Answers
Answer:
Step-by-step explanation:
Related Questions
500 sixth-grade students were surveyed. Of these students that were surveyed 375 had been to a baseball game, 270 own either a catcor a dog, 125 had traveled on an airplane. What is the ratio of sixth-grade students who traveled on an airplane to the total number of sixth-grade students surveyed?
Answers
Solution:
Given that,
Five hundred sixth-grade students were surveyed
Which means,
sixth-grade students = 500
125 had traveled on an airplane
What is the ratio of total sixth-grade students to the number of students who had traveled on an airplane?
Therefore,
total sixth-grade students : students traveled on airplane = 500 : 125
Ratio = 500 : 125
Reduce to lowest terms,
Divide both sides by 5
Ratio = 100 : 25
Further reduce to simplest terms,
Divide both sides by 25
Ratio = 4 : 1
Thus the ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 9 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?
Answers
Answer:
When the sample size is \(n_1 = 5\) ,
\(P( X < 11) = 0.9875\)
When the sample size is \(n_2 = 6\) ,
\(P( X < 11) = 0.993\)
Step-by-step explanation:
From the question we are told that
The mean is \(\mu = 9 \ min\)
The standard deviation is \(\sigma = 2 \ min\)
The first sample size is \(n_1 = 5\)
The second sample size is \(n_2 = 6\)
Generally the standard error of the mean is mathematically represented as
\(\sigma_{x} = \frac{\sigma}{ \sqrt{n} }\)
=> \(\sigma_{x} = \frac{2}{ \sqrt{5} }\)
When the sample size is \(n_1 = 5\) ,
Generally the standard error of the mean is mathematically represented as
\(\sigma_{x} = \frac{\sigma}{ \sqrt{n} }\)
=> \(\sigma_{x} = \frac{2}{ \sqrt{5} }\)
=> \(\sigma_{x} = 0.894\)
Generally the probability that the sample average amount of time taken on each day is at most 11 min is mathematically represented as
\(P( X < 11) = P( \frac{X - \mu }{\sigma } < \frac{11 - 9 }{0.8944 } )\)
\(\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )\)
\(P( X < 11) = P( Z < 2.24 )\)
From the z table the area under the normal curve to the left corresponding to 2.24 is
\(P( Z < 2.24 ) = 0.9875\)
=> \(P( X < 11) = 0.9875\)
When the sample size is \(n_2 = 6\) ,
Generally the standard error of the mean is mathematically represented as
\(\sigma_{x} = \frac{\sigma}{ \sqrt{n} }\)
=> \(\sigma_{x} = \frac{2}{ \sqrt{6} }\)
=> \(\sigma_{x} = 0.816\)
Generally the probability that the sample average amount of time taken on each day is at most 11 min is mathematically represented as
\(P( X < 11) = P( \frac{X - \mu }{\sigma } < \frac{11 - 9 }{0.816 } )\)
\(\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )\)
\(P( X < 11) = P( Z < 2.45 )\)
From the z table the area under the normal curve to the left corresponding to 2.24 is
\(P( Z < 2.45 ) = 0.993\)
=> \(P( X < 11) = 0.993\)
Which number line shows the solution of -5 + 10 > -15?
Answers
Tom, Sally, and Benny each have 8 markers.
How many markers do they have have in all ?
Answers
Answer:
24 markers
Step-by-step explanation:
8(3)= 24
What do you know to be true about the values of a and b?
60"
75"
O A. a b
O B. a = b
O c. a> b
O D. Can't be determined
Answers
Answer: B. a = b .
First of all, let's think that a is equal to b.
Then, let's link up these two triangles.
Now, we have a parallelogram.
x+y = a+60
and 75 = b . So, a = b. Then, a is also = 75.
Now apply the basic triangle rule.
75+75+x=180 .. x = 30 degree.
and for the other triangle....
y+75+60=180 .. y= 45 degree...
Now, let's consider that we want to write a as b.
So, x+b+75=180 ...x+b=105
and..
y+b+60=180...y+b = 120..
Then, let's exit the b from these two equations.
-1/ x+b=105
y+b=120
Finally, we found this: y-x =15
and we have already found y and x values.
y was 45 and x was 30 degree.
So when we put these two numbers into that equation y-x=15
we found the value of 15.
So, our answer is a=b.
Answer:
\(\huge \boxed{\mathrm{B.} \ a=b}\)
Step-by-step explanation:
The two triangles form a parallelogram.
A parallelogram has opposite angles equal.
75 = b
Adjacent angles in a parallelogram are supplementary to one another.
They add up to 180 degrees.
a + 60 + 75 = 180
a + 135 = 180
Subtract 135 from both sides.
a = 75
Therefore, a = b.
