Step-by-step explanation:
this is the problem to sum the numbers 1 ... n.
remember the old trick by adding
n + 1
n-1 + 2 = n + 1
n-2 + 3 = n + 1
...
and doing this n/2 times, giving us a sum
n×(n+1)/2
for n = 30 we get
30×31/2 = 15×31 = 465
so, 465 people will perform.
no solution, one solution, or infinitely many solutions?
8v + 3 -4v = 4v + 5 -3 has infinitely many solutions
7v - 11 = 7v + 11 has no solution
3(v-4) = 2(v-6) has one solution
5(2v+3) - 2 = 12v + 12 -2v has no solution
When does an equation have one solution, no solution or infinitely many solutions?A linear equation is said to have infinitely many solution when the variable term and the constant term are the same on both sides of the equation.
A linear equation is said to have no solution, if the coefficient of the variable term is zero and the constant term a non-zero term
A linear equation is said to have one solution if the coefficient of both the constant term and the variable terms are no zero.
Analysis:
8v + 3 -4v = 4v + 5-2
4v +3 = 4v+3
The equation has an infinitely many solutions
7v-11 = 7v+11
7v-7v = 11+11
0v = 22
The equation has no solution since the coefficient of the variable term is 0
3(v-4) = 2(v-6)
3v -12 = 2v - 12
v = 12-12 = 0
The equation has one solution
5(2v+3) -2 = 12v + 12-2v
10v+15-2 = 10v +12
0v = -1
The equation has no solution.
In conclusion,
8v + 3 -4v = 4v + 5 -3 has infinitely many solutions
7v - 11 = 7v + 11 has no solution
3(v-4) = 2(v-6) has one solution
5(2v+3) - 2 = 12v + 12 -2v has no solution
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Can someone help with number 4. I will reward brainliest.
Answer:
theta = pi/6 and
theta = 5pi/6
Step-by-step explanation:
see image. Factor the expression. Solve for sin theta. Then use a calculator or unit circle to solve for theta. See image.
Let's simplify the problem down a little:
⇒ set 'sin(θ)' as x
⇒ the new equation looks like: [tex]2x^2+5x-3=0[/tex]
Now let's solve this equation as a quadratic:
[tex]2x^2+5x-3=0\\(2x-1)(x+3)=0\\\\2x-1=0\\x = \frac{1}{2} \\\\x+3 = 0\\x=-3[/tex]
Now set the x value of '1/2', to sin(θ)
it can't be -3, because trig functions can't equal a negative numbersin(θ) = 1/2
θ = π/6, which is between the range given
Answer: π/6
Hope that helps!
Line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]
[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]
Please help
Which equation represents a line with an undefined slope?
Answer:
x = 0
Step-by-step explanation:
The slope relation is given as :
y = mx + b
Now, if we take x = 0, there is no way of finding out the value of m as the product of mx will be equal to 0.
Hence, x = 0 represents a line with undefined slope.
Factorize -3x^3 + 12x^2 - 15x + 6
With the steps please
[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]
Joshua has a ladder that is 15 feet long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.2 feet above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78 degrees. Will the ladder be safe at this height? Show your work and label the diagram
Answer:
Step-by-step explanation:
x² + 8x = 10 solve this quadratic equation by completing the square
Two socks are selected at random from a draw of loose socks- there are 4 green socks and 6 yellow socks
What is the probability that two of the socks will both be green if the socks are drawn without replacement
Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, we have that the values of the parameters are:
N = 10, k = 4, n = 2.
The probability that both are green is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333[/tex]
0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
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Find the LCM of 3, 7, 10
Find the length of the segment AB.
The number of guppies in an aquarium is doubling every day. there are 4 guppies initially in the aquarium. a) write an exponential function for the guppy population in the aquarium. b) how many guppies are in the aquarium after 4 days
if the guppies are doubling, that means whatever they were yesterday, today is 100% more, so the rate of growth is 100%.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=4(1 + 1.)^{t}\implies A=4(2)^t~\hfill \stackrel{\textit{after 4 days, t = 4}}{A=4(2)^4}\implies A=64[/tex]
A jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. Grace wins if she selects a turquoise marble from the jar. Is this game fair? Why or why not?
Yes, the game is fair because Grace has equal probabilities of winning and losing.
Yes, the game is fair because Grace has equal probabilities of choosing a marble of either color.
No, the game is not fair because Grace has equal probabilities of winning and losing.
No, the game is not fair because Grace has a higher probability of choosing a marble of another color.
What is the mean, median, and mode for this set of data:24, 20, 26, 24, 21?
Answer:
Mean = 23
Median = 24
Mode = 24
Step-by-step explanation:
Mean: The sum of all data values divided by the total number of data values.
⇒ Mean = (24 + 20 + 26 + 24 + 21) ÷ 5 = 23
Median: The middle value when all data values are placed in order of size.
Ordered data values: 20, 21, 24, 24, 26
⇒ Median = 24
Mode: The most frequently occurring data value.
20, 21, 24, 24, 26
⇒ Mode = 24
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = 2x2 +15?
OA. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units up.
OB. The graph of f(x) is horizontally stretched by a factor of 2 and
shifted 15 units up.
OC. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units to the left.
D. The graph of f(x) is horizontally compressed by a factor of 2 and
shifted 15 units to the left.
Answer:
A
Step-by-step explanation:
h(x) = 2x² + 15 = 2×f(x) + 15
so, every y value of f(x) is multiplied by 2, and that means the whole curve is stretched up and down (vertically).
and then we add constantly 15 to every y value. that moves then the previous stretched result up by 15 units.
