please answer the question attached brainliest to however answers first.
Step-by-step explanation:
number 2
number 3
number 6
number 7
Which equation can be solved to find one of the missing side lengths in the triangle?
Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.
cos(60o) = StartFraction 12 Over a EndFraction
cos(60o) = StartFraction 12 Over b EndFraction
cos(60o) = StartFraction b Over a EndFraction
cos(60o) = StartFraction a Over 12 EndFraction
Mark this and return
The fourth equation i.e. cos (60°) = [tex]\frac{a}{12}[/tex] can be used to find one of the missing side lengths in the triangle. This has been obtained using trigonometry.
What is trigonometry?
Trigonometry is a branch of mathematics that focuses on right-angled triangles, including their sides, angles, and connections.
We are given a right angled triangle with perpendicular as b, base as a and hypotenuse measuring 12 units.
We know by trigonometry that cos θ is the proportion of the adjacent side to the hypotenuse.
So, only the fourth equation is the one which can be used to find the missing length.
So, the equation is cos(60°) = [tex]\frac{a}{12}[/tex].
Hence, the fourth option is the correct answer.
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Harper uploaded a funny video of her dog onto a website.
The relationship between the elapsed time, ddd, in days, since the video was first uploaded, and the total number of views, V(d)V(d)V, left parenthesis, d, right parenthesis, that the video received is modeled by the following function.
V(d)=4^{{1.25d}}V(d)=4
1.25d
V, left parenthesis, d, right parenthesis, equals, 4, start superscript, 1, point, 25, d, end superscript
How many views will the video receive after 666 days?
After 666 days, the video will receive approximately 33,621,452 views.
We are given the function V(d) = 4^(1.25d), where d represents the number of days since the video was uploaded and V(d) represents the number of views the video has received at that time. To find the number of views the video will receive after 666 days, we need to evaluate V(666).
Plugging in d = 666 into the function, we get V(666) = 4^(1.25*666). Using a calculator, we can simplify this to V(666) ≈ 33,621,452. Therefore, after 666 days, the video will receive approximately 33,621,452 views.
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HELP FAST PLEASEEE
the M is a typo it’s supposed to be X
Answer:
x=7
Step-by-step explanation:
Because all the bases are the same you can ignore the 8's.
Instead solve for 15=x+8
in which you would subtract the 8 to the left side, and 15-8=7
Determine the values of a, b, and c in the following matrix equation.
4 a
[34]
30
52
[3
2 b5
1 8
LC
a.
b.
C.
54=
16.
The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8
Determining the values in the matrix equation.To determine the values of a, b, and c in the matrix equation:
4 a + 3 0 = 7 3
3 4 5 b c 5
By addition operation, we have
a + 0 = 3
3 + 5 = c
4 + b = 5
When the equations evaluated, we have
a = 3
c = 8
b = 1
The above are the values of a b and c
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Complete question
Determine the values of a, b, and c in the following matrix equation.
4 a + 3 0 = 7 3
3 4 5 b c 5
Find those values of x for which the given function is increasing and those values of x for which it is decreasing, y = 12x – x^3 • Increasing for x < 2, decreasing for x > 2 • Increasing for 4 4 • Increasing for X <-2.x > 2, decreasing for -2 2
The function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.
The given function is y = 12x – x^3. To determine when the function is increasing or decreasing, we need to take the derivative of the function with respect to x:
y' = 12 - 3x^2
To find where the function is increasing, we need to look for values of x where y' is positive. To find where the function is decreasing, we need to look for values of x where y' is negative.
So, y' > 0 when:
12 - 3x^2 > 0
3x^2 < 12
x^2 < 4
-2 < x < 2
Therefore, the function is increasing for x values less than -2, between -2 and 2, and greater than 2. Specifically:
• Increasing for x < -2
• Increasing for -2 < x < 2
• Increasing for x > 2
On the other hand, y' < 0 when:
12 - 3x^2 < 0
3x^2 > 12
x^2 > 4
x < -2 or x > 2
Therefore, the function is decreasing for x values between -2 and 2. Specifically:
• Decreasing for -2 < x < 2
Overall, we can summarize that the function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.
