Answers
3x-7=3*23-7=69-7=62,
so we can see that 2x+16=3x-7, that means that lines are parallel , because the corresponding angles are equal.
problem with triangle
130+a=180, a=50,
50+8x+2x=180
50+10x=180
10x=130
x=13
8x+b=180
b=180-8x=180-8*13=76
2x+c=180
c=180-2x
c=180-2*13= 154
Related Questions
At noon, ship a is 50 km west of ship
b. ship a is sailing south at 10 km/h and ship b is sailing north at 20 km/h. how fast is the distance between the ships changing at 4:00 pm? (round your answer to one decimal place.) 23.05 incorrect: your answer is incorrect. km/h
Answers
At 4:00 pm, the distance between the ships is changing at a rate of 30 km/h.
Explanation:To find how fast the distance between the two ships is changing, you can use the Pythagorean theorem, as the two ships are moving at right angles to each other (north and south). Let's denote the distance between the two ships as "D," the speed of ship A as "vA," and the speed of ship B as "vB."
At any given time, you have:
D² = (Distance ship A travels)² + (Distance ship B travels)²
Now, we can differentiate both sides of this equation with respect to time "t" to find how the distance "D" is changing:
2D * dD/dt = 2(vA * dA/dt) + 2(vB * dB/dt)
Here, dD/dt represents the rate of change of the distance between the ships, dA/dt is the speed of ship A (10 km/h), and dB/dt is the speed of ship B (20 km/h).
Plug in the values:
2 * (dD/dt) = 2 * (10 km/h) + 2 * (20 km/h)
Now, solve for dD/dt:
2 * (dD/dt) = 20 km/h + 40 km/h
2 * (dD/dt) = 60 km/h
Now, divide by 2:
dD/dt = 60 km/h / 2 = 30 km/h
So, at 4:00 pm, the distance between the two ships is changing at a rate of 30 km/h.
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in 2010 , a city's population was 55,210 and it was declining at a rate of 1.09% each year. which is the best prediction for when the city's population will first be below 48,000?
Answers
Answer: 2023
Step-by-step explanation:
Since, the initial population of the city is 55,210,
And, it is declining at a rate of 1.09%.
Thus, the function that shows the population after x years since 2010 is,
[tex]f(x) = 55210(1-\frac{1.09}{100} )^x[/tex]
[tex]f(x) = 55210(1-0.0109)^x[/tex]
[tex]f(x) = 55210(0.9891)^x[/tex]
If the population of town is 48000 in x years.
⇒ [tex] 55210(0.9891)^x= 48000[/tex]
⇒ [tex] (0.9891)^x= 0.869407715993[/tex]
⇒ [tex]x = 12.769[/tex]
Therefore, after 12.769 years the population of town will be equals to 48,000
⇒ After 12.770 years the population will first be below 48,000.
⇒ After approx 13 years the population will first below 48,000.
⇒ Around 2023 the population will be first below 48,000.
Answer:2022
Step-by-step explanation:
What fraction of a gallon is 3 pints?
Answers
Find the area of the triangle that divides the parallelogram in half
Answers
What is the answer for # 24?
A B C or D
Answers
The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.
CubeThe volume of a cube of edge length s is
... V = s³
When the edge length is 6 in, the volume is
... V = (6 in)³ = 216 in³
SphereThe volume of a sphere with radius r is
... V = (4/3)π·r³
When the radius is 3 in, the volume is
... V = (4/3)π·(3 in)³ = 36π in³
SpaceThen the volume of the space between the cube and the sphere is
... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C
The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of \$113.00$113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 45\%45%45, percent.
At what price should the manager sell the couch?
Answers
Explanation:
1) Data:
Purchase price: $ 113.00
mark up: 45%
2) Formula
selling price = purchase price + mark up
mark up = % * purchase price
3) Solution
mark up = 45% * $ 113.00 = 0.45 * $ 113.00 = $50.85
selling price = $ 113.00 + $ 50.85 = $ 163.85
Answer: $ 163.85
Answer:
163.85 bucks,bix,backs,boks :P
Step-by-step explanation:
In order to find the retail price, we must first find the amount of markup. Remember that a markup rate is a percentage of the wholesale price that a store adds to get a selling or retail price. With this knowledge, we can figure out the following equation:
markup rate× wholesale price = amount of markup
Since the markup rate is a percentage, we have to convert it into a decimal first. Percent means "out of one hundred," so 45% is equivalent to 45/100 which is also equal to 45 \ 100 so 45/100 = 0.45. 0.45 * 113 = 50.85.
