Using quadratic formula we get, Part A: The solutions for x are: x = (3 + √(57))/(3/2) and x = (3 - √(57))/(3/2). Part B: The first system solution is: ((3 + √(57))/(3/2), -(76 + 6√(57))/(9) + 5) and second system solution is: ((3 - √(57))/(3/2), -(76 - 6√(57))/(9) + 5)
Part A: To solve for x, we need to first rearrange the equation so that all terms are on one side of the equal sign. Adding (1/4)x^(2) to both sides of the equation:
-x^(2) + (1/4)x^(2) + 3x + 14 = 5
Next, combining like terms:
-(3/4)x^(2) + 3x + 14 = 5
Now, subtracting 5 from both sides:
-(3/4)x^(2) + 3x + 9 = 0
Finally, using quadratic formula to solve for x:
x = (-3 ± √(3^(2) - 4(-3/4)(9)))/(2(-3/4))
Simplifying:
x = (-3 ± √(57))/(2(-3/4))
x = (-3 ± √(57))/(-3/2)
x = (3 ± √(57))/(3/2)
Part B: To determine the system solutions, we need to plug in the values of x into the original equation and solve for y. For the first solution:
y = -(1/4)((3 + √(57))/(3/2))^(2) + 5
y = -(1/4)((9 + 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 + 6√(57))/(9/4)) + 5
y = -(19 + (3/2)√(57))/(9/4) + 5
y = -(76 + 6√(57))/(9) + 5
For the second solution:
y = -(1/4)((3 - √(57))/(3/2))^(2) + 5
y = -(1/4)((9 - 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 - 6√(57))/(9/4)) + 5
y = -(19 - (3/2)√(57))/(9/4) + 5
y = -(76 - 6√(57))/(9) + 5
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A carpenter builds a rectangular bookcase that is 115 cm long and 76 cm tall. The carpenter uses two braces along the diagonals to support the bookcase.
What is the length of the one of the braces, to the nearest tenth of a centimeter?
Answer: 137.8 cm
Step-by-step explanation:
Using Pythagorean's Theorem, a² + b² = c², we can find the length of one of the braces.
Plug in your values:
115² + 76² = c²
13225 + 5776 = c²
19001 = c²
√19001 = c
c ≈ 137.8 cm
The braces are 137.8 cm long.
Hope this helps!
How can you show that a 20% off coupon and a 10% off coupon is not the same as a 30% off coupon?
Answer:
If applying the 20% off coupon and the 10% coupon it would be separate. This would be different than a 30% coupon
Step-by-step explanation:
Let's say you are taking 20% off of $100, doing that would reduce the price to $80 because you took off $20, after this you would apply the 10% off coupon to the $80, your total would be 72 now because 10% of 80 is 8. The 20% Coupon and the 10% coupon stacked would bring your total to $72. If you flat out took 30% out of 100 dollars you would be left with $70 compared to the $72 that you got with the 20% coupon and the 10% coupon.
20% + 10% would remove less than a 30% coupon because after applying the 20% coupon, your 10% coupon would remove less because of the lower number being subtracted. Hope this helps
Solve the inequality. Write the solution set in interval notation.
19(7 − x) ≥ 88 − 14x
The solution set in interval notation, 19(7 − x) ≥ 88 − 14x, is (-∞, 9]
To solve the inequality 19(7 - x) ≥ 88 - 14x, we will first distribute the 19 on the left side of the inequality and then combine like terms to isolate the variable x.
19(7 - x) ≥ 88 - 14x
133 - 19x ≥ 88 - 14x
-5x ≥ -45
x ≤ 9
Now, we can write the solution set in interval notation. Interval notation uses brackets or parentheses to indicate the endpoints of an interval. Brackets indicate that the endpoint is included in the interval, while parentheses indicate that the endpoint is not included.
Since x is less than or equal to 9, the solution set in interval notation is (-∞, 9]. This means that any value of x less than or equal to 9 will satisfy the inequality.
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What??????????????????????????????????????
