The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?
Answers
We need to take the values of the table and check which of the options fit with the results.
In the first line of the table we have p=2 and C=27.54.
Using the equation in option A, for p=2 we would get:
[tex]\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}[/tex]Which is not value for C in the table. Thus we discard option A.
Using the equation for option B, for the value of p=2, we would get:
[tex]\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}[/tex]Which is indeed the value of the table.
To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:
[tex]\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}[/tex]Which is also the value for C in the table.
Thus we confirm that option B is the correct equation
Related Questions
Please answer all. How do you determine the dose-specific response of a drug given f(x)?
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__________________
Just replace in value of x in the function
f(0.1) = 100* (0.1)^2 / ((0.1)^2 + 0.17) = (1)/(0.18) = 5.56
f(0.1) = 5.56
f(0.8) = 100* (0.8)^2 / ((0.8)^2 + 0.17) = (64)/(0.81)= 79.01
f(0.8) = 79.01
_______________________
derivative of a quotient
Q(x)= f(x)/g(x)
Q'(x)= (f'(x)*g(x) - f(x)*g'(x)) / (g(x) ^2)
[tex]Q^{\prime}\mleft(x\mright)=\frac{f^{\prime}\mleft(x\mright)\cdot g\mleft(x\mright)-f\mleft(x\mright)\cdot g^{\prime}\mleft(x\mright)}{g\mleft(x\mright)^2}[/tex]_____________________________
If f(x) = 100* (x^2) / (x^2 + 0.17),
f'(x)= 100 * ( 2x* (x^2 + 0.17) - 2x*x^2 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x^3 + 2x* 0.17 - 2x^3 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x* 0.17 ) / (x^2 + 0.17)^2
f'(x)= 34*x/ (x^2 + 0.17)^2
_________________________
Just replace in value of x in the function
f'(0.1)= 34*(0.1)/ (0.1^2 + 0.17)^2
f'(0.1)= 3.4/ (0.18)^2
f'(0.1)= 104.9
f'(0.8)= 34*(0.8)/ (0.8^2 + 0.17)^2
f'(0.8)= 27.2/ (0.81)^2
f'(0.8)= 41.46
7 - 6u = 5u + 29 solve for u
Answers
Answer:
u = -2
Explanation:
Given the expression;
7 - 6u = 5u + 29
We are to find the value of u;
Collect like terms;
-6u - 5u = 29 - 7
-11u = 22
Divide both sides by -11;
-11u/-11 = 22/-11
u = -2
Hence the value of u is -2
The solution of u in the equation is,
⇒ u = -2
Given that;
the expression is,
⇒ 7 - 6u = 5u + 29
Now, We have to find the value of u;
⇒ 7 - 6u = 5u + 29
Combine like terms;
⇒ -6u - 5u = 29 - 7
⇒ -11u = 22
Divide both sides by -11;
⇒ -11u/-11 = 22/-11
⇒ u = -2
Therefore, the value of u is -2.
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given expression :4x-2y=11find the missing coordinate in ordered pair (-3,?)
Answers
Equations
We are given the equation:
4x - 2y = 11
And it's required to find the missing coordinate in the ordered pair (-3, ?).
The first coordinate is x=-3, thus we need to calculate the y-coordinate by solving the equation for y, using the value of x.
Substituting:
4(-3) - 2y = 11
Operating:
-12 - 2y = 11
Adding 12:
-2y = 23
Dividing by -2:
y = 23/(-2)
y = -23/2
The ordered pair is:
[tex](-3,-\frac{23}{2})[/tex]16. The area of the rectangle is x^2+14x+24.Find the length and width (the factors),then determine the perimeter of the rectangle.Length:Width:Perimeter:
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Given a rectangle of width W and length L, the area is calculated by:
A = W.L
The perimeter of the rectangle is:
P = 2(W + L)
We are given the area of a rectangle with the equation:
[tex]A=x^2+14x+24[/tex]To find the dimensions of the rectangle, we must factor the polynomial.
