The answer to the poition will be t²/2 which is the displacement of the car.
What is displacement?
When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.
The given acceleration is given in the function of velocity, v(t) = t
Let, be the function of velocity v(t) and position is x(t).
So the poition will be ∫v(t) dt = ∫t dt
=t²/2
Hence, the position of the given function will be t²/2
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What does 1 square unit look like?.
1 square unit looks like the area of a square with side measuring 1 unit.
According to the question,
We have the following information:
1 square unit
Now, we know that the square units mean that it is the area of the figure. Now, it can be for any figure whether it is a triangle or square or a circle but the measurements of the sides in such a way that the area found using the formulas of the given figure should be 1 square unit.
For example, if the side of the square is 1 unit then the area of the square is 1 square unit.
Hence, 1 square unit looks like the area of a square with side measuring 1 unit.
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there are 10 marbles in the bag 2 yellow 3 pink and 5 blue what is the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing
The probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that there are 10 marbles in the bag 2 yellow 3 pink and 5 blue.
First, we need to find the probability of drawing a blue marble on the first draw.
Since there are 5 blue marbles and 10 total, then the probability is;
5⁄10, or 1/2.
Now, we no longer have that blue marble, there are 4 blue marbles and 9 total.
The chances of drawing a blue marble are; 4/9.
Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.
1/2 x 4/9 = 4/18 = 2/9
Hence, the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.
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OThe sum of two numbers is 38. When 8
is added to twice one of the numbers, the
result is 5 times the other number. Find the
two numbers.
The two numbers are 12 and 26.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x and y be the 2 numbers
x+y=38........(1)
8+2x=5y.......(2)
(1) => x=38-y
8+2(38-y)=5y
8+76-2y=5y
84=5y+2y=7y
y=84/7 = 12
when y=12, x=38-y = 38 - 12 = 26
So, the two numbers are 12 and 26.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
Answer:
The sale price is 39.99 % off
Step-by-step explanation:
To find the percentage off,
take 49.99 - 30.00 = 19.99
Then divide by 49.99
19.99/49.99
39.9879976
The sale price is 39.99 % off
sienna has 800 yards of fencing to enclose a rectrangular area. find the dimensions of the rectangle that maximise the enclosed area
Area can be maximized by fencing a square of side 200 yards.
Explanation:
Given perimeter of a rectangle, square has the maximum area (proof given below).
Let x be one of the side and a be te perimeter then the other side would be a/2 - x
and area would be x (a/2 - x). The function will be zero when first derivative of the function is equal to zero and second derivative is negative,
As first derivative is − 2 x + a/2 and this will be zero, when − 2 x + a/2 = 0 or x = a/4. Note that second derivative is − 2. Then two sides will be a/4 each that the it would be square.
Hence if perimeter is 800 yards and it is a square, one side would be 800/4 = 200 yards.
Hence area can be maximized by fencing a square of side 200 yards.
As per the area of rectangle, the dimensions of the rectangle that maximize the enclosed area is 200 yard.
Area of rectangle:
The standard formula to calculate the are of the rectangle is.
A = l x b
l refers the length
b refers the breadth
Given,
Sienna has 800 yards of fencing to enclose a rectangular area.
Area can be maximized by fencing a square of side 200 yards.
Here we need to find the dimensions of the rectangle that maximize the enclosed area.
Let us consider x be one of the side and a be the perimeter then the other side would be written as,
=> a/2 - x
And the and area of the rectangle would be
=> x (a/2 - x).
Then the function will be zero when first derivative of the function is equal to zero and second derivative is negative,
So, as per the first derivative is written as,
=> − 2 x + a/2
And this will be zero, when the equation,
=> − 2 x + a/2 = 0 or x = a/4.
Here we have to note that second derivative is − 2.
And then the two sides will be a/4 each that the it would be square.
Therefore, if perimeter is 800 yards and it is a square, one side would be 800/4 = 200 yards.
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GIA IS THINKING OF A NUMBER WHICH CALLS N SHE ADDS 4 TO THE NUMBERAND THEN DOUBLES THE SUM
Answer:
Unknown
Step-by-step explanation:
What is N? Can you show the numberline?
Answer:
the answer is 8 or more then 8
I will give brainlest
Answer:
[tex]\huge\boxed{\sf r = 1/4}[/tex]
Step-by-step explanation:
Given that,y = rx -------------------(1)
From the table,
x = 8 when y = 2
Put in the above equation.
2 = r(8)
Divide 8 to both sides
2/8 = r
r = 2/8
r = 1/4
[tex]\rule[225]{225}{2}[/tex]
recall that two angles are complementary if the sum of their measures is 90. find the measures of two complementary angles if one angle is more than times the other angle.
The measures of the two complementary angles are 28 and 62 degrees
Complementary angles:
In math, the sum of two angles is equal to 90 degrees, they are called complementary angles.
