TEST ANSWER
PLS IGNORE
A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute.??t (min) 36 38 40 42 44?Heartbeats 2510 2647 2784 2915 3048??The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of t. (Round your answers to one decimal place.)??
(a) t = 36 and t = 42
(b) t = 38 and t = 42
(c) t = 40 and t = 42
(d) t = 42 and t = 44
Therefore , coordinate problem solution is A) 3140 pulses per minute , B) 2915 beats per minute , C) heartbeat of 2915 beats per minute (D) or 2915.5 beats per minute .
What do coordinates mean?When locating points or other mathematical objects precisely on a region, such as Euclidean space, a coordinate system is a technique that uses one or more numbers or coordinates. Locating a point or item on a the double plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y vectors are used to define a point's location on a 2D plane. a collection of numbers that indicate specific locations.
Here,
The slope method can be used to calculate the patient's heart rhythm after 42 minutes that use the secant line connecting the points with the specified values of t:
Heartbeat change / time change is the trend.
The heart rate can then be estimated using this slope value along with the number for heartbeats at t = 42 minutes.
A)Using coordinates 36, 2510, and 42, 2915 as examples:
Cardiac rate at 42 minutes = 2510 + (42 - 36) * 75 = 3140 Slope = (2915 - 2510) / (42 - 36) = 75
b) Using coordinates (38, 2647) and (42, 2915), respectively:
Cardiac rate at 42 minutes = 2647 + (42 - 38) * 67 = 2915 Slope = (2915 - 2647) / (42 - 38) = 67
c) Applying the values (40, 2784) and (42, 2915):
Heart rate at 42 minutes = 2784 + (42 - 40) * 65.5 = 2915.5 Slope = (2915 - 2784) / (42 - 40) = 65.5
Using coordinates (42, 2915), and (44, 3048), respectively:
Cardiac rate at 42 minutes = 2915 + (42 - 42) * 66.5 = 2915 Slope: (3048 - 2915) / (44 - 42) = 66.5
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How does extending vertex A further to the left of vertex B verify the relationship between sides and angles in triangles?
B
As the length AB increases, the measure of C
help help help!!!!!
Answer:
Step-by-step explanation:
As the length AB increases, the measure of C increases
As the length AB increases, the measure of C increases.
What is an angle measure?An angle is formed when two lines or rays meet at a single point. The common point is referred to as the vertex. The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.
Angles and sides in relation to one another:
The biggest side and angle of any triangle are in opposition to one another.
The smallest side and angle in every triangle are on opposing sides.
The middle side and middle angle are always in opposition to one another in triangles.
When we extend vertex A further to the left of vertex B,
we increase the side length of AB.
As the length AB increases, the measure of opposite angle increases.
Let C be the angle opposite to AB.
Therefore, as the length AB increases, the measure of C increases.
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Costs that remain constant (stay the same) in total dollar amount as the units sold increases are called
A. variable costs
B. product costs
C. mixed costs
D. fixed costs
A Moving to the next question prevents changes to this answer.
Answer: D. Fixed costs
Rent is an example of fixed costs. The amount of rent does not change based on how many items are produced. This is assuming you are not changing the size of the location or expanding to another location.
URGENT Please help!!!!!!
Divide 6.1 x 1020 by 3.2 x 105. Express your answer in scientific notation.
The value of the division of the expression will be; 19.52 x 10^{25}.
How does scientific notations work?The number is written in the form \(a \times 10^b\) where we have \(1 \leq a < 10\)
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.
Scientific notations have some of the profits; Better readability due to compact representation that value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Given the expression as 6.1 x \(10^{20}\) by 3.2 x 10⁵
We have to divide the expression
( 6.1 x \(10^{20}\) ) / (3.2 x 10⁵)
= 19.52 x \(10^{20 + 5}\)
= 19.52 x \(10^{25}\)
Therefore, the value of the division of the expression will be; 19.52 x \(10^{25}\).