Since the markup rate is a percentage of the wholesale price that is added to get the retail price, we can find the retail price with the following equation:
amount of markup + wholesale price = retail price. 50.85 + 113 = 163.85
There are 20 goldfish in a pond. Their population is increasing by 20% each year. The same pond has 100 minnows. The minnow population is increasing by 10 minnows each year. Make a graph to find the year that the two species of fish will have the same population. In what year will the fish populations be approximately the same?
Answers
We only consider the portion of the graph from x=0 on, since negative time is illogical. Tracing the graph we get the intersection point.
Answer:
13.5 years.
Step-by-step explanation:
We know that exponential growth function is in form [tex]y=a\cdot(1+r)^x[/tex], where, a is initial value and r is growth rate in decimal form.
Population of goldfish after x years would be [tex]y=20\cdot(1+0.20)^x[/tex].
We know that a linear function is in form [tex]y=mx+b[/tex], where, b is initial value and m is slope.
Population of minnow after x years would be [tex]y=100+10x[/tex].
Graphing both equations, we will get our required graph as shown in the attachment.
Since both graphs intersect at [tex]x=13.5[/tex], therefore, in the 13.5 years both populations will approximate the same.
Study the function: F(x)=3/4x−7 and select the statement that is FALSE based on the lessons you have learned about the slope-intercept form of the equation of a line.
A: The slope of the function is .75 and would increase from left to right if you were to graph the function on a coordinate plane
B: The y-intercept is (0,-7)
C:The point (12,2) is a solution to the equation
D:The x-intercept is (10,0)
Answers
The Main answer is the function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.
The statement that is FALSE based on the lessons about the slope-intercept form of the equation of a line is:
C: The point [tex](12,2)[/tex] is a solution to the equation
To check if a point is a solution to the equation, we substitute the coordinates of the point into the equation and see if it satisfies it. For the given function
[tex]F(x)= (3/4 )x-7:[/tex]
Substituting x=12 into the equation:
[tex]F(12)= 3/4 (12)-7\\F(12)=9-7\\F(12)=2[/tex]
The function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.
COMPLETE QUESTION:
Study the function: [tex]F(x)=(3/4)x-7[/tex] and select the statement that is FALSE based on the lessons you have learned about the slope-intercept form of the equation of a line.
A: The slope of the function is .[tex]75[/tex] and would increase from left to right if you were to graph the function on a coordinate plane
B: The y-intercept is [tex](0,-7)[/tex]
C:The point [tex](12,2)[/tex] is a solution to the equation
D:The x-intercept is [tex](10,0)[/tex]
For a science experiment,Juanita records the height of a plant every day in centimeters.What is the attribute measured in her experiment.
Answers
In Juanita's science experiment, the attribute measured is the plant's height, a key phenotypic trait in studying plant growth, which she records in centimeters, using consistent and precise units for scientific reliability.
The attribute measured in Juanita's science experiment is the height of a plant, which is a phenotypic trait important in plant biology. Juanita is collecting data related to plant growth by observing and recording the plant's height in centimeters daily. This meticulous tracking allows for analysis of plant growth patterns over time and the effect of various treatments, such as different fertilizers or amounts of water. The typical unit of measurement for the height of a plant is in centimeters or meters, which are part of the metric system used in scientific research.
During a laboratory experiment like the one Juanita is conducting, it is essential to measure such variables with precision and consistency. Measurements should be recorded using uniform units and methods to ensure reliability in the results, which may include the plant height, recorded in centimeters, at regular intervals. A graph representing this data might portray the number of days since the start of the experiment along the X-axis and the plant's height along the Y-axis, thereby allowing a visual assessment of the plant's growth over time.
A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
6 in3
24 in3
36 in3
48 in3
Answers
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C
A real estate agent knows that he will receive a commission of $4,250 from the sale of a property when the deal is completed 37 days from now. Needing cash today, though, he signs a discount note at a credit union, using his expected commission as the maturity value. The discount rate is 9.55%. Find the effective rate (APR).
Answers
.. effective rate = r/(1-rt)
Assuming a 365 day year, this is
.. = 9.55%/(1 -0.0955*(37/365))
.. ≈ 9.64%
A person earns 26,800 one year and gets a 5% raise in salary. What is the new salary?
