By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
To learn more about speed of wave refer
https://brainly.com/question/22673264
#SPJ13
Pablo Is choosing at random from a bag of colored marbles. The probability he will choose a red marble is1/9What are the odds in favor of him choosing a redmarble?
Given:
[tex]\text{The probability to choose a red marble=}\frac{1}{9}[/tex]The odds in favour of Pablo chosing a re marble is 1 : 8
Which form most quickly reveals the vertex? choose one answer: a. m(x)=2(x+4)^2-8 b. m(x)=2(x+6)(x+2)c. m(x)=2x^2+16x+24what is the vertex? vertex=(___,___)
The vertx from of the quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex]Where
(h, k) are the coordinates of the vertex
a is the coefficient of x^2
By comparing this form with the answers
a.
[tex]m(x)=2(x+4)^2-8[/tex]a = 2
h = -4
k = -8
The vertex point is (-4, -8)
The quickly reveals the vertex is answer a
B 961 m Solve the triangle 40° 41 С b B= degrees minutes m (Round to the nearest whole number.) b = m (Round to the nearest whole number.)
To find the angle B we can use the propertie that sya that the sum of the internal angles of a triangle is equal to 180º so:
[tex]\measuredangle b+90º+40º,41^{\prime}=180[/tex]and we solve for angle b so:
[tex]\begin{gathered} \measuredangle b=180º-90º-40º,41^{\prime} \\ \measuredangle b=49º,19^{\prime} \end{gathered}[/tex]So B is equal to: 49 degrees and 19 minutes
So now to find a we can use the trigonometric identitie of sin so:
[tex]\begin{gathered} \sin (40.68)=\frac{a}{961} \\ a=961\cdot\sin (40.68) \\ a\approx626 \end{gathered}[/tex]and to find b we use the trigonometryc identitie of cos so:
[tex]\begin{gathered} \cos (40.68)=\frac{b}{961} \\ b=961\cdot\cos (40.68) \\ b\approx729 \end{gathered}[/tex]Which system of inequalities is shown?-5O A. y>xy<4OB. y> xy> 4C. y< xy<4OD. y< xy> 45
Given:
a graph of the inequalities is given.
Find:
we have to find the correct inequalities.
Explanation:
From the graph , it is observed that the value of y > x and y < 4,
Therefore, the correct inequalities are y > x,
y < 4.
Hence, correct option is A.
A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows a six or the green dieshows a six?Hint: The two events are not mutually exclusive. So to the find theprobability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)[?]
Let's call the event of the red die to show a six as event A, and the event of the green die to show a six as event B.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. On both dices, we have 6 possible outcomes(the numbers from 1 to 6), with one favourable outcome(the number 6), therefore, the probabilities of those events are:
[tex]P(A)=P(B)=\frac{1}{6}[/tex]Each roll is independent from each other, then, the probability of both events happening simultaneously is given by their product:
[tex]P(A\:and\:B)=P(A)P(B)[/tex]Using the additive rule of probability, we have the following equation for our problem:
[tex]\begin{gathered} P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B) \\ =P(A)+P(B)-P(A)P(B) \\ =\frac{1}{6}+\frac{1}{6}-\frac{1}{6^2} \\ =\frac{2}{6}-\frac{1}{36} \\ =\frac{12}{36}-\frac{1}{36} \\ =\frac{12-1}{36} \\ =\frac{11}{36} \end{gathered}[/tex]the probability that the red die shows a six or the green die shows a six is 11/36.
Hello, a little confused on this section. Thanks for your help!
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
notation for domain and range:
we must analyze the graph to find the solution.
graph:
The domain is reflected on the x-axis and the range is reflected on the y-axis.
Inequality / Agebraic:
D:
R:
Interval:
D:
R:
Set-Builder:
D:
R:
Solve the given quadratic inequality. Write the answer in interval notation.
it takes a rat 65 seconds to run from its food source to its home. If the rat has to run 28 meters which is going faster: the rat, or a child on a bike moving at 2 m/s?
Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
r
7n + 2 - 7n How can I simplify the expression by combining like terms
In order to simplify this expression, we can combine the terms with the variable n, like this:
[tex]\begin{gathered} 7n+2-7n \\ =(7n-7n)+2 \end{gathered}[/tex]Since the terms with the variable n have opposite coefficients (+7 and -7), the sum will be equal to zero:
[tex]\begin{gathered} (7n-7n)+2 \\ =(0)+2 \\ =2 \end{gathered}[/tex]Therefore the simplified result is 2.
Identify the augmented matrix for the system of equations and the solution using row operations.
Given:
The system of equation is given as,
[tex]\begin{gathered} 7x-4y=28 \\ 5x-2y=17 \end{gathered}[/tex]The objective is identify the augmented matrix for the system of equations and the solution using row operations.
Explanation:
The required augmented matrix will be,
Performing the Gauss-Jordan elimination with the following operation,
[tex]R_2=R_2-\frac{5R_1}{7}[/tex]By applying the operation to the augmented matrix,
To find y :
On equating the second row of the matrix,
[tex]\begin{gathered} \frac{6y}{7}=-3 \\ y=\frac{-3}{\frac{6}{7}} \\ y=\frac{-3\times7}{6} \\ y=\frac{-7}{2} \end{gathered}[/tex]To find x :
On equating the first row of the matrix,
[tex]\begin{gathered} 7x-4y=28 \\ 7x=28+4y \\ x=\frac{28+4y}{7} \end{gathered}[/tex]Substitute the value of y in the above equation.
[tex]\begin{gathered} x=\frac{28+4(\frac{-7}{2})}{7} \\ x=\frac{28-14}{7} \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Thus the value of solutions are,
[tex]\begin{gathered} x=2 \\ y=-\frac{7}{2}=-3.5 \end{gathered}[/tex]Hence, option (3) is the correct answer.
an 8-foot ladder leaning against a wall makes an angle of elevation of 70 degrees with the ground how far up the wall is the ladder to the nearest Foot
The length of the ladder is L = 8 foot.
The angle of ladder with ground is 70 degree.
The ladder lean on the wall can be expressed as,
Determine height on the wall to which ladder is up on the wall.
[tex]\begin{gathered} \sin 70=\frac{h}{8} \\ h=0.9397\cdot8 \\ =7.51 \\ \approx8 \end{gathered}[/tex]So up the wall is the ladder is 8 foot.
A store is having a sale to celebrate President’s Day. Every item in the store is advertised as one- fourth off the original price. If an item is marked with a sale price of , what was its original price?
If the discount is one fourth off, it means the discount is 1/4 = 25% of the original price, so the final price will be 75% or 3/4 of the original price.
In order to find the original price, we just need to divide the final price by 3/4, this way we "remove" the discount.
For example, if the sale price is $75, the original price would be:
[tex]\text{original price}=\frac{75}{\frac{3}{4}}=75\cdot\frac{4}{3}=25\cdot4=100[/tex]So for a sale price of $75, the original price would be $100.
In general, for a discount of x%, the original price (given the sale price) can be calculated as:
[tex]\text{original price}=\frac{\text{sale price}}{1-\frac{x}{100}}[/tex]Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Do the following lengths form an acute, right, or obtuse triangle? 99 90 39 O Acute, 7921 < 7921 Right, 7921 = 7921 Obtuse, 7921 > 7921
As we can see the interior angles of this triangle are less than 90° , therefore this triangle is an ACUTE TRIANGLE
How do I find the gif and distributive property
By using the GCF and distributive property, the sum of 15+27 = 42
The expression is
15 + 27
GCF is the greatest common factor, the greatest common factor is the highest number that divides exactly into two or more numbers.
The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.
The expression is
= 15 + 27
= 3(5 + 9)
= 3 × 14
= 42
Hence, by using the GCF and distributive property, the sum of 15 + 27 = 42
Learn more about distributive property here
brainly.com/question/5637942
#SPJ1
what is the factored form of his expression ? 2x^3+5x^2+6x+15
The given expression is:
[tex]2x^3+5x^2+6x+15[/tex]It is required to write the expression in factored form.