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The tangent plane to the surface with equation - in (9) +-3 at the point (z,y,z) - (2,1,9) has the equation ________.
The equation of the tangent plane to the surface with equation - in (9) +-3 at the point (2,1,9), first need to find the partial derivatives of the function with respect to x, y, and z. However, the surface equation provided seems to be incorrect or incomplete. Please provide the correct surface equation in the form f(x, y, z) = constant.
Let's call the function f(x, y, z) = - in (9) +-3.
∂f/∂x = 0 (since there is no x term in the function)
∂f/∂y = 0 (since there is no y term in the function)
∂f/∂z = -3/((z-9)^2)
Now we can use the formula for the equation of the tangent plane at a point (a,b,c) on a surface z=f(x,y):
z - f(a,b) = (∂f/∂x)(a,b)(x-a) + (∂f/∂y)(a,b)(y-b)
+ (∂f/∂z)(a,b)(z-c)
Plugging in the values we have, we get:
z - (- in (9) +-3)|_(2,1) = 0(x-2) + 0(y-1) - (3/((z-9)^2))|_(2,1,9)(z-9)
Simplifying:
z + in (9) - 3 = -3(z-9)
4z = 30
z = 7.5
So the equation of the tangent plane is:
z - (- in (9) +-3)|_(2,1) = (-3/((z-9)^2))|_(2,1,9)(z-9)
z - in (9) - 3 = -3(7.5-9)
z - in (9) - 3 = 4.5
z = 12.5
Therefore, the equation of the tangent plane to the surface with equation - in (9) +-3 at the point (2,1,9) is:
z - in (9) - 3 = -3/((z-9)^2)(z-9)
z - in (9) - 3 = -3(z-9)/(z-9)^2
z - in (9) - 3 = -3/(z-9)
z = 3/(z-9) + in (9) + 3
or
3x + 3y - 4z = -27 + in (9)
To find the equation of the tangent plane to the surface with equation ln(9) +- 3 at the point (x, y, z) = (2, 1, 9), follow these steps:
1. Determine the gradient vector of the given surface at the point (2, 1, 9).
2. Use the gradient vector as the normal vector of the tangent plane.
3. Write the equation of the tangent plane using the normal vector and the given point.
However, the surface equation provided seems to be incorrect or incomplete. Please provide the correct surface equation in the form f(x, y, z) = constant, so that I can help you find the equation of the tangent plane.
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Simplify −2r(−16r + 3r − 18). −26r2 − 36r 26r2 + 36 26r2 + 36r −26r2 + 36r
Answer:
26r^2 + 36r.
Step-by-step explanation:
3 3/4 converted from feet to yards
Answer: 1 1/4 yards
Step-by-step explanation: To convert from feet to yards, divide the value in feet by 3. So, 3 3/4 ft = (3 3/4)/3 = 1.25 yd (exactly).
Answer:
5/4 yards
Step-by-step explanation:
Convert feet to fraction.
[tex]3+\frac{3}{4} =\frac{(3)(4)+3}{4} =\frac{15}{4}[/tex] ft.
If we know that each yard equals 3 feet, divide by 3:
[tex]\frac{\frac{15}{4} }{3} =\frac{15}{(4)(3)} =\frac{15}{12}[/tex]
Simplified:
[tex]\frac{5}{4}[/tex] yards
Hope this helps.
Write a derivative formula for the function.
f(x) = (4 ln(x))ex
The derivative formula for the function is f'(x) = 4ex(1/x + ln(x)).
How to determined the function by differentiation?To find the derivative of the function f(x) = (4 ln(x))ex, we can use the product rule and the chain rule of differentiation.