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Identify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
The total surface area of the rectangular prism is 94 cm2.
What is surface area?Surface area is the measurement of the total area of a three-dimensional object. It is the sum of all the areas of the faces or surfaces of a 3D shape.
The total surface area of a 3D object is the sum of the areas of all its faces. The formula to calculate the total surface area of a 3D object is:
Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)
Where Length, Width, and Height are the dimensions of the 3D object.
For example, if you have a rectangular prism with Length = 5 cm, Width = 4 cm, Height = 3 cm, then the total surface area is:
Total Surface Area = 2(5 cm x 4 cm) + 2(5 cm x 3 cm) + 2(4 cm x 3 cm)
= 40 cm2 + 30 cm2 + 24 cm2
= 94 cm2
Therefore, the total surface area of the rectangular prism is 94 cm2.
In conclusion, the formula to calculate the total surface area of a 3D object is: Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height). Examples can be used to better understand the concept and apply the formula to solve for the total surface area.
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Is the relation a function? Why or why not?
6.
5. Add 29 and 35. Draw to show
the regrouping. What is the
sum?
Tens
Ones
la
OOOO
Answer:
c
Step-by-step explanation:
because i said so
pls help i need help with this been working fo a bit
\(\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}(y+x)\)
\(\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}x+\dfrac{5}{7}y\)
\(\\ \sf\Rrightarrow \dfrac{6}{7}x+\dfrac{5}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}y\)
\(\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{-14+25}{35}y\)
\(\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{11}{35}y\)
Done!
\( \boxed{\huge \bf \: Question:—}\)
\( \sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} (y + x)\)
\(\boxed{\huge\bf \: Solution:—}\)
\( \boxed{\bf \: Distribute:—}\)
\(\sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} y + \dfrac{5}{7} \: x\)
\(\sf \longmapsto \dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x\)
\( \boxed{\bf \: Combining \: Like \: Terms:—}\)
\(\sf \longmapsto\dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x\)
\(\sf \longmapsto \bigg(\dfrac{6}{7} x + \dfrac{5}{7} x \bigg) \: + \bigg( \dfrac{ - 2}{5} y + \dfrac{5}{7} \: y \bigg)\)
\(\sf \longmapsto \: \dfrac{11}{7} x \: + \dfrac{11}{35} y\)
\(\boxed{\bf \: Answer:—}\)
\( \boxed{\bf \: \dfrac{11}{7} x \: + \dfrac{11}{35} y}\)
Points x and y and points C,D,E and f are shown what is true about points
The true statement is "the line that can be drawn through points D and E is contained in plane Y".
option B is the correct answer
What are the true statements about the point x and y?The points x and y and points C,D,E and f are shown in the figure, the true statement is determined as follows;
We know that, if two points lie in a plane, then the line drawn through the points will contained in the same plane.
The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contained in plane Y.
So, option (A) is NOT correct.
The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contained in plane Y.
So, option (B) is CORRECT.
Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.
So, option (C) is NOT correct.
Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.
So, option (D) is NOT correct.
Thus, the correct option is;
The line that can be drawn through points D and E is contained in plane Y.
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The complete question is below:
Points x and y and points C,D,E and f are shown what is true about points
(A) The line that can be drawn through points C and D is contained in plane Y.
(B) The line that can be drawn through points D and E is contained in plane Y.
(C) The only point that can lie in plane X is point F.
(D) The only points that can lie in plane Y are points D and E
The sum of two real numbers is 8 and their product is 14. What is the sum of their reciprocals?
Answer:
Step-by-step explanation:Let our two numbers be a and b . Then we can see that a+b=8 and ab=15 . Now consider
(a+b)3=a3+3a2b+3ab2+b3 by the binomial expansion. Now we have all the information to solve this, observe since a+b=8 and ab=15 . We have
(8)3=a3+3ab(a)+3ab(b)+b3
a3+b3+3ab(a)+3ab(b)=83
a3+b3+3ab(a+b)=83
a3+b3=83−3ab(a+b)
a3+b3=83−3(15)(8)=512−360=152
You can also observe that 3 and 5 fulfill those conditions so, then 33+53=27+125=152 . Which is our result.
