with the radius of the tank as the hypotenuse. Let x be the distance between the tank and the wall, as shown below:
```
|\
| \
r | \ x
| \
|_ _\
s
```
Using the Pythagorean theorem, we can write:
r^2 = x^2 + s^2
Rearranging this equation, we get:
x^2 = r^2 - s^2
Subtracting r^2 from both sides, we get:
x^2 - r^2 = -s^2
Multiplying both sides by -1, we get:
s^2 - x^2 = 0
Therefore, the equation for the relationship between the two radii is:
s^2 - x^2 = 0
Simplifying this equation, we get:
s^2 = x^2
or
x^2 = s^2
So, there is a zero on one side of the equals sign.
Help me please, I’m very confused on what to do
Just add the powers while it is multiply
-1+(-3)
= -1 - 3
= -4
So it is [tex]2^{-4}[/tex]
Can you help me solve this question?
The surface area of the box increases by 67.26 cm² when the height is increased by 0.7 cm.
Understanding Rectangular PrismRecall the formula, Surface Area (SA) of the rectangular prism is given as:
SA = 2lw + 2lh + 2wh
where
l = length,
w = width,
h = height
From the diagram, we know that:
l = 18cm
w = 6.3cm
h = 30cm
Substituting these values into the surface area formula, we get:
SA₁ = 2(18)(6.3) + 2(18)(30) + 2(6.3)(30) = 2376 cm²
When the height is increased by 0.7cm, the new height becomes:
h' = h + 0.7cm = 30.7cm
The new surface area can be calculated using the same formula:
SA₂ = 2(18)(6.3) + 2(18)(30.7) + 2(6.3)(30.7) = 2443.26 cm²
The increase in surface area is the difference between the new surface area and the original surface area:
SA₂ - SA₁ = 2443.26 cm² - 2376 cm²
= 67.26 cm²
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