It's easily done by inspection: find two numbers that added result in 14 and multiplied result in 24. Those numbers are 12 and 2, thus:
[tex]x^2+14x+24=(x+2)(x+12)[/tex]The factors are the width and the length of the rectangle (the width smaller than the length), thus:
Width = x+2
Length = x + 12
Now calculate the perimeter:
P = 2( x + 2 + x + 12)
P = 2( 2x + 14)
Perimeter = 4x + 28
10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)
Answers
To transform
[tex]x^2+8x+15=0[/tex]Make it a perfect square
since 8x/2 = 4x, then
We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1
[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]Now we will make the bracket to the power of 2
[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]Add 1 to both sides
[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]The answer is C
Fill in the blanks to make the question number since true
Answers
Sheliqua, this is the solution:
a. 13 divided by 5
13/5 = 2 3/5
b. 9/5
9 divided by 5
c. 7 divided by 8
7/8
d. 1 2/3
5/3
5 divided by 3
erica has 32 pairs of shoes. 5/8 of erica's shoes are high heels how many of her shoes are high heels?
Answers
Given Data:
Total number of shoes Erica has is: t=32
The portion of high heel shoes is: r=5/8
The expression to calculate the total number of high heel shoes is,
[tex]\begin{gathered} \text{Total Number of high h}eel\text{ shoes=r}\times t \\ =\frac{5}{8}\times32 \\ =5\times4 \\ =20 \end{gathered}[/tex]Thus, Erica has 20 high heel shoes.
Find the reference angle for a rotation of 334º.
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We are asked to find the reference angle for a standard angle of 334°
Recall that the reference angle is the angle that is measured with respect to the x-axis.
First, we need to find out in which quadrant the given standard angle lies.
334° lie in the 4th quadrant (180° to 360°)
So, the reference angle can be found as
[tex]\begin{gathered} \theta^{\prime}=360\degree-\theta \\ \theta^{\prime}=360\degree-334\degree \\ \theta^{\prime}=26\degree \end{gathered}[/tex]Therefore, the reference angle is 26°
find the volume of a hemisphere when the diameter is 24 cm. Leave answer in terms of Pi. I had the answer of 1152 which is not correct.
Answers
Explanation
the volume of a hemisphere is given by:
[tex]\text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3[/tex]where r is the radius
then
[tex]\begin{gathered} Diameter=2\text{radius} \\ \frac{\text{Diameter}}{2}=r \\ \frac{24\text{ cm}}{2}=r \\ r=12\text{ cm} \end{gathered}[/tex]now, replace.
[tex]\begin{gathered} \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot(12\operatorname{cm})^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot1728cm^3 \\ \text{Volume}_{hemisphere}=1152\text{ }\pi cm^3 \end{gathered}[/tex]so, the answer is
[tex]\text{Volume}_{hemisphere}=1152\text{ }\pi cm^3[/tex]I hope this helps you
Find the inverse function of f.f(x) = 7 - 9x3f^-1(x) =
Answers
ANSWER
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]EXPLANATION
We want to find the inverse function of the given function:
[tex]f(x)=7-9x^3[/tex]To do this, we have to make x the subject of the formula.
Let f(x) be y:
[tex]\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=\frac{7-y}{9} \\ \Rightarrow x=\sqrt[3]{\frac{7-y}{9}} \end{gathered}[/tex]Now, replace x with f^(-1)(x) and y with x:
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]That is the inverse function of f.
least to greatest [tex]\pi[/tex][tex] \frac{13}{4} [/tex]22/2[tex] \sqrt{12} [/tex][tex] - 2[/tex]3.07[tex] - 3.27[/tex]
Answers
We have this number and we have to sort them from least to greatest.
We start by expressing them in decimals in order to compare them easily.
Take into account some of them are irrational, so they will be expressed approximately by a decimal (for example, pi).