Please assist with this. No links or your account will be banned. Will give brainliest, show steps!!!!!
Answer:
\(\huge\boxed{\sf 16}\)
Step-by-step explanation:
Given expression is:
= 10 + 3(12 ÷ (3x))
Put x = 2 nd use PEDMAS [Parenthesis Exponents Division Multiplication Addition Subtraction "in that order"]
= 10 + 3(12 ÷ (3)(2))
Solve Parenthesis
= 10 + 3(12 ÷ 6)
Now, Divide
= 10 + 3(2)
Now, Multiply
= 10 + 6
Now, Add
= 16
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807Answer:
\(\huge\boxed{ \boxed{\tt \: 16}}\)
Step-by-step explanation:
Evaluate :
\(10 + 3(12 \div 3x)\)
When,
\(x = 2\)
Solution:-
\(\sf \implies10 + 3(12 \div 3x)\)
This expression may be rewritten as,
\(\sf \implies10 + 3 \bigg(\cfrac{12}{3x} \bigg)\)
Put 2 instead of x as x = 2 :-
As we know that x is multiplied with 3 on this expression so,
\(\sf \implies10 + 3 \bigg(\cfrac{12}{3 \times 2} \bigg)\)
\(\sf \implies10 + 3 \bigg(\cfrac{12}{6} \bigg)\)
Cancel off 12 and 6(By 6) :-
\(\sf \implies10 + 3 \bigg({\cfrac{ \cancel{12}}{ \cancel{6}} ^{2} }\bigg)\)
\(\sf \implies10 + 3 (2)\)
According to BODMAS Rule we know that, First Multiplication and then addition.(According to this expression)
So,Multiply 3 and 2 :-
\(\sf \implies10 + 3 \times 2\)
\(\sf \implies10 + 6\)
Simply add :-
\(\sf \implies16\)
Hence, the answer of the given expression would be 16.
_____________________________________
I hope this helps!
Let me know if you have any questions.
Mary reduced the size of a painting to a width of 3.3 inches . What is the new height if it was originally 32.5 inches tall and 42.9 inches wide?
Answer:
x
=
2.5
inches
Step-by-step explanation:
This can be regarded as two quantities in DIRECT PROPORTION because the shape of the painting will stay the same.
x
3.3
=
32.5
42.9
←
←
compare the heights
compare the widths
42.9
x
=
3.3
×
32.5
←
cross multiply
x
=
3.3
×
32.5
42.9
←
solve for
x
x
=
2.5
inches
Sprint offers the new iPhone 12 for a down payment of $30, plus $95 per month. Verizon offers the new iPhone 12 for a down payment of $45, plus $35 per month. In how many months will the phones cost the same amount?
the fastest man in the world can run 100 metres in 9 seconds how far can He run in 1 minute and 2 seconds
With steps plz......
(Its not usain)
Answer:
Step-by-step explanation:
Rate per sec = 100 ÷ 9 = 11.111
1 min and 2 sec = 3600 + 2sec = 3602 sec
Metre = 324.21 metre
Help, please! College precalc! TIA.
Answer:
I believe that the answer is 0
Step-by-step explanation:
All you have to do is add f and g and substitute -2 for x. When you substitute -2, simplify.