The mean of the values will be 9.4, the median will be 3 points and the mode will be 4
How to calculate the mean,median and the modeIt should be noted that mean in mathematics simply means the total added values of all the data in a set of divided by the number of days in a set.
The mean of the values will be:
= (10 + 8 + 11 + 12 + 6) / 5
= 47 / 5
= 9.4
The median of the set of numbers is the number on the middle when arranged ascending or in a descending manner. This is 3 points. The mode is 4.
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The table represents a quadratic function C(t).
t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(x − 3)2
C(t) = (x − 3)2
C(t) = −x2 + 3
C(t) = x2 + 3
The value for the quadratic equation is C(t) = t² + 3.
What is vertex?When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.
The standard form of the quadratic function is given as:
C(t) = at² + bt + c
Using different values of t from the table we have:
a(-2)² + b(-2) + c = 7
a(-1)² + b(-1) + c = 4
a(0)² + b(0) + c = 3
Simplifying the equations we have:
4a - 2b + c = 7
a - b + c = 4
c = 3
Substituting the value of c = 3 in equation 2:
a - b = 1
Further solving the equation for a and b we have:
a = 1
b = 0
Hence, the equation for the quadratic equation is C(t) = t² + 3.
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Someone PLEASE PLEASEE help me asap i dont have time. I need the answers today please im really struggling right now. 50 points to answer. Please no wrong answers or guesses.
(-2, 3)
(2, -3)
(-3, -2)
(3, -2)
it definitely should be (-2,3)
Ann et Barbara comparent leurs âges. Elles trouvent que Barbara a l'âge qu'avait Ann lorsque Barbara avait l'âge qu'avait Ann quand Barbara avait la moitié de l'âge qu'a Ann aujourd'hui. Si la somme de leurs âges actuels est égale à 44 ans, quel est l'âge d'Ann aujourd'hui ?
Answer:
Traduction:
Ann and Barbara are comparing their ages. They find that Barbara is the age that Ann was when Barbara was the age that Ann was when Barbara was half the age that Ann is today. If the sum of their current ages is 44 years, what is Ann's age today?
Soit x l'âge d'Ann aujourd'hui.
On sait que l'âge de Barbara est x - (x/2) = x/2 (car Barbara avait la moitié de l'âge d'Ann lorsque l'écart d'âge entre elles était de x/2).
On sait également que l'âge d'Ann lorsque Barbara avait x/2 ans est (x/2 - x) = -x/2 ans de moins que son âge actuel.
Donc, l'âge d'Ann lorsque Barbara avait l'âge qu'avait Ann à ce moment-là est x - (x/2) - (-x/2) = 2x/2 = x ans.
Ainsi, l'âge de Barbara aujourd'hui est également x ans.
La somme de leurs âges actuels est 44 ans, donc :
x + x = 44
2x = 44
x = 22
Donc, l'âge d'Ann aujourd'hui est 22 ans.
Austin invested $92,000 in an account paying an interest rate of [tex]5\frac{7}{8}[/tex]
% compounded daily. Josiah invested $92,000 in an account paying an interest rate of [tex]5\frac{3}{4}[/tex] % compounded continuously. After 17 years, how much more money would Austin have in his account than Josiah, to the nearest dollar?
Austin would have approximately $2,108 more than Josiah.
What is approximately?Approximately means "nearly" or "close to" an exact amount or number. It is often used to describe a quantity that is not exact, but can be estimated or rounded off. For example, "There were approximately 25 people in the room" means that the number was close to 25, but not necessarily exactly 25.
Using the formula A = P(1 + r/n)^nt, where P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the number of years, we can calculate the amount of money Austin and Josiah would have in 17 years.
For Austin: A = $92,000(1 + 5.875/365)^365*17 = $120,308.05
For Josiah: A = $92,000(1 + 0.0575)^17 = $118,200.43
Therefore, Austin would have approximately $2,108 more than Josiah.
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Find the area of this composite shape. Include correct units.
Show all your work.
The area of the figure composed of a rectnagle and a triangle is 128in².