Find the intervals on which f is increasing or decreasing, and find the local maximumand minimum values of f.\(f(x) = x + \frac{4}{x^2}\)Now I know the first derivative is \(f'(x) = 1 - \frac{8}{x^3}\) but I don't know how to get the critical points
Answers
Given the function f(x) defined as:
\(f(x)=x+\frac{4}{x^2}\)Taking the derivative of the function:
\(f^{\prime}(x)=1-\frac{8}{x^3}\)Now, we calculate the critical points using the equation:
\(\begin{gathered} f^{\prime}(x)=0 \\ 1-\frac{8}{x^3}=0 \\ 1=\frac{8}{x^3} \\ x^3=8 \\ x=2 \end{gathered}\)Now, we explore the intervals of increasing and decreasing for f(x) using the critical point, taking into account the discontinuity in x = 0:
\(\begin{gathered} x>2\colon f^{\prime}(x)>0\text{ (Increasing)} \\ 00\text{ (Increasing)} \end{gathered}\)The intervals are:
\(\begin{gathered} \text{Increasing}\colon(-\infty,0)\cup(2,\infty) \\ \text{Decreasing}\colon(0,2) \end{gathered}\)The function has a local minimum at x = 2, because f''(2) > 0. There is no local maximum.
How is the sum expressed in sigma notation?
22 + 27 + 32 + 37 + 42 + 47
Enter your answer by filling in the boxes.
the sum from i is equal to 1 to blank of open paren close paren$$
Answers
The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the value of A is
A = 22 + 27 + 32 + 37 + 42 + 47
The number of terms n = 6
So , the value of i ranges from 1 to 6
Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)
when n = 1
S₁ = 5 ( 1 ) + 17 = 22
when n = 2
S₂ = 22 + 5 ( 2 ) + 17
S₂ = 22 + 27
when n = 3
S₃ = 22 + 27 + 5 ( 3 ) + 17
S₃ = 22 + 27 + 32
Hence , the sum of the arithmetic sequence is S = 207
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particle travels from(-1/3 ,1, -2) to(9,9,6) . Its motion is described by the position function r(t)=(t^3/3, t^2,2t).
a) Find the distance the particle travels along the path, its average speed, and its
displacement [the distance it could have traveled if in a straight line].
b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by
time) including curvature and torsion.
Answers
The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.
To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.
The velocity vector is the derivative of the position function r(t):
\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)
\(= (t^2, 2t, 2)\)
The speed of the particle at any given time t is:
|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)
= √(t^4 + 4t^2 + 4)
= √((t^2 + 2)^2)
To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.
distance = ∫[from -1/3 to 9] |v(t)| dt
= ∫[from -1/3 to 9] |t^2 + 2| dt
= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt
= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)
Evaluating the definite integrals:
distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]
= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]
= [1/27 + 2/3] + [729/3 + 18]
= 1/27 + 2/3 + 729/3 + 18
= 1/27 + 18/27 + 729/3 + 18
= (1 + 18 + 729)/27 + 18
= 748/27 + 18
= 27.63 + 18
= 45.63 units (approximately)
Therefore, the particle travels approximately 45.63 units along the path.
To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.
average speed = distance / time
= 45.63 / (28/3)
= 45.63 * (3/28)
= 4.9179 units per unit time (approximately)
The displacement is the straight-line distance between the initial and final positions of the particle.
displacement = |r(9) - r(-1/3)|
= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|
= |(27, 81, 18) - (-1/27, 1/9, -2/3)|
= |(27 + 1/27, 81
= 2781.
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I need help with 10 please it says to find the area of each shaded sector. And round to the hundredth place
Answers
Given:
SR = 26 m.
To find:
The area of shaded region.
Solution:
Here, QR ~ PS. So, angle PTS = angle QTR.
So, angle PTS = 73 degrees.
To find the area of the shaded region, we have to subtract the area of unshaded region from the area of the circle.
Here, SR is the diameter and SR = 26. So, the radius of the circle is 13 m.
Since, the unshaded regions are similar to each other. So, the total area of the unshaded region is:
\(\begin{gathered} A=2\times\frac{73}{360}\times\frac{22}{7}\times(13)^2 \\ =\frac{542828}{2520} \\ =215.41m^2 \end{gathered}\)The area of the circle is:
\(\begin{gathered} A=\pi r^2 \\ =\frac{22}{7}\times(13)^2 \\ =\frac{3718}{7} \\ =531.14 \end{gathered}\)So, the area of shaded region is:
\(531.14-215.41=315.73m^2\)Thus, the area of the shaded region is 315.73 m^2.
Question 2: Benjamin rolls an ordinary six-sided dice and flips a coin. List all the possible outcomes.