Answers
The new yearly salary is $28,140.
Explanation:Amount of raise.
5%=0.05
Multiply the original salary times the percentage of the raise.
$26,800×0.05=$1,340
New salary .
$26,800+1,340=$28,140
HOPE THIS HELPS! :)
This question is based on the concept of percentage. Therefore new salary when there is 5% raise in 26,800 is 28,140. There are many uses of calculating percent.
What is percent ?Percent is a proportionate of a number. Percent is a dimensionless quantity that is it has no unit. Percent is always out of hundred whereas fraction is always from 1. It is represented with the sign %. There are many uses of calculating percent. It is used in calculating interest in bank. It used in calculating inflation rate.
Mathematically,
The new yearly salary of a person is 28,140.
percentage of raise in salary is
5%=0.05
Multiply the original salary and the percentage of the raise in salary
26,800×0.05=1,340
New salary =26,800+1,340=28,140
Therefore new salary when there is 5% raise in 26,800 is 28,140
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A high school has 3636 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing greater than or equal to 194194 pounds?
Answers
To calculate the percentage of players weighing 194 pounds or more from a box plot, we need to know where 194 pounds falls in relation to the quartiles on the plot. Without the box plot details, we cannot perform the needed analysis.
The student's question appears to concern the analysis of a box plot depicted in their materials to find the percentage of players weighing 194 pounds or more on a football team. However, to accurately answer this question, we need the specific details from the box plot, including the median (Q2), first quartile (Q1), third quartile (Q3), and any outliers if provided. From the box plot, we would determine where the weight of 194 pounds falls in relation to the quartiles. If 194 pounds is at or above Q3, then you would expect a lower percentage of players above this weight; if it is below Q3, then the percentage could be higher.
The approach typically involves identifying the number of players within each quartile and calculating the corresponding percentages. Without the specific box plot data, we cannot perform these calculations. Should you provide the box plot details, we can review the quartiles and calculate the exact percentage of players weighing 194 pounds or more.
Six girls share 5 pints of milk equally.What fraction of a pint of milk does each girl get?
Answers
All you have to do is divide 6 by 5.
The square footage of a house is 1200 square feet. What type of data is this?
Answers
The explanation is shown above:
1- By definition, the area is the measure of a two-dimensional surface.Its units can be written in m^2, ft^2, in^2...However, in the International System of Units is m^2.
2. This is very useful when you want to know the surface of a house. If it is a rectangular house, you can calculate the area as below:
A=LxW
Where L is the length and W is the width
a customer deposits $2000 in a savings account that pays 5.2% interest compounded continuously. how much will be earned between the 3rd and 5th yeards?
Answers
FV=p(1+r/100)^n
where:
FV=future value
r=rate
n=time
The amount earned in the first 3 years will be:
FV=2000(1+5.2/100)^3=$2,328.50
The amount earned in 5 years will be:
FV=2000(1+5.2/100)^5=$2,576.97
The amount earned between 3rd and 5th
=2,576.96-2,328.50
=$248.46
In which graph does y vary directly as x? It’s not C, I got it wrong.
Answers
Answer:
A
Step-by-step explanation:
A graph where y varies directly as x is a straight line that passes through the origin (0, 0). This is because when two variables vary directly, their ratio is constant, and in the case of y and x, this ratio is the slope of the line.
The equation for direct variation is y = kx, where k is the constant of variation. When we plot this equation on a graph with y on the vertical axis and x on the horizontal axis, we get a straight line that passes through the origin, with a slope of k.
For example, if we have a set of data points that vary directly, such as (1, 2), (2, 4), (3, 6), and so on, we can plot these points on a graph and draw a straight line that passes through the origin and all the points. This line represents the direct variation between y and x, and any other points that satisfy the equation y = kx will lie on this line.
In summary, a graph where y varies directly as x is a straight line that passes through the origin, with a constant slope representing the constant of variation.
6yd 9ft 4in times 2 equals
Answers
What are the zeros of the polynomial function?
f(x)=x^2+9x+20
Enter your answers in the boxes.
Answers
9^2-4*1*20=1.
Using the quadratic formula, we get the solutions:
[tex] \frac{-9-1}{2} =-5\\ \frac{-9+1}{2}=-4 [/tex]
the solutions are then -4 and -5.
Suppose f(x) = 0.125x for 0 < x < 4. determine the mean and variance of x. round your answers to 3 decimal places.