What is the area of the composite figure?The figure in the the image is composed of rectangle and a triangle.
The area of a rectangle = length × width
Area of a triangle = 1/2 × base × height
Hence;
Area of the composite figure will be;
A = area of a rectangle + area of a triangle
From the image;
Length of the rectangle = 12 inWidth = 9 inBase of the triangle = 9 - 4 = 5inHeight = 20 - 12 = 8inNow, we solve for thr area of the composite figure.
A = area of a rectangle + area of a triangle
A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )
A = ( 108in² ) + ( 20in² )
A = 128in²
Therefore, the total area of the figure id 128 squared inch.
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What is the constant of proportionality between
�
yy and
�
xx in the graph?
The response to the given question would be that Hence, 2 is the proportionality constant between y and x.
what is proportionality?Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.
We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.
The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.
Hence, 2 is the proportionality constant between y and x.
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Friends
Jennifer and Jose are planning to meet at the
playground. Jennifer is already there, but her
friend Jose needs to take the shortest
path possible on his e-bike. Jose has two ways
he can go:
Option 1: he can follow the roads getting to the
park- first heading south 3 miles, then heading
west 4 miles.
Option2: he can get there by cutting through
some open fields and riding directly to the park.
Draw a diagram to illustrate the two options.
Apply Pythagorean Theorem to find the total
distance for option 2 and make a
recommendation. Explain which option is
shorter any by how much
The shortest distance Jose can ride to park is 5 miles.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, Jose can follow the roads getting to the park- first heading south 3 miles, then heading west 4 miles.
Let the shortest root Jose can choose be x miles.
By using Pythagoras theorem, we get
x²=3²+4²
x²=9+16
x²=25
x= 5 miles
Therefore, the shortest distance is 5 miles.
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d the product of the following two matrices. [[-2,0],[1,-1]][[-1,0,5,1,0],[1,-1,3,1,-1]]
[[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]]
The product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
To calculate the product of two matrices, multiply each row of the first matrix with each column of the second matrix. Begin by multiplying the first row of the first matrix [-2, 0] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values -2, 0, 10, 2, 0 which will be the first row of the product matrix.
Next, multiply the second row of the first matrix [1, -1] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values 1, -1, 9, 2, -1 which will be the second row of the product matrix.
Therefore, the product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
The given matrices are:
[[-2, 0],
[1, -1]]
[[-1, 0, 5, 1, 0],
[1, -1, 3, 1, -1]]
To find the product of two matrices, we need to follow a few steps:
Multiply the first row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the first row of the first matrix by the second column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the second column of the second matrix, and then add the results.
By following these steps, we can obtain the product of the matrices. So, we can proceed as follows:
-2×(-1) + 0×1 = 2
-2×0 + 0×(-1) = 0
1×(-1) + (-1)×1 = -2
1×0 + (-1)×(-1) = 1
Hence, the product of the given two matrices is:
[[2,0,10,2,0],
[-2,2,-8,-2,2]]
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In the figure shown, lines f and g are parallel. Select all angles that are congruent to angle 1.
Answer:
Step-by-step explanation:
I can't see anything.
Write a function rule for "The output is three less than the input x ." y=
Answer:
x to the power of 67000 to the 5th power.
Step-by-step explanation:
The length of a rectangle is represented by 6x + 5. The width of the rectangle is represented by 3x. The perimeter is 100 centimeters. Which equations represent the perimeter? Choose all the correct answers
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
simply because the perimeter means to go along every side the shape has.
I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.
so, that means for us
2(6x + 5) + 2×3x = 100
12x + 10 + 6x = 100
18x = 90
x = 90/18 = 5
solve question please
Answer:
kindly update the question
In the triangle shown below AB=BC=10
and AC=12.
To
A) 0.4
B) 0.6
C) 0.8
D) 1.2
10
B
12
What is the value of sin ?
10
#
0
point
The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.
What is Pythagorean theorem?
The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.
The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.
The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.
The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.
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Why is |x| + 2 >|x|.
|x| + 2 is always greater than |x| because |x| is always positive or zero.