[tex]\begin{gathered} \text{ Factor out }x^2\text{ in the first two terms of the expression:} \\ x^2(2x+5)+6x+15 \end{gathered}[/tex]
Next, factor out 3 in the last two terms of the expression:
[tex]x^2(2x+5)+3(2x+5)[/tex]Factor out the binomial 2x+5 in the expression:
[tex](2x+5)(x^2+3)[/tex]The expression in factored form is (2x+5)(x²+3).Find the equation of the line, in slope-intercept form, that passes through the points (-2, -4) and (2,8).A) y = 1/3x + 22/3B) y = 3x + 14C) y = 3x + 2 D) y = - 3x + 14
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
x1 and y1 are the x and y coordinates of the initial point
x2 and y2 are the x and y coordinates of the final point
From the information given, the initial point is (- 2, - 4) and final point is (2, 8)
Thus,
x1 = - 2, y1 = - 4
x2 = 2, y2 = 8
By substituting these values into the slope formula,
m = (8 - - 4)/(2 - - 2) = (8 + 4)/(2 + 2) = 12/4 = 3
We would find the y intercept, c by substituting m = 3, x = - 2 and y = - 4 into the slope intercept equation. We have
- 4 = 3 * - 2 + c
- 4 = - 6 + c
Adding 6 to both sides of the equation,
- 4 + 6 = - 6 + 6 + c
c = 2
By substituting m = 3 and c = 2 into the slope intercept equation, the equation of the line is
C) y = 3x + 2
A random sample of 41 people is taken. What is the probability that the main IQ score of people in the sample is less than 99? Round your answer to four decimal places if necessary(See picture )
Solution:
Given:
[tex]\begin{gathered} \mu=100 \\ \sigma=15 \\ n=41 \\ x=99 \end{gathered}[/tex]From the Z-scores formula;
[tex]\begin{gathered} Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \\ Z=\frac{99-100}{\frac{15}{\sqrt{41}}} \\ Z=-0.42687494916 \\ Z\approx-0.4269 \end{gathered}[/tex]From Z-scores table, the probability that the mean IQ score of people in the sample is less than 99 is;
[tex]\begin{gathered} P(xTherefore, to 4 decimal places, the probability that the mean IQ score of people in the sample is less than 99 is 0.3347
Evaluate each expression for the given value of the variable. #9 and #10
Part 9
we have
(c+2)(c-2)^2
If c=8
substitute the value of c in the expression
so
(8+2)(8-2)^2
(10)(6)^2
(10(36)
360
Part 10
we have
7(3x-2)^2
If x=4
substitute the value of x in the expression
7(3(4)-2)^2
7(10)^2
7(100)
700
35% of the employees in a company receive an incentive in the month of April. What is theprobability that among 4 employees chosen at random, all 4 do not receive the incentive inApril?
ANSWER :
0.1785
EXPLANATION :
35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.
So an employee has 65% chance of NOT receiving an incentive.
The probability that among 4 employees do not receive the incentive is :
[tex](0.65)^4=0.1785[/tex]A bag contains 5 red marbles and 3 blue marbles. A marble is selected at random and not replaced into the bag. Another marble is then selected from the bag. How would you describe these two events?
Marble Events
there are 5 + 3 = 8 marbles
If one marble is selected then there are now
8 - 1 = 7 marbles
Then answer is
The two events are Dependent
Event B is dependent on Event A
How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.
To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:
[tex]6+6+8.5=20.5[/tex]Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:
[tex]21\cdot0.59=12.39[/tex]Therefore the cost will be $12.39
Not everyone pays the same price for the same model of a car that the figure is the streets a normal distribution for the price paid for the particular model of a new car the meanest $24,000 and a standard deviation is $1000 user 68–95-99.7 Raw to find a percentage of buyers who paid more than $27,000
The Solution:
The correct answer is 0.15%
Given the data in the given question,
We are required to find the percentage of buyers who paid more than $27,000.
