Answer: a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation: The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
PLS GIVE ME BRAINLIESTA DN FRIEND REQUEST ME PLS AND THANK YOU
Finn, Michael, Luke, and Tommy are going to have a movie night this weekend. Together, they have 33 movies. If they decide to
randomly choose four movies, what is the probability that the four they choose will consist of each of their favorite movies?
Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest
millionth
Answer:
1/982080 as a fraction
0.000001 when rounded to the nearest millionth
Step-by-step explanation:
Each time they pick a movie the odds change
the first pick is 1/33
the second is 1/32
the next is 1/31
the last is 1/30
multiply these fractions
Given a line with slope = 5 and passing through ( 5 , 9 ) , which of the following is the correct point-slope equation of the line?
The point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
As per the question statement, we are supposed to find the point - slope equation of the line passing through the point (5,9) and having a slope equal to 5.
Before solving this, we need to know that point slope form of the equation is given as y - y1 = m (x - x1)
Where (x1, y1) are the points through which line is passing and "m" is the slope of the line.
Here x1 = 5 and y1 = 9 and m = 5
Substituting the values in the formula written above, we get
y- 9 = 5(x - 5)
y - 9 = 5x - 25
5x - y = 25 - 9
5x - y = 16
Hence the point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
Point slope form: The equation of a line in which we utilize any point which lies on the line and its slope to find the line's equation.Slope: This value indicates about the steepness of the line.To learn more about line and its characteristics, click on the link given below:
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Find the slope through ( 0, 0) and ( -2, 4) by computing
ANSWER:
The slope is - 2
STEP-BY-STEP EXPLANATION:
We have the slope, we calculate it by means of the following formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The points are (0,0) and (-2, 4), replacing:
[tex]m=\frac{4-0}{-2-0}=\frac{4}{-2}=-2[/tex]Can you help me with number 13? Thank you I am having trouble with it.
In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)
We can use the cosine rule to find the length of each side
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}[/tex]From the given figure we can see triangle ABC, where We will use the cosine rule to find c
[tex]c=\sqrt[]{a^2+b^2-2ab\cos 90^{\circ}}[/tex]Since cos(90) = 0, then
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]The expression equivalent to c is
[tex]\sqrt[]{a^2+b^2}[/tex]Look at the following problem, find the mistake.Solve for x. 6x − 3x + 14 = 176x − 3x + 14 = 17 9x + 14 = 17 - 14 -14 9x = 3 /9 /9 x = 1/3Solve for x. 6x − 3x + 14 = 17
Please help! Functions and Relations. The function h(x) is a transformation of the square root function, f(x)= square root of x. What function is h(x)? Thanks!
In general, given a function g(x), a horizontal shift is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow g(x-a) \\ a>0\rightarrow\text{ a units to the right} \\ a<0\rightarrow\text{ a units to the left} \end{gathered}[/tex]Thus, in our case, notice that the graph of h(x) is that of f(x) shifted 1 unit to the left; then,
[tex]h(x)=\sqrt{x+1}[/tex]The answer is option C.A man has 32 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 545 cents, how many dimes does he have?
A dime is worth 10 cents and a quarter is worth 25 cents.
Let D be the number of dimes and Q be the number of quarters.
Since the total amount of coins in the pocket is 32, then:
[tex]D+Q=32[/tex]On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:
[tex]10D+25Q=545[/tex]Notice that we have found a 2x2 system of equations:
[tex]\begin{gathered} D+Q=32 \\ 10D+25Q=545 \end{gathered}[/tex]Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:
[tex]\begin{gathered} D+Q=32 \\ \Rightarrow D=32-Q \\ \\ 10D+25Q=545 \\ \Rightarrow10(32-Q)+25Q=545 \\ \Rightarrow320-10Q+25Q=545 \\ \Rightarrow25Q-10Q=545-320 \\ \Rightarrow15Q=225 \\ \Rightarrow Q=\frac{225}{15} \\ \\ \therefore Q=15 \end{gathered}[/tex]Replace back Q=15 into the expression for D to find the amount of dimes:
[tex]\begin{gathered} D=32-Q \\ =32-15 \\ =17 \end{gathered}[/tex]Therefore, the amount of dimes that the man has is 17.
y is the midpoint of xz.x has coordinates (8,-10)and y has coordinates(-12,1)find the coordinates of z
Answer:(-32,12)
Step-by-step explanation:
Find the change in x and change in y from point x to point y. In this case it is -20 for x and +11 for y. Since the definition of a midpoint splits the line into 2 equal segments you can use the changes to calculate z. Use the midpoint coordinates and add the changes like this: (-12-20,1+11) and you will get (-32,12) for z.