What is Absolute Value of a Number?Absolute value of a number is defined as the positive value of the number. even the number is negative, the absolute value is the positive value of that number.
Consider |x| for any number x.
The possibilities of x are positive number, zero or negative number.
If x is a positive number, |x| is also the same positive number.
2 adding to |x| is also positive number.
So |x| + 2 > |x|
If x is a negative number, |x| is the positive value of that negative number.
So |x| + 2 > |x|.
If x is 0, the |x| = 0
|x| + 2 = 0 + 2 = 2 > |x| = 0
Hence in all cases, |x| + 2 > |x|.
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You are planning a vacation. The hotel you are going to stay at charges $135 per night. This can be represented by the function p(x) = 135x. The car rental company charges a $45 insurance fee plus $79 per day. This can be represented by the function p(x) = 45 + 79x. Formulate a function to represent the total charges for your hotel and car rental.
A,) p(x) = 259x
B,) p(x) = 135(79x + 45)
C,) p(x) = 45 + 214x
D,) p(x) = 45(135x + 79x)
The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x
What is the equation?In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.
Also, car rental company charges a $45 insurance fee plus $79 per day.
It can be represented by the function p(x) = 45 + 79x.
Daily rental fee = $135 per night,
Write the equation for the total fees
p(x) = 45 + 214x
Thus, x represents the number of days.
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Feb 23, 11:43:37 AM Write the augmented matrix for the following system of equations. -2+5x=-2z 4y-6+8z+3x=0 0=6y-6x-3z
The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]
An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.
To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:
5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0
Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:
[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]
Finally, we can combine these rows into a single matrix to get the augmented matrix:
[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]
This is the augmented matrix for the given system of equations.
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How many days is in February
Answer: there 28/29 days
Step-by-step explanation:
Answer: 28/29
Step-by-step explanation:
28 Days
29 Days for a leap year
A ticket for the spring musical is $4.50.
Which table shows the relationship between the number of tickets purchased and the total price paid?
OA
B.
Tickets Total
Purchased Price
1
$4.50
2
$9.00
3
$13.50
$18.00
Tickets Total
Purchased Price
4
1
2
3
4
$4.50
$9.00
$18.00
$36.00
C.
D.
Tickets Total
Purchased
Price
$4.50
$9.00
$14.50
$19.00
1
2
3
4
Tickets
Purchased
1
2
3
4
Total
Price
$4.50
$8.00
$12.50
$16.00
Answer:
Step-by-step explanation:
1 ticket costs 1 × $4.50 = $4.50
2 tickets cost 2 × $4.50 = $9.00
3 tickets cost 3 × $4.50 = $13.50
4 tickets cost 4 × $4.50 = $18.00
The first table is the only one that matches these values.
3x+4y=36
Y=1/2x+8
Find x and y
Answer:4/5 and y = 9/5.
Step-by-step explanation:We can start by substituting the second equation into the first equation, replacing y with 1/2x+8:
3x + 4(1/2x+8) = 36
Simplifying, we get:
3x + 2x + 32 = 36
Combining like terms, we get:
5x + 32 = 36
Subtracting 32 from both sides, we get:
5x = 4
Dividing both sides by 5, we get:
x = 4/5
Now that we have found x, we can substitute it back into the second equation to find y:
y = 1/2x + 8 = 1/2(4/5) + 8 = 9/5
Therefore, the solution to the system of equations is x = 4/5 and y = 9/5.
7. What are the coordinates of the intersection point? Does this match your answer from question 4? (2 points: 1 point each question)
8. Answer the original questions. (2 points: 1 point each question)
a) How long is each individual act?
b) How long is each group act?
9. Discussion.
Discuss the reasonableness of your answers. (2 points: 1 point for each part)
a) Is the answer you found reasonable? Does it seem like enough time?
b) Would a negative solution such as (–5, –10) be acceptable in this situation? Why or why not?
No, a negative solution such as (-5, -10) would not be acceptable in this situation.