Then, we have:
[tex]\begin{gathered} \pi\approx3.14 \\ \frac{13}{4}=3.25 \\ \frac{22}{2}=11 \\ \sqrt{12}\approx3.46 \\ -2 \\ 3.07 \\ -3.27 \end{gathered}[/tex]The least will be the negative numbers of this group, so we start with the negative value with the most absolute value: -3.27.
Then, we continue with -2.
Then, we start with the positive values: 3.07, pi, 13/4, sqrt(12) and 22/2.
Then, we can write them in order as:
[tex]\begin{gathered} -3.27 \\ -2 \\ 3.07 \\ \pi \\ \frac{13}{4} \\ \sqrt{12} \\ \frac{22}{2} \end{gathered}[/tex]Find the general equation of the circle having a diameter with endpoints at A(-2,3) and B(4,5).
Answers
The equation of a circle whose center is (a, b) and which has a radius r is given as:
(x - a)² + (y - b)² = r²
For the circle with endpoints at A(-2,3) and B(4,5).
The center (a, b) of the circle is calculated as:
[tex]\begin{gathered} a=\frac{-2+4}{2} \\ a=\frac{2}{2} \\ a=1 \\ b=\frac{3+5}{2} \\ b=\frac{8}{2} \\ b=4 \end{gathered}[/tex]The center, (a, b) = (1, 4)
The diameter(D) of the circle is the distance between the endpoints A(-2,3) and B(4,5).
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(4-(-2))^2+(5-3)^2} \\ D=\sqrt[]{(4+2)^2+2^2} \\ D=\sqrt[]{6^2+2^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \end{gathered}[/tex]The diameter of the circle = √40
Radius = Diameter / 2
r = d/2
r = √40 / 2
Substituting a = 1, b = 4, and r = √40 / 2 into the general equation of a circle:
[tex]\begin{gathered} (x-1)^2+(y-4)^2=(\frac{\sqrt[]{40}}{2})^2 \\ (x-1)^2+(y-4)^2=\frac{40}{4} \\ (x-1)^2+(y-4)^2=\text{ 10} \end{gathered}[/tex]The general equation of the circle is:
[tex](x-1)^2+(y-4)^2=\text{ 10}[/tex]11. You want to tape five posters on a wall so that the spaces between posters are the same. You alsowant the spaces at the left and right of the group of posters to be three times the space between anytwo adjacent posters. The wall is 15 feet wide and the posters are 1.5 feet wide.a. Draw a diagram that represents theb. Write and solve an equation to find howsituation.to position the posters.
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Let's use the variable x to represent the spaces between posters.
So the spaces at the left and right of the group will be 3x.
Drawing the diagram, we have:
Writing an equation to solve for x, we have:
[tex]\begin{gathered} 3x+3x+1.5+1.5+1.5+1.5+1.5+x+x+x+x=15 \\ 6x+7.5+4x=15 \\ 10x+7.5=15 \\ 10x=15-7.5 \\ 10x=7.5 \\ x=\frac{7.5}{10} \\ x=0.75 \end{gathered}[/tex]So the space between each pair of posters is 0.75 feet.
Find the unit price. If necessary, round your answer to the nearest cent. You would enter an answer like $0.49/pound, the value (like 0.49) in the first box and the appropriate unit (like pound) in the second boX $8.39 for 12 kg
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For a determined product you can buy 12Kg for $8.39. To determine how much 1Kg of said product costs, you can apply cross multiplication to calculate it:
If 12 Kg cost $8.39
1 Kg costs $x:
[tex]\begin{gathered} \frac{8.39}{12}=\frac{x}{1} \\ \frac{8.39}{12}=x \\ x=0.699\cong0.70 \end{gathered}[/tex]The cost is $0.70/Kg
Which of the following expressions represents the simplified version of the expression below
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we have the expression
[tex](5x^3y^2-3xy+2)+(2x^3y^2-3x^2y^2+4xy-7)[/tex]step 1
Combine like terms
so
[tex](5x^3y^2+2x^3y^2)+(-3xy+4xy)+(2-7))-3x^2y^2[/tex][tex](7x^3y^2)+(xy)+(-5)-3x^2y^2[/tex]therefore
the answer is the second optionIf 14 people want to share 24 oranges equally, how many oranges will each person get?