Let g(x) = 4 ln(x) and h(x) = ex. Then, we have:
f(x) = g(x)h(x)
Using the product rule, we get:
f'(x) = g'(x)h(x) + g(x)h'(x)
Now, we need to find g'(x) and h'(x):
g'(x) = 4/x (since the derivative of ln(x) with respect to x is 1/x)
h'(x) = ex
Substituting these back into the formula for f'(x), we get:
f'(x) = (4/x)ex + 4 ln(x)ex
Simplifying this expression, we get:
f'(x) = 4ex(1/x + ln(x))
Therefore, the derivative formula for the function f(x) = (4 ln(x))ex is:
f'(x) = 4ex(1/x + ln(x)).
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it takes 17 seconds for a train to pass a 206-meter long bridge at normal speed. it takes 45 seconds for the same train to pass 170-meter long bridge at one-third of the normal speed. what is the length of the train in meters?
When a train takes 17 seconds to pass a 206-meter long bridge at normal speed. The length of train is equals to the 227.86 metres.
We have a train with a normal speed. With a normal speed, the length of long bridge covered by train in 17 seconds
= 206 meter
Let the length of train and normal speed of train be 'x meter' and 's m/sec ' respectively. As we know speed of an object ratio of covered distance to the time taken by object to covered the distance
=> s = (206 + x)/ 17 m/sec --(1)
In case second, the speed of same train which covered a length 170 m of bridge in 45 seconds = one-third of the normal speed
=> s/3 = (170 + x) /45 m/sec --(2)
We have to determine the length of train.
Using substitution, substitute value of s in equation(2) from equation (1) ,
=> (206+ x)/17 = (170 + x)/45
Cross multiplication
=> 45( 206 + x) = ( 170 + x) 17
=> 45 x - 17x = 45× 206 - 170 × 17
=> x = 227.86 m
Hence, required value is 227.86 m.
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Find the point on the line y = 8x - 5 closest to the point (0, – 6). The function giving the distance between the point and the line is S = ? (Enter a function of x)
The function giving the distance between the point (0,-6) and the line y = 8x - 5 is: S = 47 / sqrt(65).
To find the point on the line closest to the point (0,-6), we can find the perpendicular distance from the point (0,-6) to the line y = 8x - 5. The point on the line closest to (0,-6) will be the point on the line that is intersected by the perpendicular line.
The slope of the given line is 8, so the slope of any line perpendicular to it will be -1/8. Let (a,b) be the point on the line y = 8x - 5 that is closest to (0,-6). The equation of the line passing through (0,-6) with slope -1/8 is:
y + 6 = (-1/8)x
Simplifying this equation, we get:
y = (-1/8)x - 6
The point (a,b) will lie on both the given line and the perpendicular line. Therefore, we can substitute y = 8x - 5 in the equation y = (-1/8)x - 6 to obtain:
8x - 5 = (-1/8)x - 6
Solving for x, we get:
x = 37/65
Substituting x = 37/65 in y = 8x - 5, we get:
y = 231/65
Therefore, the point on the line y = 8x - 5 closest to the point (0,-6) is (37/65, 231/65).
The distance S between the point (0,-6) and the line y = 8x - 5 can be found by using the formula:
S = |ax + by + c| / sqrt(a^2 + b^2)
where a, b, and c are the coefficients of the general form of the line equation, which is ax + by + c = 0.