Step-by-step explanation:
(f+g)=(x-4)+(x^2-x)=x^2+x-x-4=x^2-4
when x=-2
(f+g)(-2)=(-2)^2-4=0 ans.
solve the simultaneous equation x + y = 2 and x - y = 1
Answer:
(3/2, 1/2)
Step-by-step explanation:
Solve by elimination:
\(x+y=2\\+x-y=1\)
The y's cancel
\(2x=3\)
Divide by 2
\(x=\frac{3}{2}\)
Plug back in
\(\frac{3}{2} +y=2\)
subtract
\(y=2-\frac{3}{2}\)
\(y=\frac{1}{2}\)
So, your answer:
\((\frac{3}{2},\frac{1}{2})\)
Step 4 A-452.16 i3) Find the area of the composite figure.18 cm126 cm
Area of the composite figure = 361.25cm²
Explanations:The composite figure consists of a cone and semicircle
Area of the semicircle = 0.5πr²
The diameter of the semicircle = 18 cm
The radius, r = diameter/2
r = 18/2
r = 9 cm
Area of the semicircle = 0.5πr²
Area of the semicircle = 0.5 x 3.142 x 9²
Area of the semicircle = 127.25cm²
Area of the triangle = 0.5 x base x height
Area of the triangle = 0.5 x 18 x 26
Area of the triangle = 234 cm²
Area of the composite figure = Area of the semicircle + Area of the triangle
Area of the composite figure = 127.25cm² + 234 cm²
Area of the composite figure = 361.25cm²
X + 8y > 16
A
B
C
D?
Answer:
Its C i think. Sorry if Im wrong
Step-by-step explanation:
WHO IS RIGHT?
Drag the word RIGHT onto the character
that is right and drag the WRONG on
the character that is wrong. Explain
your answers below.
RIGHT
2(x + 6)=2x+6 WRONG
RHINO
LION
2(x + 6)=2x + 12
Explain your answer here
Explain your answer here:
Answer:
Right
Step-by-step explanation:
Trust me
Answer:
lion
Step-by-step explanation:
you multiply what is outside the parenthesis to everything inside the parenthesis
After watching baking shows on T.V., Angie signs up for a cake-decorating class. To practice her new skills, she decorates a batch of cupcakes with sugar flowers. Angie puts 4 sugar flowers on each cupcake. In all, Angie puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Angie decorates?
Solve this equation for c to find the number of cupcakes Angie decorates.
Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.
To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.
4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.
To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8
Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8
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V=u+ at
u=2 a= -5 t=1/2
work out the value of v
Answer:
V = -0.5
Step-by-step explanation:
Step 1: Define
V = u + at
u = 2
a = -5
t = 0.5
Step 2: Substitute and Evaluate
V = 2 + (-5)(0.5)
V = 2 - 2.5
V = -0.5
A local hamburger shop sold a combined total of 392 hamburgers and cheeseburgers on Thursday. There were 58 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Thursday?
Answer:
Step-by-step explanation:
x = hamburgers
x - 58 = cheeseburgers
392 = total of both sold
x + (x - 58) = 392
x + x - 58 + 58 = 392 + 58
x + x = 450
2x = 450
Divide both sides by 2
2x/2 = 450/2
x = 225
The number of hamburgers sold was 225
4) Use the figure to answer the
following question.
The figure below is made up of two rectangular prisms.
Which answer below
*190
*170
*120
*70
The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.
How to Find the Volume of the Composite Solid that Involves Rectangular Prisms?Note that the formula for finding the volume of a rectangular prism is given as:
Volume of rectangular prism = length * width * height.
Find the volume of each rectangular prism and add them together:
Volume of prism 1:
length = 10 m
width = 4 m
height = 3 m
Volume = 10 * 4 * 3 = 120 m³
Volume of prism 2:
length = 10 m
width = 1 m
height = 7 m
Volume = 10 * 1 * 7 = 70 m³
Total Volume = 120 + 70 = 190 m³.
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5x-3(-5y+6x) +4y i need help please
To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.
