The sum of the expressions 12√23x¹³ + 14√23x¹³ is in its simplest form if x > 0 is 26x⁶√23x
Calculating the sum of the radical expressionFrom the question, we have the following parameters that can be used in our computation:
12\sqrt{23x^{13}}+14\sqrt{23x^{13}}
Express the summation expression, properly
So, we have
12√23x¹³ + 14√23x¹³
Next, we add the terms of teh expression
Using the above as a guide, we have the following:
12√23x¹³ + 14√23x¹³ = 26√23x¹³
Take the square root of x¹³
12√23x¹³ + 14√23x¹³ = 26x⁶√23x
The above expression is in its simplest form if x > 0.
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Find the missing probability.
P(B)=1/4P(AandB)=3/25P(A|B)=?
The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.
P(B) = 1/4
P(A and B) = 3/25
The conditional probability is used to find the P(A|B):
P(A|B) = P(A and B) / P(B)
Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.
By substituting the given values in the given probability, we get:
P(A|B) = (3/25) / (1/4)
Divide the fraction and multiply it with its reciprocal:
P(A|B) = (3/25) * (4/1)
P(A|B) = 12/25
Therefore, we can conclude that the missing probability is P(A|B) is 12/25.
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The complete question is:
Find the missing probability.
P(B)=1/4P
(AandB)=3/25P
P(A|B)=?
Which point would be a solution to the system of linear inequalities shown below?
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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What is the definition of postulate? A. an assumption, presumed to be true, that is used as the basis for a logical argument B. a statement that has been shown to be false by logical argument C. a statement that has been shown to be true by logical argument D. a statement, known to be false, that is used as the basis for a logical argument
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
We have,
A postulate is a statement or proposition that is accepted as true without proof.
It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.
In mathematics,
Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.
They are often used as the starting point for deriving other mathematical concepts and theorems.
Postulates are also known as axioms or assumptions.
Thus,
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
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1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.
these algebraic expressions are also composed of mathematical operations. These operations includes;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom the information given, we have that;
1/ 4(8 - 6x + 12)
expand the bracket, we have;
Add the like terms
1/4(20 - 6x)
now, multiply the values, we have;
20 - 6x/4
Divide by the denominator
5 - 3x/2
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The complete question:
Simply the expression:
1/ 4(8 - 6x + 12)
I do not understand why the answer is a) for this equation: y'=2y+x. I assumed that the answer is c) or a), because numbers in the equation are positive, but I'm not sure this is the correct method here
The slope field for the differential equation would be D . Graph D .
What are slope fields ?A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .
The length of line segments represents the magnitude, while the direction indicates the sign of the slope.
The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.
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please help me solve for x image is attached ive been stuck on it for a few days now
The value of x will be 10.
Given a triangle we need to set a proportion to solve for the value of x,
Therefore, according to the definition of the similar triangles,
x / 5 = 15+5 / x
x² = 5 × 20
x² = 100
x = 10
Hence the value of x will be 10.
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4 3/8 + 5 1/2= in fractions
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
I NEED HELP WITH STATISTICS
The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.
Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.
Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.
Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.
Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.
Correct options are A and B.
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The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:
Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.
How the number is determined:Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:
Order: Zocor 40 mg po qd for 60 days
= 60 tabs since it is once per day (qd)
Total mg = 2,400 mg (40 mg x 60 tabs)
On hand: 20 mg tabs
Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs
Total mg = 2,400 mg (20 mg x 120 tabs)
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Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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Is this negative and odd or even and positive or negative and even and positive and odd?
Answer:
Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load
Step-by-step explanation:
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Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
The amount of poster board left over will be 1275 square inches, the equation used is A = (b₁ + b₂)h/2.
To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,
we need to find the area of the trapezoid window and subtract it from the area of the poster board.
The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.
Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.
Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.
To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.
Finally, we subtract the area of the window from the area of the poster board using the equation:
1500 - 225 = 1275 square inches.
Therefore, the amount of poster board left over will be 1275 square inches.
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The complete question is
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
Can anyone help me w tvis
The number of weeks that the puppies weigh the same amount will be A. 6 weeks.
The equation that has no solution is A. 13 - 7x = -7x + 13.
The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.
How to calculate the number of weeksPuppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.
After how many weeks will the puppies weigh the same amount will be calculated thus:
4 1/5 + 3/4x = 5 2/3 + 1/2x
4.2 + 0 75x = 5.67 + 0.5x
Collect the like terms
5.67 - 4.2 = 0.25x
Divide
x = 1.47 / 0.25
x = 6
Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.
It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.
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Need help, show work please
Using the first two points we can get an exponential model:
[tex]y = (225/23)*(23/15)^x[/tex]
How to find the exponential equation?
The general exponential equation can be written as:
[tex]y = A*(b)^x[/tex]
We can replace any two values of the table to get the system of eqautions:
[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]
Taking the quotient between the second and the first equation we get:
[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]
Replacing that on the first equation we will get:
[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]
Then an exponential model is:
[tex]y = (225/23)*(23/15)^x[/tex]
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Round 73,609 to the nearest thousand
Answer:
74,000
Step-by-step explanation:
use intelligence
(4,2)
I
5
(x, y)
Given that the circle to the left has a center at
point (4,2), and point (x, y) is on the
circle,write the equation for the distance (x, y)
is away from the center. Rearrange this
equation so it contains no radicals.
The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²
What is the general form of the equation of a circle?The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a
The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.
The coordinates of the center of the circle, (h, k) = (4, 2)
The radius of the circle, r = a = 5
The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;
Equation of a circle; (x - h)² + (y - k)² = a²
Equation from the center; (x - 4)² + (y - 2)² = 5²
Where;
5 = The radius, a = The distance from the center of the circle
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What are the solutions to the system of equations graphed?