Find the y-value when x = -5 for the equation y = -3x
Answer:
y=15 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
I will give brainliest! 40 points!
ling wants to determine the average distance she travels each day in her car. she records the odometer reading, which measures the distance the car has traveled, each morning for a week.
day 1 2 3 4 5 6 7
odometer (mi) 10,150 10,211 10,424 10,769 10,884 11,155 11,477
what is the mean distance ling travels each day? show your work.
Answer:
221.16
Step-by-step explanation:
Find the difference between each day. Add all the differences together, then divide that number by 6 (the number of differences) to find the mean.
Answer:
189.57 miles per day.
Step-by-step explanation:
I took the test
If Q, DE=FG. Which must be true? Select all that apply.
Answer:
A and E
Step-by-step explanation:
A is already given by the basic fact that DE = FG. this makes the 2 lines automatically also congruent.
but this does not tell us anything about EF.
E and F could be very close together or far apart, and still DE = FG can be true in either case.
and that is why B, C and D could be true, but they are not in all cases true, and therefore these statements are in general false.
What is the sign of m/n X (-m X n squared )
positive
Negative
zero
Step-by-step explanation:
mx=n
⟹x=mn
Since m and n are both negative, x=mn will be positive.
Hence, the solution of mx=n will be a positive number.
other sulotion :-
1 pound is equivalent to ____ grams.
Answer:
1 pound is equivalent to 453.59237 Grams.
✎let's answer it :3
☟ answer
-> ( 453.59237 grams )
hope it helps
by #galadohannadivine29These box plots show the basketball scores for two teams.
Which statement is the most appropriate comparison of the spreads?
The most appropriate statement is the interquartile range for the Wolverines, 30 is less than the IQR for the panthers, 40.
What is the correct statement?
The box plot is used to show the distribution of data. The box plot can be used to determine the range, interquartile range and median of the data set.
The range is the difference between the two ends of the whiskers.
Range for the Wolverines = 96 - 35 = 61
Range for the Panthers = 107 - 33 = 74
The interquartile range is the difference between the first and third lines on the box
IQR for the Wolverines = 85 - 55 = 30
Range for the Panthers = 90 - 50 = 40
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brainiestI WILL GIVE BRAINLIEST look at the right angled triangle abc
the square fits exactly inside the triangle
work out the sizes of angles x y and z
Answer:
x = 90°
y = 40°
z = 40°
Explanation (Concepts) :
A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.
Workouts:
z + 90° + 50° = 180°
z = 180° - 90° - 50°
z = 40°
=================
x + 90° = 180°
x = 180° - 90°
x = 90°
==================
50° + 90° + y = 180°
y = 180° - 90° - 50°
y = 40°
Answer:
x = 90°y = 40°z = 40°Step-by-step explanation:
x = 90°
…………………
y = 90 - 50
= 40°
……………………………
z = 180 - (50 + 90)
= 180 - 140
= 40°
what type of parent function is f(x) = |x|
Answer: Absolute value function
The type of parent function is f(x)= |x| is Absolute valued function
What is Absolute valued function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
Given function:
f(x)= |x|
As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.
The above property perfectly resemble the absolute valued function.
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f(-2)for the function f(x)=3x-1
Step-by-step explanation:
From what I know
3x-1=0
3*(-2)-1=0
-6-1=0
=-7.
I'm not sure but u can try it.
The value of f(-2) in this function is f(-2) = -7
To solve this expression, just replace 'x' with -2. When the expression is ready, let's calculate it.
First we multiply or divide, then add or subtract.
Resolutionf( x ) = 3x - 1
f(-2) = 3 · (-2) - 1
f(-2) = -6 - 1
f(-2) = -7
So, the alternative value is f(-2) = -7
The measure of angle Q is 70 degrees. Find the measure of angle p
Please answer quick please! 30 points
Please Help! The value of x is:
Answer:
9
Step-by-step explanation:
5*x=15
X=3
3*3=9
[tex]\\ \rm\dashrightarrow \dfrac{5}{3}=\dfrac{15}{x}[/tex]
[tex]\\ \rm\dashrightarrow 5x=45[/tex]
[tex]\\ \rm\dashrightarrow x=\dfrac{45}{5}[/tex]
[tex]\\ \rm\dashrightarrow x=9[/tex}
I need help with area
The question 5 and 6
answer the question below, will give brainliest to first answer
Answer:
deductive reasoning
Step-by-step explanation:
it is based on what is true based on what happened before
Answer:
2 option, deductive reasoning
Step-by-step explanation:
based on true events
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a negative one-half meter per second. the toy sinks at a rate of no more than a negative one-half meter per second.
The answer choices which could be a constraint to the scenario are;
the pool is 1 meter deep.the pool is 2 meter deep.Which constraint could be part of the scenario?It follows from the task content that the scenario is modelled by means of a system of inequalities. However, only the variables in the model can be constrained and hence, only time and depth factors could be part of the constraints.
On this note, the constraints area as indicated above.
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Answer:
A
Step-by-step explanation:
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
The pool is 1 meter deep.
The pool is 2 meters deep.
The toy falls at a rate of at least a Negative one-half meter per second.
The toy sinks at a rate of no more than a Negative one-half meter per second.
Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. a = 51, b = 21, c = 68
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is given as:
a² = b² + c² - 2bc * cosA
Given that a = 51, b = 21, c = 68, hence:
51² = 21² + 68² - 2(21)(68) * cosA
A = 30.37°
21² = 51² + 68² - 2(51)(68) * cosB
B = 12.02°
68² = 21² + 51² - 2(21)(51) * cosC
C = 137.61°
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
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A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting a tree or a flower?
Express the Probability as a reduced fraction
The probability of randomly selecting a tree or a flower is 8/15.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of randomly selecting a tree or a flower = (number of trees / total number of flash cards) + (number of flowers / total number of flash cards)
8/30 + 8/30 = 16/30 = 8/15
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