Using \(\displaystyle\sf \) tags for formatting, the expression becomes:
\(\displaystyle\sf 5x-3(-5y+6x)+4y\)
First, we simplify the expression within the parentheses:
\(\displaystyle\sf 5x-3(-5y+6x)+4y\)
\(\displaystyle\sf 5x+15y-18x+4y\)
Next, we can combine the like terms:
\(\displaystyle\sf 5x-18x+15y+4y\)
\(\displaystyle\sf -13x+19y\)
Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Draw a square with one vertex on the origin (-3,5) and a perimeter of 20.
The drawing of the square is introduced in the image attached below.
How to draw a square from a given point and perimeterIn this question we must determine the location of the four vertices of the square. A square is a quadrilateral with four sides of equal lengths and four right angles. Hence, the side length equals a quarter of the perimeter. The locations of all points can be found by using the following three operations:
\(B(x,y) = A(x,y) + (5, 0)\) (1)
\(C(x,y) = B(x,y) + (0, 5)\) (2)
\(D(x,y) = C(x,y) + (-5,0)\) (3)
If we know that \(A(x,y) = (-3, 5)\), then the coordinates of the remaining vertices are:
\(B(x,y) = (-3, 5) + (5,0)\)
\(B(x,y) = (2,5)\)
\(C(x,y) = (2,5) + (0,5)\)
\(C(x,y) = (2, 10)\)
\(D(x,y) = (2,10) + (-5, 0)\)
\(D(x,y) = (-3, 10)\)
Now we draw the square with a graphing tool (i.e. Desmos).
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Which sum or difference is modeled by the algebra tiles?
As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.
what is expression ?It is possible either multiply, distribute, add, or negate in mathematics. The trying to follow is how a expression is put together: Number, expression, and scientific operator The ingredients of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) It is possible to combine expressions and phrases. An expressions, often known as an arithmetic operation, is any mathematical statement that contains variables, numerals, and a numerical operation between them. That instance, the word m there in given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.
given
To address this issue, we just need to determine the total or difference that yields 2x2 + 2x + 2
Option A: ( x2 + 4x -2) + (x2 - 2x - 4) = 2x2 + 2x - 6
Option B: ( x2 + 4x - 2 ) + ( x2 + 2x + 4 ) = 2x2 + 6x + 2
Option C: ( x2 + 4x - 2) - ( -x2 + 2x - 4)= x2 + 4x - 2 + x2 - 2x + 4
= 2x2 + 2x + 2
As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.
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The complete question is:-
Select the correct answer.
Which sum or difference is modeled by the algebra tiles?
A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2
B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2
C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2
D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2
If x = 8, how much more wallpaper will Tara need for the living room than the bedroom?
Answer:
sorry theres not enough information to tell.
Step-by-step explanation:
:(
Given: 2(10 - 13x) + 9x = -34x + 60. Step 1: 20 – 26x + 9x = -34x + 60. Step 2: -17x = -34x + 40 Step 3: 17x = 40 Step 4: X = 40/17. Justify each step of the solution by stating the property that was used to get to each step. ( Please only answer if you truly know how to. Will Mark Brainliest).
The properties applied in the steps are distributive property, additive property and the division property
How to determine the property used in each step?The equation is given as
2(10 - 13x) + 9x = -34x + 60.
This means that preliminary step is
Given: 2(10 - 13x) + 9x = -34x + 60.
Next, we apply the distributive property
So, we have
Step 1: Apply the distributive property
20 – 26x + 9x = -34x + 60.
Next, we evaluate the like terms
So, we have
Step 2: Evaluate the like terms
-17x = -34x + 40
Next, we evaluate the like terms
So, we have
Step 3: Evaluate the like terms
17x = 40
Lastly, we apply the division property of equation
So, we have
Step 4: Division property of equation
X = 40/17.
Hence, the properties applied in the steps are distributive property, additive property and the division property
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10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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What is the simplest form of the radical expression?
33√2a−63√2a
**Please show me the steps so I can understand what I did wrong on my test.
Thank you!
Step-by-step explanation:
(33 - 63)root2a
- 30root2a✅