Given,
Here the two angles are complementary if the sum of their measures is 90.
And we need to find the measures of two complementary angles if one angle is more than 6 times the other angle.
Let us consider A is the measure of the smaller angle and B is the measure of the larger angle.
Here we know that they are complementary
=> A + B = 90
Here we also know that,
=> 2A + 6 = B
Now, we have to replace B in the first equation with the second equation, then we get,
=> A + 2A + 6 = 90
Now, solve for A:
=> 3A + 6 = 90
=> 3A = 84
Therefore, the value of A is 28
Then the value of B is,
=> 2(28) + 6 = 62
Therefore, the two angles that complementary are: 28 and 62 degrees
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a city has 9 coffee shops. 3 starbucks, 2 caribou coffees, and 4 crazy mocho coffee. if a person selects on shop at random to buy a cup of coffee, find the probability that it is either a starbucks or crazy mocho coffee.
Answer:
7/9
Step-by-step explanation:
total: 3+2+4
starbucks or crazy mocho: 3+4
(3+4)/(3+2+4)=7/9
How will the solution of the system Y 2x two thirds and Y 2x one third change if the inequality sign on both inequalities is reversed to?.
The system of inequalities did not have any solution, but after reversing the sign we will get a solution of the system of inequalities.
The inequalities are : y > 2x + 2/3 and y < 2x + 1/3
There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.
Now when the signs are changed we get:
y < 2x + 2/3 and y > 2x + 1/3
The region below the line y = 2x + 2/3 is the solution of the inequality
y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.
Disclaimer: The complete question is :
How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
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Answer:
There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
Step-by-step explanation:
Sample answer
the width of a rectangular patio is increased by 10 % 10%. its length is increased by 20 % 20%. by what percentage has its area increased?
Answer: 32%
Step-by-step explanation:
Let's set the original dimensions of the rectangular patio as:
width = wlength = lThat'll set the original area(a) of the patio as a = w · l.
The new dimensions of the patio can be calculated as:
width = w + 0.1w = 1.1wlength = l + 0.2l = 1.2lThe new area can then be calculated as 1.1w · 1.2l = 1.32 · w · l = 1.32a
Using the two areas, the percent increase can be calculated as:
[tex]\frac{1.32a-a}{a}*100 =\frac{1.32-1}{1}*100 =0.32*100=32[/tex]
use cross products to determine whether the ratios and form a proportion. do they form a proportion?
No , they do not form a proportion because 77 and 60 are not equal
Hence , not form proportion
Set up a proportion as 4/7 = 11/15
Cross multiply:
7×11
4×15
You should get 77 and 60 for the products. Since the products don't equal each other, they are not proportional.
complete question is
use cross products to determine whether the ratios 4/7 and 11/15 form a proportion. Do they form a proportion? Explain your steps and your conclusion
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T/F study unit 7.1 the dynamic nature of memory match each term to the corresponding process. drag each item on the left to its matching item on the right. retrieval storage memory encoding
The matching terms and processes are;
1. The nervous system's ability to acquire, retain, and retrieve information- memory
2. Remembering stored information- retrieval
3. Processing information for storage- encoding
4. Retention of information- storage
Given,
The nervous system's capacity for information acquisition, storage, and retrieval is known as memory. Information is processed for storage by encoding, whereas information is remembered from storage through retrieval. Information is retained through storage.
Memory is the process of storing and recalling previously acquired information. The act of storing involves adding new information to the memory, which the brain alters for improved storage. It is easier for the brain to access and bring into conscious mind information that has been encoded.
Information is stored so that it will last throughout time. Modern memory psychology distinguishes between two basic types of memory storage: short-term memory and long-term memory.
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Given question is incomplete. Completed question is here;
Match the terms with their corresponding processes.
a. memory
b. encoding
c. retrieval
d. storage
1. the nervous system's ability to acquire, retain, and retrieve information
2. remembering stored information
3. processing information for storage
4. retention of information
What is the angle of each side of a circle?.
The central angle states the property of the center of the circle, So It is called the central angle.
What is a Central Angle?
The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.
Hence,
The central angle states the property of the center of the circle, So It is called the central angle.
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Please Help, I need to get a 100%
Answer:
C
Step-by-step explanation:
Denominator can't be 0
Therefore, [tex]x-7\neq 0[/tex]
Adding 7 to both sides gives [tex]x\neq 7[/tex]
Only C corresponds to our answer.
Provide an appropriate response.
Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Answer:
A) 0.7938---------------------------
Givenμ = 100, σ = 15Find the area between x = 85 and x = 125.