Answers
Given data:
The total number of oranges is: 24
The total number of people is: 14
The expression to calculate the number of oranges a person has is,
[tex]\begin{gathered} \frac{Total\text{ number of oranges}}{\text{Total number of people}}=\frac{24}{14} \\ =1+\frac{5}{7} \\ =1.714\text{ oranges.} \end{gathered}[/tex]Thus, each person gets 1 orange and 5/7 of an orange.
Which of the following completes the statement below?MZBAC = {(MBC + mED00חוBERXRmZEADA0DBDC
Answers
Answer:
m(arc)ED
Explanation:
In the diagram:
[tex]m\angle\text{BAC}=\frac{1}{2}(m\widehat{BC}+m\widehat{ED})[/tex]The first option is correct.
Completing the square can be use to find the minimum value of the function represented by the equation y=x^2+4x+7. Where is the minimum value of the function located?
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Given:
[tex]y=x^2+4x+7[/tex]Find: the manimum value of the function.
Explanation:
[tex]\begin{gathered} y=x^2+4x+7 \\ y^{^{\prime}}=2x+4 \\ y^{^{\prime}}=0 \\ 2x+4=0 \\ x=-2 \end{gathered}[/tex]ar x=-2,
the function will be
[tex]\begin{gathered} y=x^2+4x+7 \\ y(-2)=(-2)^2+4(-2)+7 \\ =4-8+7 \\ =11-8 \\ =3 \end{gathered}[/tex]Flnd the value of x for the triangle or rectangle. Then find the length of the sides of the triangle or rectangle.Q1: Perimeter = 18 meters Q2: Perimeter = 23 feet
Answers
The perimeter of a rectangle is given by:
P = 2w + 2h
Where:
w = width = 2x
h = height = x
P = 18
Replacing the data into the equation:
18 = 2(2x) + 2(x)
18 = 4x + 2x
18 = 6x
Solving for x:
x = 18/6
x= 3
Therefore:
w = 2(3) = 6m
h = 3m
---------------------------------------------------------------------------------
P = x + 2x + (x + 3)
23 = 3x + x + 3
23 = 4x + 3
Solving for x:
23 - 3 = 4x
20 = 4x
20/4 = x
5 = x
Therefore its sides are:
x = 5 ft
2x = 2(5) = 10ft
x + 3 = 5 + 3 = 8ft
Which two European nations took control of the regions in the Middle East that had been controlled by the Ottoman Empire?d
Answers
The two European nations took control of the regions in the Middle East that had been controlled by the Ottoman Empire are Britain and France.
The Ottoman Empire had long held the top position among Islamic nations in terms of geography, culture, and theology. Due to the division of the Ottoman Empire after the war, Western powers like Britain and France came to dominate the Middle East, and the modern Arab world and the Republic of Turkey were established.
The Turkish National Movement initiated opposition to these forces, but it did not extend to the other post-Ottoman states until the time of quick decolonization following World War II.
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I need to know the answer and how to solve
Answers
We have by theorem that supplementary angles add up to 180° [The sum of both angles gives as result a straight line; then, the following is true:
[tex]151+x=180\Rightarrow x=29[/tex]So, the value of x is 29°.