Answers
Answer:
Step-by-step explanation:
20% of 50. Mathmethics
Answers
Answer:
1000%
Step-by-step explanation:
just multiply both
brainliest pls
Answer:
10
Step-by-step explanation:
20 x 50
100
The height h of an object thrown from the top of a ski lift 1240 feet high after t seconds is h=-16t2 +32t+1240. For what times is the height of the object at least 1000 feet?
←
The height of the object is at least 1000 feet from seconds to seconds.
Answers
Check the picture below.
so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.
\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)
now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.
So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark happened between 0 and 5 seconds.
Evan is earning some extra cash by mowing lawns. It takes Evan 6 ¾ hours to mow 3 lawns. The first lawn takes him 2 ⅞ hours and the second lawn takes him 1 ¾ hours to mow. How long did it take Evan to mow the third lawn?
PLS HELP PLS HELP ME PLS
Answers
If the graph of y = - x ^ 2 translated horizontally 7 units to the right and translated vertically 6 units upwards, what’s the new equation?
Answers
9514 1404 393
Answer:
y = -(x -7)² +6
Step-by-step explanation:
Replacing x with (x-h) translates the graph h units to the right. You want h=7.
Replacing f(x) with f(x)+k translates the graph k units upward. You want k=6.
These transformations make the new equation be ...
y = -(x -7)² +6
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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Simplify negative three fifths times m times quantity negative two sevenths times m minus one fourth end quantity.
A: 6 over 35 times m squared plus 3 over 20 times m
B: negative 6 over 35 times m squared minus 3 over 20 times m
C: 6 over 35 times m squared plus one fourth
D: negative 6 over 35 times m squared plus 3 over 20 times m
Answers
The required simplified value of the given expression is 6 / 35m² - 1/4. Option C is correct.
To determine the simplified value of the negative three-fifths times m times quantity negative two-sevenths times m minus one-fourth end quantity.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
negative three-fifths times m times quantity negative two-sevenths times m minus one-fourth can be interpreted as,
= -3/5m * - 2/7m - 1/4
= 6 / 35m² - 1/4
Thus, the required simplified value of the given expression is 6 / 35m² - 1/4. Option C is correct.
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In a direct variation, y=9 when x=3. Write a direct variation equation that shows the relationship between x and y.
Answers
In a direct variation, y=9 when x=3. A direct variation equation that shows the relationship between x and y is y=3x
What do you mean by direct variation?
Direct variation is a type of proportionality when one quantity changes right away in reaction to a change in another variable. This implies that if one number rises, the other will follow suit in a comparable manner. Similar to the last illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.
Given,
In a direct variation, y=9 when x=3.
Formulate an equation based on the conditions stated: y=kx
We put the value of the y and x in this equation
9=k*3
Subtract the coefficient of the variable from both sides of the equation
k= 3
We can write the equation of the function by putting the value of k: y=3x
Hence the correct answer is y=3x
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Find an equation in slope-intercept form for the line containing the following points.
(1,−3) and (3,−5)
Answers
Answer:
y=-x-2
Step-by-step explanation:
slope-intercept form is y = mx+b
slope is change in y over change in x, which is -5-(-3)/(3-1) = -1
y = -x+b
plugging in a point, like (1,-3), we have -3 = -1+b. b = -3+1 = -2
y = -x-2
Slope
m=(-5+3)/3-1m=-2/2m=-1Equation in point slope form
y+3=-1(x-1)y+3=-x+1y=-x+1-3y=-x-210. A rectangle with area of 3cm2 has lengths
(x + 4)cm and (x + 2)cm. Find its dimensions.
Answers
Step-by-step explanation:
We have (x + 4)(x + 2)cm² = 3cm².
=> x² + 6x + 8 = 3
=> x² + 6x + 5 = 0
=> (x + 5)(x + 1) = 0
=> x = -5 or x = -1
x = -5 is rejected as both side lengths would have negative values.
Therefore x = -1;
(x + 4)cm = (-1 + 4)cm = 3cm(x + 2)cm = (-1 + 2)cm = 1cmHence the dimensions are 3cm by 1cm.
The coordinates of the point � G are ( 0 , 8 ) (0,8) and the coordinates of point � H are ( 8 , 8 ) . (8,8). What is the distance, in units, between the point � G and point � ? H?
Answers
The distance between the points G and H is D = 8 units
Given data ,
Let the distance between 2 points be represented as D
Now , let the first point be G ( 0 , 8 )
Let the second point be H ( 8 , 8 )
Now , let the distance between G and H be D , where
D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
D = √ ( 0 - 8 )² + ( 8 - 8 )²
D = √64 units
D = 8 units
Hence , the distance is 8 units
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PLEASE HELP ON QUESTION ASAP !