In this case, the equation of the line is y - 8x + 5 = 0. Therefore, a = -8, b = 1, and c = 5. Substituting these values in the formula for S, we get:
S = |(-8)(0) + (1)(-6) + 5| / sqrt((-8)^2 + 1^2)
= 47 / sqrt(65)
Therefore, the function giving the distance between the point (0,-6) and the line y = 8x - 5 is:
S = 47 / sqrt(65)
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Optimize: e-222-4xy-2y2 (1 point) Consider the optimization problem: Subject to 0x2 – 4xy + ly2 = 10 The method of Lagrange gives a system of three equations in three unknowns that you must solve to find the critical points. Write out those three equations (in any order). Use an l' in place of the usual .. =
To optimize the given function e - 222 - 4xy - 2y^2 subject to the constraint 0x^2 - 4xy + ly^2 = 10, we'll first set up the Lagrange function L(x, y, λ) as follows:
Langrange- L(x, y, λ) = e - 222 - 4xy - 2y^2 + λ(0x^2 - 4xy + ly^2 - 10)
Now, we'll get the partial derivatives of L with respect to x, y, and λ and set them equal to zero:
Step:1. ∂L/∂x = -4y - λ(-4y) = 0
Step:2. ∂L/∂y = -4x - 4y - 2λy = 0
Step:3. ∂L/∂λ = 0x^2 - 4xy + ly^2 - 10 = 0
These three equations represent the system of equations we need to solve to find the critical points. To reiterate, the equations are:
1. -4y + 4yλ = 0
2. -4x - 4y - 2λy = 0
3. -4xy + ly^2 - 10 = 0
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Choose all the expressions that are equal to 45×67 4 5 × 6 7. A. 2435 24 35 B. 4×75×6 4 × 7 5 × 6 C. 4×56×7 4 × 5 6 × 7 D. 6×54×7 6 × 5 4 × 7 E. 6×45×7 6 × 4 5 × 7
None of the given expressions (A, B, C, D, E) are equal to 45 x 67.
How to find which expressions are equal to multiplication?To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.
Starting with option A, 24 x 35, this is not equal to 45 x 67.Moving on to option B, we have 4 x 75 x 6. Simplifying this, we get 1,800, which is not equal to 45 x 67.Option C is 4 x 56 x 7, which simplifies to 1,568, not equal to 45 x 67.Option D is 6 x 54 x 7, which simplifies to 2,268, not equal to 45 x 67.Finally, option E is 6 x 45 x 7, which simplifies to 1,890, also not equal to 45 x 67.Therefore, none of the expressions are equal to 45 x 67.
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On the curve y = x3, point p has the coordinates (2, 8). what is the slope of the curve at point p?
The slope of the curve y = x^3 at point P(2, 8) is 12.
To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.
Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.
Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.
Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.
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Brian has two rectangular sheets of paper.
The length of the larger sheet is 12 times the length of the
smaller sheet.
The width of the larger sheet is 15 times the width of the
smaller sheet.
By what factor is the area of the larger sheet greater than the area of the
smaller sheet?
The area of the larger sheet is 180 times greater than the area of the smaller sheet.
How to find the area of sheets?To determine which sheet has a larger area, Let's assume that the length of the smaller sheet of paper is l and the width of the smaller sheet is w. Then, we can express the dimensions of the larger sheet in terms of l and w as follows:
Length of larger sheet = 12l
Width of larger sheet = 15w
The area of the smaller sheet can be calculated as:
Area of smaller sheet = length × width = lw
Similarly, the area of the larger sheet can be calculated as:
Area of larger sheet = length × width = (12l) × (15w) = 180lw
To find the factor by which the area of the larger sheet is greater than the area of the smaller sheet, we can divide the area of the larger sheet by the area of the smaller sheet:
Factor = Area of larger sheet / Area of smaller sheet
Factor = (180lw) / (lw)
Simplifying the expression, we get:
Factor = 180
Therefore, the area of the larger sheet is 180 times greater than the area of the smaller sheet.
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The product of 5 & 10 is equal to a third of a number
Write as an equation and solve.
The equation that represents the statement is
50 = x/3 and x is 150
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Word problem are brain teaser that allows people to think properly. The first step is to represent the unknown by a letter.
Representing the number by x
therefore:
The product of 5 and 10 is 5 × 10
5 × 10 = 1/3 × x
50 = x/3
therefore the equation is 50 = x/3 and the value of x is 150.
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Consider the diagram shown. The sphere and cylinder have the same diameter. The height of the
cylinder is equal to the diameter of the sphere.