The percentage of the total buyers is 100%
The percentage of buyers that paid between $21,000 and $27,000 is given to be 99.7%
This means that the total percentage of buyers who paid less than $21,000 and the buyers who paid more than $27,000 is
[tex]100-99.7=0.3\text{ \%}[/tex]Since the distribution is a normal distribution, it follows that half of 0.3% is the percentage of buyers who paid more than $27,000.
[tex]\frac{0.3}{2}=0.15\text{ \%}[/tex]Thus, the percentage of buyers who paid more than $27,000 is 0.15%
9=3(x+2) simplified
x=1
Explanation
Step 1
[tex]9=3(x+2)[/tex]apply distributive property
[tex]\begin{gathered} 9=3(x+2) \\ 9=3x+6 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} 9=3x+6 \\ \text{subtract 6 in both sides} \\ 9-6=3x+6-6 \\ 3=3x \end{gathered}[/tex]Step 3
finally, divide both sides by 3
[tex]\begin{gathered} 3=3x \\ \frac{3}{3}=\frac{3x}{3} \\ 1=x \end{gathered}[/tex]so, the answer is x=1
I hope this helps you
What will be the coordinates of the vertex s of this parallelogram? Which answer choice should I pick A B C or D?
Answer:
A
Step-by-step explanation:
the opposite sides of a parallelogram are parallel
then QT is parallel to RS
Q → T has the translation
(x, y ) → (x + 2, y- 7 ) , so
R → S has the same translation from R (0, 3 )
S = (0 + 2, 3 - 7 ) → S (2, - 4 )
Write a SITUATION that can be represented with this graph. Not an equation.
We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.
State the domain and range for each graph and then tell if the graph is a function(write yes or no)
For the point 1)
- The domain will be: (note that this is not an interval, it is a set of two points)
[tex]\mleft\lbrace-3,2\mright\rbrace[/tex]-The range is the set R of all real numbers (since the line extends to infinite)
-The first graph is NOT a function
For the point 2)
-The domain will be the interval
[tex](-5,5\rbrack[/tex]-The range is the interval:
[tex]\lbrack-2,2\rbrack[/tex]-The second graph is a function.
can you please find the slope and the y intersept of the graph of the linear equation y= 4x-5
the slope of the linear equation is 4 and the y intercept is -5
Explantion:we apply the equation of line to find the slope and intercept
Equation of line is in the form: y = mx + c
where m = slope and c = y - intercept
comparing the given equation with the equation of line:
linear equation y= 4x-5
y = y
4x - 5 = mx + c
This means m = 4
4x = mx
m = 4
-5 = c
Hence, the slope of the linear equation is 4 and the y intercept is -5
A building is 5 feet tall. the base of the ladder is 8 feet from the building. how tall must a ladder be to reach the top of the building? explain your reasoning.show your work. round to the nearest tenth if necessary.
The ladder must be 9.4 ft to reach the top of the building
Here, we want to get the length of the ladder that will reach the top of the building
Firstly, we need a diagrammatic representation
We have this as;
As we can see, we have a right triangle with the hypotenuse being the length of the ladder
We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Thus, we have;
[tex]\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}[/tex]Calculate the average rate of change for the function f(x) = 3x4 − 2x3 − 5x2 + x + 5, from x = −1 to x = 1.
a
−5
b
−1
c
1
d
5
Average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from
x =-1 to x=1 is equal to -1.
As given in the question,
Given function :
f(x) = 3x⁴ -2x³ -5x² +x +5
Formula for average rate of change for (a, f(a)) and (b, f(b))
[f(b) -f(a)] / (b-a)
Substitute the value of a=-1 and b=1
f(-1)=3(-1)⁴ -2(-1)³-5(-1)² +(-1) +5
= 3+2-5-1+5
=4
f(1)=3(1)⁴ -2(1)³-5(1)² +(1) +5
= 3-2-5+1+5
= 2
Average rate of change = (2-4)/(1-(-1))
= -2/2
=-1
Therefore, average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from x =-1 to x=1 is equal to -1.
Learn more about function here
brainly.com/question/28744270
#SPJ1