Answers
- mean: 2.667
- variance: 0.889
Explanation:
To get the mean and variance of x, we need to verify first whether...
- x is discrete or continuous random variable
- f is probability mass or probability density function
because if we cannot verify the 2 statements above, we can't compute the mean and the variance.
Since 0 < x < 4, x is a continuous random variable because x can be any positive number less than, which includes a non-integer.
Note that if the random variable is continuous and [tex]0 \leq f(x) \leq 1[/tex] for any values of x in the domain of f, then f is a probability density function (PDF).
Note that
[tex]0 \ \textless \ x \ \textless \ 4 \\ \Leftrightarrow 0.125(0) \ \textless \ 0.125x \ \textless \ 0.125(4) \\ \Leftrightarrow 0 \ \textless \ 0.125x \ \textless \ 0.5 \\ \Leftrightarrow 0 \ \textless \ f(x) \ \textless \ 0.5 \\ \Rightarrow 0 \ \textless \ f(x) \ \textless \ 1 (\text{Because }0 \ \textless \ f(x) \ \textless \ 0.5 \ \textless \ 1)[/tex]
Hence, for any x in the domain of f, 0 < f(x) < 1. Moreover, since x is a continuous random variable, thus f is a PDF.
First, we use the following notations for mean and variance:
E[x] = mean of x
Var[x] = variance of x
Since f is a probability density function, we can use the following formulas for the mean and the variance of x:
[tex]\boxed{\text{mean of }x = E[x] = \int_{-\infty}^{\infty}{xf(x)}dx}[/tex]
[tex]\boxed{\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2}} [/tex]
To compute for the mean of x,
[tex]\text{mean of }x = E[x] \\ = \int_{-\infty}^{\infty}{xf(x)}dx} \\ = \int_{-\infty}^{\infty}{x(0.125x)}dx} \\ \boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx}}[/tex]
The integral seems complicated because of the infinity sign. But because the domain of f is the set of positive numbers less than 4, that is,
[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]
the bounds of the integral for the mean can be changed from [tex]-\infty \ \textless \ x \ \textless \ \infty[/tex] to [tex]0 \ \textless \ x \ \textless \ 4[/tex] so that
[tex]\boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx = \int_{0}^{4}{0.125x^2}dx}[/tex]
Hence, the mean is computed as
[tex]\text{mean of }x = \int_{0}^{4}{0.125x^2}dx \\ = \left[ \frac{0.125x^3}{3} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^3}{3} \right] - \left[ \frac{0.125(0)^3}{3} \right] \\ \\ \boxed{\text{mean of }x = \frac{8}{3} \approx 2.667} [/tex]
Since the formula for variance is computed as
[tex]\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2[/tex]
we must first compute for [tex]E[x^2][/tex] for which
[tex]E[x^2] = \int_{-\infty}^{\infty}{x^2 f(x)}dx \\ \\ = \int_{-\infty}^{\infty}{x^2(0.125x)}dx \\ \\ \boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx}[/tex]
Similar to the computation of integral of the mean, we take note that
[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]
so that we can change the bounds of the integral, that is,
[tex]\boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx = \int_{0}^{4}{0.125x^3}dx}[/tex]
Hence,
[tex]E[x^2] = \int_{0}^{4}{0.125x^3}dx \\ \\ = \int_{0}^{4}{0.125x^3}dx \\ \\= \left[ \frac{0.125x^4}{4} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^4}{4} \right] - \left[ \frac{0.125(0)^4}{4} \right] \\ \\ \boxed{E[x^2] = 8}[/tex]
Because [tex]E[x] = \frac{8}{3} [/tex],
[tex]\text{Variance of }x \\ \\ = E[x^2] - (E[x])^2 \\ \\ = 8 - \left( \frac{8}{3} \right)^2 \\ \\ \boxed{\text{Variance of }x = \frac{8}{9} \approx 0.889}[/tex]
The mean of x is 1.35 and the variance of x is approximately 1.267.
Explanation:To find the mean of x, we need to calculate the expected value. We can do this by multiplying each value of x by its corresponding probability and then summing up the results. In this case, using the given values and probabilities, we have 0(0.20) + 1(0.45) + 2(0.20) + 3(0.10) + 4(0.05) = 1.35. Therefore, the mean of x is 1.35.
