Final answer:
By setting up a linear equation, it is determined that Charlie is 13 years old based on the given information that his father is two years more than three times Charlie's age and is 41 years old.
Explanation:
The problem presented is a classic example of a linear equation in the subject of mathematics. We are given that Charlie's father is 41 years old, and his age is two years more than three times Charlie's age.
To determine Charlie's age, we can set up the equation as follows: Let x represent Charlie's age. The father's age is then described by the expression 3x + 2.
Since we know the father is 41 years old, we have:
3x + 2 = 41
Subtract 2 from both sides of the equation to isolate the terms with x:
3x = 39
Now, divide both sides by 3 to solve for x:
x = 39 / 3
x = 13
Therefore, Charlie is 13 years old.
1 mile is equal to 5280 feet. You've walk 0.20 mile on a track. How many feet have you watched?
The base of a triangle is 7 inches more than its height. If the area of the triangle is 60 square inches, find the base and height of the triangle.
Let x be the total number of customers in a one-hour interval and y be the total number of female customers in the same interval. find the joint pmf of x and y.
The joint PMF of X and Y is [tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \cdot \frac{x!}{y!(x-y)!} \cdot \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad \text{for } y = 0, 1, \ldots, x \text{ and } x = 0, 1, 2, \ldots[/tex]
Distributions of X and Y
X is the total number of customers visiting the store in an hour, which follows a Poisson distribution with mean [tex]\lambda = 10[/tex]
[tex]P(X = x) = \frac{e^{-10} \cdot 10^x}{x!}, \quad x = 0, 1, 2, \ldots[/tex]
Given X = x the number of female customers Y follows a binomial distribution because each customer is independently female with probability [tex]p = \frac{3}{4}[/tex]
[tex]P(Y = y \mid X = x) = \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad y = 0, 1, \ldots, x[/tex]
Joint PMF of X and Y
To find the joint PMF P(X = x, Y = y, we use the law of total probability:
[tex]P(X = x, Y = y) = P(Y = y \mid X = x) \cdot P(X = x)[/tex]
Substitute the expressions for [tex]P(Y = y \mid X = x)[/tex] and P(X = x)
[tex]P(X = x, Y = y) = \left( \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y} \right) \cdot \left( \frac{e^{-10} \cdot 10^x}{x!} \right)[/tex]
Simplify the expression:
[tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}.[/tex]
What the answer to this
The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.
Solve for r.
Answer: [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]
Step-by-step explanation
Compound interest is the addition of interest to the principal sum of a deposit or a loan.
Let P = principal amount which was taken as a loan then the accumulated amount A is given by
[tex]A=P(1+r)^t[/tex].......(1)
where, r is the rate of simple annual interest in decimal.
t is the time applied for interest.
For solving r divide both sides of equation by P in (1),we get
[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].
A polygon has an area of 144 square inches and one of its sides is 10 inches long. If a second similar polygon has an area of 64 square inches, what is the length of the corresponding side in the second polygon?
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10
Answer:
C. [tex]x=50[/tex], [tex]y=10[/tex]
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.
We know that when two line intersect each other, then vertical angles are congruent.
Using vertical angles theorem, we will get a system of equations as sown below:
[tex]3y=x-20...(1)[/tex]
[tex]5x-100=y+140...(2)[/tex]
From equation (1), we will get:
[tex]x=3y+20[/tex]
Upon substituting this value in equation (2), we will get:
[tex]5(3y+20)-100=y+140[/tex]
[tex]5*3y+5*20-100=y+140[/tex]
[tex]15y+100-100=y+140[/tex]
[tex]15y=y+140[/tex]
[tex]15y-y=y-y+140[/tex]
[tex]14y=140[/tex]
[tex]\frac{14y}{14}=\frac{140}{14}[/tex]
[tex]y=10[/tex]
Therefore, the value of y is 10.
To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:
[tex]3*10=x-20[/tex]
[tex]30=x-20[/tex]
[tex]30+20=x-20+20[/tex]
[tex]50=x[/tex]
Therefore, the value of x is 50 and option C is the correct choice.
Answer:
Option C) x = 50, y = 10
Step-by-step explanation:
We are given a two pairs of vertically opposite angle in the image.
Vertically opposite angle is formed when two lines intersect anf they are always equal.
Thus, we can write:
[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]
Solving the two equations in two variable, we get:
[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]
The value of x is 50 and y is 10.
Hi guys can I plz get some help I don't understand and can I plz get the answers so I can get a 4 on this paper thx
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed ti
Answer:
n = 6.2f
Step-by-step explanation:
A playground has two poles that are used for games. The first pole is 1.83 m tall. The second pole is 2.172 m tall.