Find z-scores for each endz = (x - μ)/σz₁ = (85 - 100)/15 = - 15/15 = - 1z₂ = (125 - 100)/15 = 25/15 ≈ 1.67Find the corresponding probabilities from z-score tablez₁ = 0.1587z₂ = 0.9525Find the differencez₂ - z₁ = 0.9525 - 0.1587 = 0.7938The matching choice is A
Answer:
0.7938
Step-by-step explanation:
The given graph is a normal distribution curve.
If a continuous random variable X is normally distributed with mean μ and variance σ²:
[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]
Given:
mean μ = 100standard deviation σ = 15[tex]\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}[/tex]
Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.
Method 1
Using a calculator:
[tex]\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}[/tex]
Method 2
Converting to the z-distribution.
[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]
[tex]x=85 \implies Z_1=\dfrac{85-100}{15}=-1[/tex]
[tex]x=125 \implies Z_2=\dfrac{125-100}{15}=1.67[/tex]
Using the z-tables to find the corresponding probabilities (see attachments).
[tex]\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}[/tex]
the histograms show the results of three simulations of a sampling distribution of a sample mean. for each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. the value of n was different for each of the three simulations.
The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
A histogram is a bar graph-like representation of data that groups a range of classes into columns along the horizontal x-axis. The vertical y-axis represents the number count or percentage of occurrences in the data for each column. Columns can be used to visualized as patterns of data distributions.
Lesser the value of n larger the variablity.
Arranging from the least value of n to the naximum value, the order is A, C, B
Therefore, The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
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What is the ratio of the number of days in the week that do not begin with the letter "T" to the number of days in the week that do begin with the letter "T"? (1 point)
a
7 over 2
b
2:5
c
2 to 7
d
5 over 2
Answer:
i believe it is b)
the no. of days beginning with T (2)
the no. of days not starting with T (5)
Which expression can be used to show a roster of twenty-four players divided into four teams?.
A roster of twenty-four players divided into four teams can be represented by the expression 24/4.
Given
24 players total
(4) teams total.
This can be expression as = 24 / 4.
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What are the different types of cubicles?.
5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles
Dedicated Cubicles: A professional cubicle is typically mid-sized and can combine various cubicle designs to improve output across a wide range of vocations.Cubicles for private offices: For some people, private office cubicles are the best option. These types of cubicles are typically designed for executive cubicles rather than the plainer designs used for the majority of workers employing drywall and flat materials."L" shaped: These sectional or "L" shaped cubicles can greatly influence the number of diverse looks your cubicle collection can take on. Of course, this view is superior to cubicle stations with three or four sides everywhere.Circular Cubicles: A circular cubicle is another novel feature of the workplace. These can introduce a fresher perspective that is fashionable, a sight that is not typically present in the majority of offices today.High-Walled Cubicles: The majority of workstations kinds can be categorized according to the heights of their panels and walls, which directly affects the amount of employee privacy your business will provide.
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In hypothesis testing, the critical value is O a. the probability of a Type II error b. the same as the p-value O c. the probability of a Type I error O d. a number that establishes the boundary of the rejection region
In hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
The hypothesis testing is defined as the process of collecting the data and using that as inference draw the calculation about the population parameter.
The reject region of the hypothesis testing is defined as the set of values for the test statistic for which the null hypothesis is rejected.
Therefore, the critical value is a number that establishes the boundary of the rejection region of the graph
Hence, in hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
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three less than eight times a number is at least 15
The value of Three less than eight times a number is at least 15 is x≥6
What is meant by mathematical equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or explain the overall situation, this is known as an equation.
Given ,
8x
3 less goes to 8x-3
then there is at least 15 which changes to
8x-3≥15
Then solve for x:
add 3 to the sides--> 3x≥15+3
3x≥18
Divide both of the sides by 3
x≥6
Therefore the value of three less than eight times a number is at least 15 is x≥6
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Is a vertical and horizontal line proportional or non proportional?
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
order = 8p
What is the sum of all positive integers that have twice as many digits when written in base $2$ as they have when written in base $3$? Express your answer in base $10$.
2 in base 10 =10 in base 2 = 2 in base 3
8 in base 10 =1000 in base 2 = 22 in base 3.
2 + 8 = 10 the sum of positive integers.
The least common multiple of $1!+2!$, $2!+3!$, $3!+4!$, $4!+5!$, $5!+6!$, $6!+7!$, $7!+8!$, and $8!+9!$ can be expressed in the form $a\cdot b!$, where $a$ and $b$ are integers and $b$ is as large as possible. What is $a+b$?
LCM[1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800. This can be written as:
1. 10! = 1 + 10 = 11, which is a + b
Sum of all positive integers having twice as many digits when written in base $2$ as they have when written is base $3$ is 10.
This is because the only two integers which fits the constraint are 2 and 8,
2 in base 10 =10 in base 2 = 2 in base 3
8 in base 10 =1000 in base 2 = 22 in base 3.