Answer:
(- 2, 0 ) , (1, - 3 )
Step-by-step explanation:
the solutions to the system of equations are at the points of intersection with the curve and the straight line.
points of intersection are at (- 2, 0 ) and (1, - 3 ) , then
solutions are (- 2, 0 ) , (1, - 3 )
Convert from radians to degrees.
1/4π
1/4π radians is approximately equal to 45 degrees.
To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.
Degrees = Radians × 180/π.
Therefore, to convert 1/4π radians to degrees, we have:
Degrees = (1/4π) × (180/π) ≈ 45°
Hence, 1/4π radians is approximately equal to 45 degrees.
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Mary is building a fence around her triangular garden. How much fencing, in feet, does she
need? Round to the nearest foot.
AC=13 ft
C=40°
B=49°
The length of fencing needed around her triangular garden is 41 feet.
What is a triangle?A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.
For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.
So that;
A + B + C = 180^o
A + 49 + 40 = 180
A = 180 - 89
= 91
A = 91^o
Applying the sine rule, we have;
a/Sin A = b/Sin B = c/Sin C
a/Sin A = b/Sin B
a/Sin 91 = 13/ Sin 49
aSin 49 = 13*Sin 91
= 12.998
a = 12.998/ 0.7547
= 17.22
a = 17 ft
Also,
b/Sin B = c/Sin C
13/Sin 49 = c/ Sin 40
cSin 49 = 13*Sin 40
= 8.3562
c = 8.3562/ 0.7547
= 11.0722
c = 11 feet
Thus the amount of fencing required = 13 + 17 + 11
= 41
The fencing required is 41 feet length.
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How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points
10. Kipp constructed a pentagonal pyramid for his social studies report. The base had an area of 12 cm². It took 48 cubic centimeters of clay to make his model. Find the height of the pyramid.
We can use the formula for the volume of a pentagonal pyramid to solve this problem:
Volume = (1/3) × Base Area × Height
We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:
48 = (1/3) × 12 × Height
Multiplying both sides by 3 gives:
144 = 12 × Height
Dividing both sides by 12 gives:
Height = 12
Therefore, the height of the pentagonal pyramid is 12 centimeters.
Select the matrix that represents the parallelogram
The correct matrix representation is; [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,
Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)
Given here the points are P₁(1, 3) and P₂(5, 2)
Thus, by the coordinates of the two vectors, we can represent the matrix ;
[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Hence, Option A) is the correct answer.
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What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]
[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]
[tex]\sf V = \dfrac{433.44 }{3}[/tex]
[tex]\sf V = 144.48 \ cubic \ feet[/tex].
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
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Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.
This can be written as S = 400+35v , where v is the number of vacuums sold.
If Carlos earns $1590 for a week's work, how many vacuums did he sell?
Answer:
34
Step-by-step explanation:
1. Plug in the week's salary into the formula
S=400+35v
1590=400+35v
2. Solve for v.
1590=400+35v
Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.
1190=35v
Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.
34=v
please help me important question in image
Segment BF is 36 will be the accurate statement.
Similarity theorem of triangleA triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.
From the given triangle, the following expression is true:
EC/FC = AC/BF+FC
Substitute the given parameters into the formula to have:
20/30 = 24+20/BF+30
20/30 = 44/BF+30
2/3 = 44/BF + 30
2(BF+30) = 132
2BF + 60 = 132
2BF = 132 - 60
2BF = 72
BF = 36
Hence the correct statement will be that segment BF is 36
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the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
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I need help please guys
The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Here, we have,
The designated sum can replace either row. Consult your curriculum materials for the intent.
Here, we'll replace row 2 with the sum.
3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)
After the row operation replaces the second row, the augmented matrix is ... [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Hence, The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
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A small toy rocket is launched from a 48-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t2 +0t + 48. How long will it take the rocket to hit the
ground?
t =
Okay, here are the steps to solve this problem:
1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48
2) We want to find the time (t) when the rocket hits the ground (h = 0)
3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0
4) Factor the left side: - 3(t2 - 0t) + 48 = 0
5) Solve for t2 - 0t: t2 - 0t = 16
6) Add 0t to both sides: t2 = 16 + 0t
7) Take the square root of both sides: t = 4
Therefore, the time for the rocket to hit the ground is 4 seconds.
So in this case, t = 4
Let me know if you have any other questions!
Answer:
4 seconds.
Step-by-step explanation:
When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]
Now set this equal to 0
[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.
[tex]-48 = -3t^2[/tex]
[tex]16 = t^2[/tex]
From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.
Hope this helps
There are 3 feet in a yard. How many centimeters are in a yard?
pls solve this question its a nest pyq
After considering the given interval we reach the conclusion that the coefficient of t² is 1/2(3w² - 1), under the condition that the given expression is [tex](1-2 t w+t^{2})^{-1/2}[/tex] with range of (t<<1)
To evaluate the value for the given expression we have to apply the principles of binomial theorem
Then
[tex](1-2 t w+t^{2})^{-1/2} = (1 + (-2 t w + t^{2})/2 + (-2 t w + t^{2})^{2/8} + (-2 t w + t^{2})^{3/16} + ...)[/tex]
= 1 - t w + 3/8 * t² * w² - 5/16 * t³ * w³ +
The coefficient of t is the coefficient of the first term with a power of t.
Therefore, the coefficient of t is 1/2(3w² - 1).
The binomial theorem refers to the statement regarding any positive integer n, the nth power of the sum of two numbers a and b could be expressed as the sum of n + 1 terms of the form. The binomial theorem is applied in algebra and probability theory.
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