To find the variance of x, we need to calculate the squared difference between each value of x and the mean, weighted by their respective probabilities. We then sum up these values. Using the formula for variance, we have (0-1.35)²(0.20) + (1-1.35)²(0.45) + (2-1.35)²(0.20) + (3-1.35)²(0.10) + (4-1.35)²(0.05). By simplifying this expression, we find that the variance of x is approximately 1.267.
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What is the probability that a five-card poker hand contains the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts?
Answers
There is exactly 1 way to have all 5 of these cards. For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:
(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.
The probability of drawing the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts in that order from a 52-card deck is approximately 1 in 380,204,032.
Explanation:The subject of the question is the probability of drawing specific cards from a 52-card deck. This problem involves choosing five specific cards: the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts.
To find the probability, we need to consider that the deck contains 52 distinct cards. Assuming that each card is equally likely to be drawn, the probability of drawing any specific card is 1 out of 52 (or 1/52). And because we want to draw these cards one after another, we multiply these probabilities together.
Thus, the probability of drawing these five specific cards from a 52-card deck in this order is (1/52) * (1/52) * (1/52) * (1/52) * (1/52), which is approximately 1 in 380,204,032. Please note that this probability is infinitesimally small because the event is highly specific. Also, the order of the cards matters in this calculation. If the order does not matter, the probability will be higher.
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Prime numbers have less 1.than two factors.
2.more than two factors. 3.exactly two factors. 4.less than or equal to two factors.
Answers
exactly 2 factors
Answer:
They just have 2 factors :/
Step-by-step explanation:
Bc yes
what is the area of the white rectangle in square units
Answers
The length of the grey rectangle below is 4 units, so the length of the white rectangle below is 13 units - 4 units = 9 units.
The width of the white rectangle is 6 units.
A = LW = 9 units * 6 units = 54 units^2
Answer: 54
G let x be an exponentially distributed random variable with parameter λ = 1 / 2 . determine the probability distribution function of the random variable y = x 2 . what kind of distribution does y have?
Answers
[tex]F_X(x)=\mathbb P(X\le x)=\begin{cases}1-e^{-\lambda x/2}&\text{for }x\ge0\\0&\text{otherwise}\end{cases}[/tex]
The CDF of [tex]Y[/tex] is then
[tex]F_Y(y)=\mathbb P(Y\le y)=\mathbb P(X^2\le y)=\mathbb P(X\le\sqrt y)=F_X(\sqrt y)[/tex]
[tex]\implies F_Y(y)=\begin{cases}1-e^{-\lambda\sqrt y/2}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies F_Y(y)=\begin{cases}1-e^{-(y/(4/\lambda^2))^{1/2}}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}[/tex]
which is the CDF of a Weibull distribution with shape parameter [tex]\dfrac4{\lambda^2}[/tex] and scale parameter [tex]\dfrac12[/tex].
what is -6x = -24
13 points
Answers
.. (-6x)/-6 = (-24)/-6
.. x = 4
_____
You asked "what is ..."
Answer: it is a "one-step" linear equation in x.
1.3 to the second power
Answers
1.3^2 = 1.3 x 1.3 = 1.69
If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2
Answers
= 16 + 2 (8)
= 16 + 16
= 32
Attached is my work.
Which rule describes a translation that is 8 units to the right and 2 units up?
(x, y) (x - 8, y + 2)
(x, y) (x - 8, y - 2)
(x, y) (x + 8, y - 2)
(x, y) (x + 8, y + 2)
Answers
When translating figures, a translation to the right subtracts from the x-coordinate (sort of the opposite of how we think of graphs that go to the right). Translations up would be adding to the y-coordinate.
Hal wants to make a 2 ½ foot banner from a 5-foot length of cloth. If he has marked 2.0 on the cloth, what does he have to do to find 2 ½ feet?
Answers
---
Hope this helps!
Two friends mix blue paint and yellow paint to make batches of green paint, as shown in the tables. Jarrod Cups Blue Cups Yellow 3 2 Ian Cups Blue Cups Yellow 5 2 Which correctly compares their ratios of blue to yellow paint?
Answers
Cups Blue Cups Yellow
3 2
Ian:
Cups Blue Cups Yellow
5 2
We have that their ratios are:
Jarrod: 3/2
Ian: 5/2
Comparing both ratios:
Jarrod uses 60% yellow paint and 40% blue paint.
Ian uses 71.4% yellow paint and 28.4% blue paint.
Answer:
Jarrod: 3/2
Ian: 5/2