The result of the expression $a+b$ is 11
This is because the LCM of [1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800
Which can be written as : 1. 10! = 1 + 10 = 11
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A lamina occupies the region inside the circle x2 + y2 = 18y but outside the circle x2 + y2 = 81. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
If the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
Given that,
The area inside the circle where x² + y² = 18y and outside the circle where x² + y² = 81 is occupied by a lamina.
We have to find if the density at any place is inversely proportional to its distance from the origin, locate the center of mass.
We know that,
Take the equation
x² + y² = 18y
x² + y² - 18y=0
Adding and subtracting 9².
x² + y² - 18y+ 9²-9²=0
x² + y² - 18y+ 9²=9²
x² + (y-9)²=9²
Which is a circle of radius 9 and center (0,9), And now the second equation
Now,
x²+y²=81
Which is a circle with radius 9 and center (0,0).
We can plot the curves in the picture we can see.
The density will be evenly distributed around the lines x=0 and y=4.5, which are the lines of symmetry, in a more complicated scenario where we would need to utilize integration to identify the Center of Mass.
Therefore, if the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
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2(x - 2) = -2
solve for x.
Answer:
x = 1
Step-by-step explanation:
2(x - 2)= -2
2x - 4 = -2
2x = 2
x = 1
Answer:
x = 1
Step-by-step explanation:
2(x - 2) = -2
Solve for x
Divide each side by 2
2/2(x - 2) = -2/2
x-2 = -1
Add 2 to each side
x - 2+2 = -1+2
x = 1
(10 points) suppose two fair dice are rolled. find each probability of getting (a) a sum of 5 or sum of 7 (b) the first die shows a 3 or the sum of the result is 6 or 8
The required probability of a sum of 5 or sum of 7 and the first die shows a 3 or the sum of the result is 6 or 8 are 5/18 and 1/18 receptively.
What is probability?Probability is just the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions administered by likelihood is called statistics.
According to given data:Two fair dice are thrown then the number of possible way is 6×6 = 36
a) a sum of 5 or sum of 7 :-
The total possible way for dice occurs sum 5 or sum 7 is (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 4), (3, 4), (4, 3), (5, 2), (6, 1).
So, the total number possible way for dice occurs sum 5 or sum 7 = 10.
Probability = 10/36 = 5/18
Hence, the probability is 5/18.
b) The first dice shows 3 or the sum of the result is 6 or 8 :-
As, first dice shows 3 we have fixed 3 in first dice or results sum is 6 or 8 then second dice possibilities only consist two number either 3 or 5,
So, total possible ways for first dice shows 3 or sum of result is 6 or 8 is (3, 3), (3, 5).
There are only two ways,
Therefore, probability = 2/36 = 1/18
Hence, the probability is 1/18.
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A regular hexagonal prism is cut by a plane parallel to its base.
What is the shape of the cross section?
rectangle
regular hexagon
irregular hexagon
trapezoid
please help me
Answer:
regular hexagonStep-by-step explanation:
if a regular hexagonal prism is cut by a plane parallel to its base the shape of the cross section will be a regular hexagon(BH 10.27) As in Exercise 36 from Chapter 3, there are n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates, A and B. Each voter chooses randomly whom to vote for, independently and with equal probabilities (a) Use a Normal approximation (with continuity correction) to get an approximation for the probability of a tie, in terms of Φ. (b) Use a first-order Taylor expansion (linear approximation) to the approximation from Part (a) to show that the probability of a tie is approximately 1/Ven, where c is a constant (which you should specify).
We have given a election data of n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates, A and B. Thus,
a) Using Normal approximation, the probability of tie the election is φ (1/√n) - φ(-1/√n) in terms of φ
b) Using Talyor expansion, the probability of a tie is approximately c/√n where c = √2/π.
We have given that,
Total number of voters in an election = n where n is large and even .
Number of candidates who elected the election
= 2 = { A,B}
Each voter choose randomly one of both independently.
a) Using Normal approximation we have calculate to the probability of a tie, in terms of Φ.
n is a large even number
let X be a random variable of number of votes
Tie will occur when X = n/2 , here p = 1/2
X ~ Bin (n,1/2) = N (n/2 , n/4)
P(X = n/2) = P(n/2 - 1/2 < X < n/2+1/2)
= P(-1/2/(sqrt(n/4) < Z< 1/2/(sqrt(n/4))
= P(-1/sqrt(n) <Z< 1/sqrt(n))
= φ (1/√n) - φ(-1/√n)
b) Using the Taylor's Expansion in answer of part(a)
φ (x) = 1/√2π ( x - x³/6 + x⁵/40 - x⁷/336+---)
= φ (1/√n) - φ(-1/√n)
= 1/√2π (1/√n - (-1/√n))
= 1/√2π ( 2/√n)
= √2/π ×1/√n = c/√n
where , c = √2/π
Hence, the required probability is c/√n.
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