Hi please help on question.If you get answer correct is be willing to give brainliest,a thanks, five stars and 10pts.
My question:
As an analogy of a circuit with resistance, think of an obstacle race . Which parts of a circuit do the obstacles represent? which part of the circuit do the people respresent?
Answers
The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.
In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:
Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.
Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.
People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.
The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.
Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.
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write the number with the same value as 28 tens..
Answers
Answer:
280 ones
Step-by-step explanation:
Answer:
280
Step-by-step explanation:
The value of 28 ten is 280 because ur adding ten to the number tht u have
which mixed number is equivalent to the improper fraction of 41/10
Answers
Answer:
4 1/10 when u have a inproper fraction like that every 10 is one whole number
(p^2n^1/2)^0
√ p^5n^4 equivalent to p^18n^6 √p?
Answers
The two expressions are not equivalent.
To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.
Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.
Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:
√ p^5n^4 =
(p^5n^4)^(1/2)
= p^(5/2)n^(4/2)
= p^(5/2)n^2
Combining this result with the previous step, we have:
(p^2n^1/2)^0 √ p^5n^4
= 1 * p^(5/2)n^2
= p^(5/2)n^2
This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression. ,
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A cereal box is 2 inches wide 7 inches long and 13 inches high what is the surface area of a cardboard?
Answers
The surface area is 272 square inches.
What is cube?The term "cube" refers tο a sοlid three-dimensiοnal shape in mathematics οr geοmetry that has six square faces, eight vertices, and twelve edges. It is alsο asserted tο be a cοnventiοnal hexahedrοn. Yοu must be familiar with the three-by-three Rubik's cube, which is the mοst prevalent example in daily life and can help tο increase brain capacity. Similar tο this, yοu'll run intο a lοt οf real-wοrld examples, like 6 sided dice, etc.
Sοlid geοmetry is the study οf three-dimensiοnal οbjects with surface areas and vοlumes. Cube, cylinder, cοne, and sphere are sοme οf the οther sοlid shapes. Here, we'll talk abοut its definitiοn, attributes, and relevance tο mathematics.
A Bοx cοntains,
Length by 8 inches, Breadth by 2 inches, Height by 12 inches.
using fοrmula:
Surface area = 2lw+2lh+2wh
Length by 8 inches, Breadth by 2 inches, Height by 12 inches
= (2×8×2)+(2×8×12)+(2×2×12)
=32+192+48
=272
Hence, the surface area is 272 square inches.
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MATH
MATH
MATH
PLS HELP MEHHhhHhh
Answers
A perfect square means if you find the square root of the number it will be a whole number .
A perfect square is square of a number(whole)
Like
\(\\ \bull\longmapsto 169=13^2\)
\(\\ \bull\longmapsto 900=30^2\)
Step-by-step explanation:
hope it's helpful for you
pls mark me as brainliest if my answer is helpful
⭐ Question
I have 30 red marbles, 28 blue marbles, 13 green marbles, and 6 magenta marbles.
What is the probability I pull 3 blue marbles? Write as a fraction, no need to simplify.
Answers
Answer:
im thinking that is 3/74 because i count them
Step-by-step explanation:
3/74 rhe answer but 3/77 are wrong he just thinking
Answer:
3 over 77, 3/77
Step-by-step explanation:
You add up all of the marbles. (including the blue ones)
30+28+13+6 = 77.
So. You have a 3/77 chance of pulling a blue marble.
I need help with this math problem please
Answers
The scale factor of dilation is 4/9
How to determine the scaled factorFrom the question, we have the following parameters that can be used in our computation:
The triangles
Given that the right is the scaled copy of the left
We have the following representation
Scaled factor = Right/Left
Substitute the known values in the above equation, so, we have the following representation
Scaled factor = 4/9
Hence, the scale factor is 4/9
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An expression is written as m−5(m+3) +7m.
What is the value of the expression when m=x+1?
Answers
(x+1)-5(x+4)
x + 1 - 5x - 20
-4x - 19
5. If a circle has an area of 706.5 cm what is its circumference?
94.2 cm
329.6 cm
140.5 cm
398.1 cm
Answers
Answer: 94.2 cm
Step-by-step explanation:
First, we know the formula to solve for the radius if given the area. It is a transformed version of the equation to solve for the area (A = πr²). We will substitute our area (A) and solve by dividing and finding the square root.
\(\displaystyle r = \sqrt{\frac{A}{\pi} }\)
\(\displaystyle r = \sqrt{\frac{706.5\; cm}{\pi} }\)
r = 15
Next, we will solve for the circumference using this radius and the given formula.
C = 2πr
C = 2π(15)
C ≈ 94.24778 ≈ 94.2 cm