How much taller is the second pole than the first pole?
Enter your answer in the box.
pls help, will matrk brainliest
Answer:
mark me brainliest plz im a beginner and the answer is .342 becuase the m ok lo, xd
Step-by-step explanation:
write a trinomial expression equivalent to (2x+5)(3x-2)
The required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
According to the question, we have to determine the trinomial expression that is equivalent to the (2x+5)(3x-2).
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Given expression in the question,
= (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10
Thus, the required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
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Final answer:
The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.
Explanation:
To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).
Multiply the first terms: 2x × 3x = 6x²
Multiply the outside terms: 2x × (-2) = -4x
Multiply the inside terms: 5 × 3x = 15x
Multiply the last terms: 5 × (-2) = -10
Combine like terms:
6x² + (15x - 4x) - 10 = 6x² + 11x - 10
The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
Find the derivative of the function y = sin(tan 4x)
The sum of two binomials is 3z-6. If one binomial is z+4, what is the other binomial?
How many yards equals 765 inches?
Enter your answer, as a decimal.
Write an equation for the translation of y = |x| and the translation is up 4 right 2.
Steven bagged 52 pounds of potatoes. About what is that measure in kilograms? Round to the nearest hundredth
What can a doctor use to determine a patient's body fat percentage?
Bioelectrical impedance machine
MRI machine
Waist measurement
Weight measurement
Bioelectrical impedance machine can be used to determine a patient's body fat percentage
What is Fat percentage?The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100
A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.
This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.
Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.
Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage
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Please help guys im stuck. THanks
Angle 3 = 70 ( opposite angles equal each other)
Angle 1 = 90-70 = 20 ( angle 1 plus 70 = 90 )
angle 3 - angle 1 = 70 -20 = 50
Answer is B
Jack has 5 craft sticks he needs four times that number for a project how many craft sticks does Jack need all together
Solving this problem simply only requires us the knowledge of multiplication.
So we are initially given that there are 5 craft sticks. So if we need four times that amount, that is written as:
5 x 4
Which is equal to 20
So Jack needs 20
Witch set of orderd pairs contains only points that are on the graph of the function y=12-3x
A.(-3,-27),(0,0),(6,54)
B.(-18,10),(-6,6),(18,-2)
C(-5,27),(-1,15),(8,-12)
D(-7,-9),(-4,0)(2,18)
cory earns 52.50 in 7 hours. find the unit rate
divide them:
52.50 / 7 = 7.50 dollars per hour
Given right triangle def what is the value of sin e
Answer:
Step-by-step explanation:
From the given triangle DEF, we have
[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]
[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]
[tex]100-64=(DF)^2[/tex]
[tex]DF=6[/tex]
Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus
[tex]SinE=\frac{DF}{EF}[/tex]
[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]
Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].
A town's population has been growing linearly. In 2003, the population was 60000, and the population has been growing by 2700 people each year.
Write an equation for the population x years after 2003.
You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school./7425116/3d9f02b9?utm_source=registration
Andrew make six dollars an hour +9 dollars an hour for every hour of overtime overtime hours or any hours more than 40 hours for the week create an equation that shows amount of wages earned for working x hours no overtime
The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is s(t) = -16t2 - 64t + 80, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)
Select one:
a. 256 ft/sec
b. -96 ft/sec
c. 0 ft/sec
d. 112 ft/sec
The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4. (2 points)
Select one:
a. 24π
b. 16π
c. 64π
d. 20π
The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.
The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.
Part 1: Instantaneous Velocity of the Ball
The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).
First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.
Part 2: Rate of Change of Surface Area
The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.
17,325 round to the nearest thousand
Determine the slope and y-intercept of the line. y = 8.5x + 6
Answer: Slope = 8.5 and y-intercept = 6
Step-by-step explanation:
The intercept form of a linear equation is given by :_
[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.
The given equation in intercept form : [tex]y = 8.5x + 6[/tex]
Here , the coefficient of c = 8.5
thus , the slope = 8.5
Also, the constant term = 6
Thus, the y-intercept =6
Solve for y: 10y + 3.8 = 38.8
The solution for ( y ) is ( y = 3.5 ).
To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:
Start with the given equation:
[tex]\[ 10y + 3.8 = 38.8 \][/tex]
Subtract 3.8 from both sides to isolate the term with y:
[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]
[tex]\[ 10y = 35 \][/tex]
Divide both sides by 10 to solve for y :
[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]
y = 3.5
So, the solution for ( y ) is ( y = 3.5 ).
If <0 <90 and cos0=11/15 what is the value of sin (90-0)