I don’t know the answer for this one and others I need help
Answers
x = 1, y = 3
Explanation:The given system of equations is:
y = 4x - 1.......................(i)
y - 2x = 1..................(ii)
Substitute equation (i) into equation (ii)
4x - 1 - 2x = 1
4x - 2x = 1 + 1
2x = 2
x = 2/2
x = 1
Substitute x = 1 into equation (i)
y = 4x - 1
y = 4(1) - 1
y = 4 - 1
y = 3
The solution to the system of equations is x = 1, y = 3
Find the volume of the triangular pyramid to the nearest whole number.HighlightA)181 in 3B)361 in 3722 inD)1,082 in 3what's the answer
Answers
the volume of a pyramid is
[tex]V=\frac{1}{3}Ah[/tex]where A is the area of the basis and h is the height of the pyramid.
[tex]A=\frac{12.3\text{ in }\times10\text{ in}}{2}=61.5in^2[/tex]Then the volume is
[tex]\begin{gathered} V=\frac{1}{3}(61.5in^2)(17.6in) \\ =360.8in^3 \end{gathered}[/tex]Then rounding the number, the answer is B).
Got cut off while saying thanks to last tutorial t bg at helped me.
Answers
We are given the following equation.
[tex]A=p+prt[/tex]we are asked to find an equation for "t". To do that, we are going to solve for "t", first by subtracting "p" on both sides, like this:
[tex]\begin{gathered} A-p=p-p+prt \\ A-p=prt \end{gathered}[/tex]Now we will divide both sides of the equation by "pr"
[tex]\begin{gathered} \frac{A-p}{pr}=\frac{prt}{pr} \\ \frac{A-p}{pr}=t \end{gathered}[/tex]A thus we found a relationship for "t".
Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75° what are the approximate length of side AC and measure of A?O AAC = 18.9;m SA = 66.99OB.OC.AC = 20.3 m A = 34.8°AC = 18.9: m A = 37.8°AC = 20.31 m A = 58.9°ODResetNext
Answers
Draw the triangle ABC.
Determine the length of side AC.
[tex]\begin{gathered} (AC)^2=(AB)^2+(BC)^2-2\cdot AB\cdot BC\cdot\cos B \\ =(12)^2+(18)^2-2\cdot12\cdot18\cdot\cos 75 \\ =356.190 \\ AC=\sqrt[]{356.19} \\ =18.87 \\ \approx18.9 \end{gathered}[/tex]So side AC is equal to 18.9 m.
Determine the measure of angle A.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{18.9}{\sin75}=\frac{18}{\sin A} \\ \sin A=\frac{18}{18.9}\cdot\sin 75 \\ A=\sin ^{-1}(0.9199) \\ =66.9 \end{gathered}[/tex]So mesure of angle A is 66.9 degree.
each student in a class received some textbooks one third of these were english books which expresión shows how manys english books each student received
Answers
Let x be the total number of books each student recieved, since one third of them is an english book we have that the expression is:
[tex]\frac{1}{3}x[/tex]Good morning I could really use some help solving this problem!
Answers
If the new line passes through the point (-6, 2), let's use x = -6 and y = 2 in the equation and then solve it for 'a':
[tex]\begin{gathered} y=\frac{1}{2}x+a\\ \\ 2=\frac{1}{2}(-6)+a\\ \\ 2=-3+a\\ \\ a=2+3\\ \\ a=5 \end{gathered}[/tex]Therefore the value of 'a' is 5.
Rewrite the following equation in slope-intercept form.6x+y=12Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
According to the given data we have the following equation:
6x+y=12
To rewrite the following equation in slope-intercept form we would have to make the following steps:
6x+y=12
Move 6x to the other side, by doing this it would change its sign
So,
y=-6x + 12
So, equation in slope-intercept form would be y=-6x + 12
The peak of Mt. Whitney in California is 14,494 feet above sea level. Write this number as an integer.
Answers
The peak of the mountain is 14, 494 ft above sea level therefore the number can be represented as follows as an integer
[tex]+14,494\text{ feet}[/tex]The mountain is plus 14,494 ab
someone help me please this is the last question and can't get it wrong
Answers
We can use the fact that the sum of angles in a triangle is 180degrees and the sine rule to find the missing angle and sides. This will give us a single unique triangle.
So the right answer is 1 triangle