What is coordinates?Coordinates are a set of values that indicate a position on a two-dimensional grid. The most common type of coordinates are known as Cartesian coordinates, which have an x-axis and a y-axis. Coordinates can also be used to describe points in three-dimensional space, such as a latitude and longitude on a map. Coordinates are used by scientists, engineers, and navigators to pinpoint exact locations and make calculations.
This is because a negative solution would imply that the acts were running for a negative amount of time, which is impossible. Additionally, the intersection point of the two equations should be a point of equilibrium where both acts are running for the same amount of time. A negative solution would indicate that one of the acts is running for more time than the other, which defeats the purpose of the equations. Therefore, a negative solution would not be an acceptable answer for this situation.
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Which formula can be used to determine the n ^ (th) term of the arithmetic sequence 6, 15, 24, 33, 42;
A f(n) = - 3 - 9n;
B f(n) = - 3 + 9n;
C f(n) = 6 - 9n;
D f(n) = 6 + 9n
The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)
What is arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The nth term of a n arithmetic sequence is given as:
a(n) = a+(n-1)d
where a is the first term and d is the common difference
a = 6
d = 15-6 = 9
a(n) = 6+( n-1) 9
= 6+9n -9
a(n) = 9n-3
a(n) = 3(3n-1)
therefore the formula for the nth term of the sequence is 3(3n-1)
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Given the equations of two lines, describe how to determine if the lines are parallel.
Answer:
For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;
To determine if two such straight lines are parallel, then you should check for the following conditions :
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.
if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.
for instance,
let's say we have two lines :
x + 2y - 4 = 0,
2x + 4y - 12 = 0;
Now to check if they are parallel you simply check if the condition for parallel lines is met or not.
for these two lines :
a₁ = 1 , b₁ = 2, and c₁ = -4;
a₂ = 2, b₂ = 4, and c₂ = -12;
evaluating the values in the condition we have :
[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{4}[/tex] ≠[tex]\frac{-4}{-12}[/tex] ;
since the condition for parallel is true for these two lines, we can conclude they are parallel.
Maria drops a stone from the top of a building. The stone falls 2. 0 meters in the 1st second. If it has fallen 149 meters by the 50th second. How many meters would the stone have fallen after 10 seconds?
If the stone dropped by Maria falls 2 meter in 1st second, then the stone would have fallen 30 meter after 10 seconds.
The distance that the stone falls in the first second is = 2 meters;
The distance that the stone falls in the 50th second is = 149 meters;
So, the rate of fall of the stone can be calculated as:
⇒ (149 - 2)/(50 - 1);
⇒ 147/49;
⇒ 3.
So , the stone is falling at the rate of 3 meter per second,
The distance fall by the stone after 10 second can be calculated as :
⇒ 10×3
⇒ 30 meter.
Therefore, After 10 seconds the stone would have fallen 30 meter.
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evaluate the expression using scientific notation. Express the result in scientific notation.
(2.5 X 10^-2)(4.2 X 10^6)
The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.
What is scientific notation in mathematics?Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers
Solution for scientific notation according to the information given:
(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶
= 2.5 × 4.2 × 10⁴
= 10.5 × 10⁴
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153
% of
840.78
kg
i need this fast please help :)
Answer:
1286.3934 kg
Step-by-step explanation:
Convert 153% to a decimal:
153 / 100 = 1.53
Multiply 840.78 by 1.53:
840.78 * 1.53 = 1286.3934
The price of drugs for human doses and the animal doses from different pharmacies were gathered. At 1% level, the prices for the animal doses are claimed to be significantly less than the prices for the human doses. Assume that data is normally distributed and the groups have equal variances. The output of the test is given below. For the next questions, please refer to this problem. Using p-value method, form a statistical decision. 1 point a. Failed to reject the alternative hypothesis. b. Reject the null hypothesis. c. Failed to reject the null hypothesis.
d. Reject the alternative hypothesis.
The correct answer is c. Failed to reject the null hypothesis.
Failed to reject the null hypothesis.
Explanation:
In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.
To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.
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