Find the approximate volume of the sphere by using 3.14 for 7. Round to the nearest tenth
of a cubic unit.
8.4
8.4
Answer:
310.2 cubic units
Step-by-step explanation:
since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]
The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]
Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2
Ayuda doy corona porfavor porfavor!!!!!!!
INVENTEN UN PROBLEMA QUE PUEDA RESOLVERSE CON EL CALCULO A) Y OTRO QUE SE PUEDA RESOLVERSE CON EL CALCULO B)
a) 45 x 2 + 150 x 4 x 3 b) ( 45 x 2 + 150 x 4) x 3
Lo siento, pero los problemas que ha proporcionado no están relacionados con el cálculo. El problema a) es simplemente una operación de multiplicación y suma, y el problema b) es una operación de multiplicación y suma agrupada. Para crear un problema que pueda resolverse con cálculo, podría plantear algo como:
a) ¿Cuál es la tasa de cambio de la función f(x) = x^2 en el punto x = 3?
b) ¿Cuál es el valor máximo de la función g(x) = 3x^2 - 12x + 5 en el intervalo [0, 4]?
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Fill in the blank: Some of the most common symbols used in formulas include (addition), - (subtraction), * (multiplication), and / (division). These are called _____
The basic arithmetic operators (+,-,*,/) are commonly used in formulas to perform mathematical calculations. They are collectively known as "operators" and are an essential component of mathematical formulas, allowing us to perform complex calculations quickly and efficiently.
The symbols mentioned in the question, i.e., (+,-,*,/) are the basic arithmetic operators that are used in mathematical formulas to perform different types of calculations. These symbols are collectively referred to as "operators" or "mathematical operators."
Operators are an essential part of mathematical formulas as they allow us to perform complex mathematical calculations in a concise and efficient manner. They act as a shorthand way of representing mathematical operations and make it easier to perform calculations without having to write out the entire equation every time.
In addition to the basic arithmetic operators mentioned above, there are other types of operators that can be used in formulas depending on the specific mathematical operation being performed. For example, there are logical operators like AND, OR, and NOT that are used in Boolean algebra to perform logical calculations.
Other operators that can be used in formulas include exponentiation (^), which is used to raise a number to a certain power, and modulo (%), which is used to find the remainder when one number is divided by another.
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You spin the spinner once. 6, 7, 8,9 what’s the p(prime?
The probability of getting a prime number on the spinner is 2/4 or 1/2.
There are four possible outcomes on the spinner: 6, 7, 8, and 9. To determine the probability of getting a prime number, we need to first identify which of these numbers are prime. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves without leaving a remainder.
Out of the four possible outcomes, only two of them are prime: 7 and 9. Therefore, the probability of getting a prime number is the number of favorable outcomes (2) divided by the total number of possible outcomes (4), which simplifies to 1/2.
To see why this is true, we can think of the probability as a fraction where the numerator is the number of ways to get a prime number and the denominator is the total number of possible outcomes. In this case, there are two ways to get a prime number (7 and 9), and four possible outcomes (6, 7, 8, and 9). Therefore, the probability r is 2/4 or 1/2.
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The box plot represents the miles Emilia ran after school for 21 days.
3
4
5
9
10
6 7
8
Miles Run
Part B
Can you use the box plot to find the IQR? Explain.
This value will represent the range within which the middle 50% of Emilia's daily miles are distributed
Hi! The box plot represents the miles Emilia ran after school for 21 days. To find the IQR (Interquartile Range), you can use the box plot by identifying the values of the first quartile (Q1) and the third quartile (Q3).
The IQR is calculated by subtracting Q1 from Q3 (IQR = Q3 - Q1). By examining the box plot, locate Q1 and Q3 on the plot, and perform the subtraction to find the IQR.
This value will represent the range within which the middle 50% of Emilia's daily miles are distributed.
