The percent error of the house of the pizza would be 2.
The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.
How to calculate the percent error?Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.
Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
slope= 2; point on the line (-2,1) in slope intercept form I know y=m*x+b but all I know is 2 would be m
y=2x+5
1) Since we were told the slope is m=2, one point on the line (-2,1), and the slope-intercept form is:
[tex]y=mx+b[/tex]2) The next step is to find the value of "b", the y-intercept. So, let's pick that point, the slope, and plug them into the Slope-Intercept form:
[tex]\begin{gathered} y=mx+b,m=2,(-2,1) \\ 1=2(-2)+b \\ 1=-4+b \\ 1+4=b \\ b=5 \end{gathered}[/tex]3) Now that we know the y-intercept (b), we can write the function's rule as
[tex]y=2x+5[/tex]Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
use the half angle identity to find the exact value of the trigonomic expression. given 0
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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A tree casts you say shadow that is 9 feet long at the same time a person standing nearby casts a shadow that is 3 feet long if the person is five point feet tall how tall is the tree
we have that
Applying proportion
x/9=5.5/3
solve for x
x=9*(5.5/3)
x=16.5 ft
therefore
the answer is 16.5 ftWhich number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
How are the strategies the same and how are they different
Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
a rectangular prisim has a volume of 80cm cubed it has a length of 2cm and a width of 5cm. What is the prisms height?
rectangular prism volume is ,
[tex]\begin{gathered} V=l\times b\times h \\ 80=2\times5\times h \\ h=\frac{80}{10} \\ h=8\text{ cm } \end{gathered}[/tex]Please help I'm not sure what should I substitute the variable (x) by
From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
The vertex of the parabola below is at the point
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these
Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.
Given the triangles ADH and ECK,
We know that
[tex]\angle ADH\cong\angle ECK[/tex]That is, the angle at D is congruent to the angle at C in the respective triangles.
In this case, we can think of the congruency between the triangles in the following diagram:
Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.
This means that opposite sides are parallel and have the same measure (length).
The opposite sides are AD and CB and DC and AB.
In this case, we find that only AD and CB are an option to this question, therefore the correct answer.
In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.
AE isn't a segment drawn and hence not parallel to any other segment.
The correct answer is the option A).
Rierda Elwynn Garvey takes home $1250 each month. In addition to other expenses, she also makepayments to her debt of $230 per month. What is her Debt Payments to Income Ratio?
The debt payments to income ratio is the amount that Rierda spend paying her debt each mount divided by her monthly income:
[tex]\text{Ratio}=\frac{230}{1250}=\frac{23}{125}=0.184[/tex]Determine the vertex and the axis of symmetry based on the equation, y =-12 -8x - 36
Solution
Determine the vertex and the axis of symmetry based on the equation:
[tex]y=-x^2-8x-36[/tex]Therefore the correct answer is Option A
Find x when the f(x) = 350 - 125x ; when f(x) = 0.
ANSWER
x = 2.8
EXPLANATION
The function given is:
f(x) = 350 - 125x
We want to find the value of x when f(x) = 0.
This means that:
[tex]\begin{gathered} f(x)\text{ = 350 - 125x} \\ \Rightarrow\text{ 0 = 350 - 125x} \\ \Rightarrow\text{ 125x = 350} \\ \frac{125x}{125}\text{ = }\frac{350}{125} \\ x\text{ = 2.8} \end{gathered}[/tex]That is the value of x
How does g(t) = 4t change over the interval t = 3 to t = 4?
Over the interval t = 3 to t = 4, g(t) increases.
The increasing factor (f) is computed as follows:
[tex]f=\frac{g(4)}{g(3)}[/tex]where g(4) is g(x) at t = 4, and g(3) is g(x) at t = 3. Substituting with the formula of g(t) and evaluating each expression, we get:
[tex]\begin{gathered} f=\frac{4^4}{4^3} \\ f=\frac{4\cdot4^3}{4^3} \\ f=4 \end{gathered}[/tex]Then, g(t) increases by a factor of 4
how would u decide if 3/5 or 59% is greater?
SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]Given the following confidence interval for a population mean compute the margin of error E
Given that the Confidence Interval for a population mean:
[tex]11.81<\mu<13.21[/tex]In this case, you can set up these two equations:
[tex]\bar{x}+E=13.21\text{ \lparen Equation 1\rparen}[/tex][tex]\bar{x}-E=11.81\text{ \lparen Equation 2\rparen}[/tex]Because by definition:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex]Where "ME" is the margin of error and this is the mean:
[tex]\bar{x}[/tex]In this case, in order to find the "ME", you need to follow these steps:
1. Add Equation 1 and Equation 2:
[tex]\begin{gathered} \bar{x}+E=13.21 \\ \bar{x}-E=11.81 \\ -------- \\ 2\bar{x}=25.02 \end{gathered}[/tex]2. Solve for the mean:
[tex]\begin{gathered} \bar{x}=\frac{25.02}{2} \\ \\ \bar{x}=12.51 \end{gathered}[/tex]3. Substitute the mean into Equation 1 and solve for "ME":
[tex]12.51+E=13.21[/tex][tex]\begin{gathered} E=13.21-12.51 \\ E=0.7 \end{gathered}[/tex]Hence, the answer is:
[tex]E=0.7[/tex]0.0032% in fraction
Recall that the x% in fraction form is:
[tex]\frac{x}{100}\text{.}[/tex]Therefore 0.0032% as a fraction is:
[tex]\frac{0.0032}{100}=\frac{\frac{32}{10000}}{100}\text{.}[/tex]Simplifying the above result we get:
[tex]\frac{\frac{32}{10000}}{100}=\frac{32}{100\times10000}=\frac{1}{31250}\text{.}[/tex]Answer:
[tex]\frac{1}{31250}[/tex]In boot camp, a cadet must use a rope swing to cross an obstacle withoutfalling into the water hazard below. Unfortunately, they miss the platform onthe other side and swing back to where they started. If it takes the cadet 3.5seconds to swing from one side of the obstacle to the other and back, howlong is the rope swing? Use the formula:
Answer:
Choice C: 3.0 m
Explanation:
We are basically asked to solve for L using
If a cell disruptor is purchased with a frequency of 60Hz, what is the wavelength traveling through human tissue? (1540 m/s).
The wavelength traveling through human tissue when the velocity is 1540 m/s and frequency is 60Hz will be 25.67 m.
According to the question,
We have the following information:
Frequency of a cell disruptor = 60 Hz
Velocity of the cell disruptor = 1540 m/s
We know that the following formula is used to find the wavelength:
Wavelength = Velocity/frequency
Wavelength = 1540/60 m
(Note that when velocity is given m/s and frequency is given in Hz then the unit of wavelength is m. Every physical quantity has to be expressed with its units.)
Wavelength = 25.67 m
Hence, the wavelength traveling through human tissue is 25.67 m.
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if a ray QT bisects
EXPLANATION
If a ray QT bisects
(3x - 5) + (x+1) = 180 [By the Linear Pair Theorem]
Removing the parentheses:
3x - 5 + x + 1 = 180
Grouping like terms:
3x + x + 1 - 5 = 180
Adding like terms:
4x -4 = 180
Adding +4 to both sides:
4x = 180 + 4
Adding numbers:
4x = 184
Dividing both sides by 4:
x = 184/4
Simplifying:
x=46
Now, we need to compute the resulting angles:
m m
As QT bisects
47/2 = 23.5 degrees
The answer is 23.5°
I dont know the steps to solve this expression, help.
5
1) Let's solve that expression step by step
[tex]\frac{35}{2^3-1}[/tex]2) As we have an exponent, let's firstly solve this
[tex]\frac{35}{8^{}-1}[/tex]Now proceeding with the subtraction, and then divide it:
[tex]\frac{35}{7}=5[/tex]3) Hence, the answer is 5
I need help answering the questions for person 2 on my group assignment
The equation for the relation of sides of triangle can be obtained by similar triangle property.
Consider triangle ABC and triangle DBE.
[tex]\begin{gathered} \angle CAB=\angle EDA\text{ (Each angle is right angle)} \\ \angle CBA=\angle EBD\text{ (common angle)} \\ \Delta CBA\cong\Delta EBD\text{ (By AA similarity condition)} \end{gathered}[/tex]Determine the ratio of corresponding sides of simillar triangle.
[tex]\frac{CB}{EB}=\frac{BA}{BD}=\frac{CA}{ED}[/tex]Thus similar triangle property is used to set up the equation.
3. Convert the angle 3π/4 to degrees.
Answer:
135°
Step-by-step explanation:
To convert an angle from radians to degrees, multiply by [tex]180/\pi[/tex].
[tex]\frac{3\pi}{4} \cdot \frac{180}{\pi}=135^{\circ}[/tex]
For what values of a are the following expressions true?/a+5/=-5-a
Explanation:
The expression is given below as
[tex]|a+5|=-5-a[/tex]Concept:
We will apply the bsolute rule below
[tex]\begin{gathered} if|u|=a,a>0 \\ then,u=a,u=-a \end{gathered}[/tex]By applying the concept, we will have
[tex]\begin{gathered} \lvert a+5\rvert=-5-a \\ a+5=-5-a,a+5=5+a \\ a+a=-5-5,a-a=5-5 \\ 2a=-10,0=0 \\ \frac{2a}{2}=\frac{-10}{2},0=0 \\ a=-5,0=0 \end{gathered}[/tex]Hence,
The final answer is
[tex]a\leq-5[/tex]help me solve the volume of the cylinder? 20 ft x 17 ft
Remember that the formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
• r, is the ,radius, of the base
,• h ,is the height of the cylinder
Notice that the base has a diameter of 20 ft. Therefore, the radius is 10 ft.
Using this data and the formula, we get that:
[tex]\begin{gathered} V=\pi(10^2)(17) \\ \rightarrow V=5340.71 \end{gathered}[/tex]The volume of the cylinder is:
[tex]2540.71ft^3[/tex]what is the value of the q that makes the equation true? 3(q+4)-10q=2q+3