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A rectangular prism has a square
base with edge length (x + 1). Its
volume is (x + 1)2(x – 3). What
does the expression (x + 1)(x – 3)
represent?
area of the base
area of one side
height of the prism
surface area of the prism
The expression (x + 1)(x - 3) represents the Area of base of the prism.
What is Prism?a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.
According to question:The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).
We can find the height of the prism by dividing the volume by the area of the base:
B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)
Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.
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Already Know The Vertex but need help on the opens and axis of symmetry
Answer: x = -3
Step-by-step explanation:
Hope this helps.
What's 2x = 20 if 4y = 80
Answer:
x=10 and y=20, 2x=20=y
Step-by-step explanation:
2x=20 | Divide by 2 on both sides
x=10
4y=80 | Divide by 4 on both sides
y=20
Answer: 40
80 ÷ 2 = 20, so x = 40.
To check your answer;
40 x 2 = 80
A random sample of small business stock prices has a sample mean of x¯=$54. 82 and sample standard deviation of s=$8. 95. Use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81. 67. Round your answer to the nearest hundredth
Using the Empirical Rule. The percentage of small business stock prices that are more than $81. 67 is 0.30%
To use the Empirical Rule, we need to assume that the distribution of small business stock prices is approximately normal.
First, we need to find the z-score for $81.67:
z = (81.67 - 54.82) / 8.95 = 2.99
Next, we can use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81.67:
About 99.7% of the data falls within 3 standard deviations of the mean.
Therefore, about 0.3% of the data falls more than 3 standard deviations above the mean.
Since $81.67 is more than 3 standard deviations above the mean, we can estimate that the percentage of small business stock prices that are more than $81.67 is about 0.3%.
Rounded to the nearest hundredth, the estimated percentage is 0.30%.
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A skier can purchase a daily or season pass.
The daily pass costs $48 per day and included
the price of ski rentals. The season pass costs
$190 plus a daily fee of $10 to rent the skis.
How many days would a skier have to go skiing
in order for both options to cost the same?
A.
5 days
C. 240 days
D. 10 days
B.
3 days
We know that the skier would have to go skiing for 5 days in order for both options to cost the same.
To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.
For the daily pass option:
Total cost = $48 x d
For the season pass option:
Total cost = $190 + ($10 x d)
Now we can set up the equation:
$48 x d = $190 + ($10 x d)
Simplifying this equation, we get:
$38 x d = $190
Solving for "d", we get:
d = 5
Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.
So the answer is A. 5 days.
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The volume of this cone is 339. 12 cubic feet. What is the height of the cone?
Answer:
Not enough info
Step-by-step explanation:
Volume of cone formula is: V = 1/3 π r²h
You did not give the radius so it is not possible to find the solution
If radius is given, isolate h by dividing the V by 1/3 π r²
Then simplify the left side of the equation and that is what h is
Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.
To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:
1/4 x 1/4 = 1/16
This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.
Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:
(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)
(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69
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A line passes through the points (–
3,–
18) and (3,18). Write its equation in slope-intercept form
The equation of the line with given coordinates in slope intercept form is given by y = 6x.
Use the slope-intercept form of the equation of a line,
y = mx + b,
where m is the slope of the line
And b is the y-intercept.
The slope of the line is equals to,
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.
Using the coordinates (-3, -18) and (3, 18), we get,
⇒m = (18 - (-18)) / (3 - (-3))
⇒m = 36 / 6
⇒m = 6
So the slope of the line is 6.
Now we can use the slope-intercept form of the equation of a line .
Substitute in the slope and one of the points, say (-3, -18) to get the y-intercept,
y = mx + b
⇒ -18 = 6(-3) + b
⇒ -18 = -18 + b
⇒ b = 0
So the y-intercept is 0.
Putting it all together, the equation of the line in slope-intercept form is,
y = 6x + 0
⇒ y = 6x
Therefore, the slope intercept form of the line is equal to y = 6x.
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