What principal would you need to invest at a rate of 4% to earn $500 in 6 months? Round your answer to the nearest cent.
From the information available, we have the following;
Rate = 4% (0.04)
Time = 0.5 (half a year/6 months)
Interest = 500
Principal = ???
Therefore, we would substitute these into the simple interest formula as shown below;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Make P the ubject of the equation;} \\ \text{Divide both sides by R x T and you'll have;} \\ \frac{I}{R\times T}=\frac{P\times R\times T}{R\times T} \\ \frac{I}{R\times T}=P \\ \frac{500}{0.04\times0.5}=P \\ \frac{500}{0.02}=P \\ P=25000 \end{gathered}[/tex]ANSWER:
The principal to be invested therefore is $25,000
Help needed! please help math
PLEASEEE!!! Math 8th grade
Total gallons of water used in the park after the ride is installed
= 9.51 * 10^5 GALLONS.
What is exponent addition?Exponent addition is the process of multiplying a number by its exponents or powers, whether or not the base is the same. Exponents, which show how many times a number can be multiplied by itself, are also known as the power of numbers. As an illustration, 3^2 = 3*3, where 3 is the base and 2 the exponent.
How to add exponents?When the base and exponents are the same, exponents can be added. Sometimes the base and exponent will differ, but adding can still be done for certain formulas. Let's examine the procedures for adding exponents.
Step 1: Verify that the expression's terms all have the same base and exponents. 22 + 22, as an illustration. As can be seen, the exponent and base are both 2.
Step 2: Calculate the expression using individual terms if the base and exponent are different. for instance, 53 plus 42. Exponents and bases are different.
Step 3: Add the results together.
As per the question:water used in the park initially = 8.6*10^5 gallons
water used by the additional ride added = 9.1 *10^4 gallons
=0.91*10^5 gallons
Total gallons of water used in the park after the new ride is installed
= (8.6*10^5 + 0.91*10^5) gallons
= (8.6+0.91) *10^5 gallons
= 9.51* 10^5 gallons
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For the diagram below, angles 4 and 6 would be referred to as _______ angles.Select one:a.supplementaryb.verticalc.alternate interiord.alternate exterior
Answer:
c. alternate interior
Explanation:
If a transversal line intersects two parallel lines, the angles formed on the interior are called the interior angles. For example, in the given diagram, angles 3, 4, 6, and 5 are interior angles.
Now the pair of angles that formed in the interior but on the opposite side of the transversal line are called alternate interior angles. For example, angels 4 and 6 are alternate interiors. angles 3 and 5 also alternate interior.
Therefore, choice C is the correct answer choice that describes angles 4 and 6.
DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E. if M
From the question and the given diagram, we were told that:
DG and EG are tangent to circle C and circle F.
The point of tangency are A, B, D, and E.
If M
We are to find m
In solving this, we will have to need or consider the similarity theorem.
Its says that if corresponding angles are congruent, then their angles are similar.
It in essence states that, C
Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got an "B".
ANSWER:
0.6875
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the probability that the gender is male and also the probability that the grade is B, separately, like this:
[tex]\begin{gathered} P(\text{male})=\frac{42}{80} \\ P(B)=\frac{19}{80} \end{gathered}[/tex]Therefore, since it is the probability that it is male OR got and "B", it is the union of both events, and it would look like this:
[tex]P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B)[/tex]Now, the intersection of both events would be the probability that he is a man and gets a B, it would look like this:
[tex]P(male\cap B)=\frac{6}{80}[/tex]We replace to be able to calculate the union, like this:
[tex]\begin{gathered} P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B) \\ P(\text{male}\cup B)=\frac{42}{80}+\frac{19}{80}-\frac{6}{80} \\ P(\text{male}\cup B)=\frac{55}{80}=\frac{11}{16}=0.6875 \end{gathered}[/tex]The probability that the student was male OR got an "B" is 0.6875
Consider the function f(x)=(x+4)(x+2). Dilate f(x) by x to create a new function of a higher degree.
f(x) = (x+4)(x+2).
f(x) = x² + 2x + 4x + 8
f(x) = x² + 6x + 8
Dilate by x:
x³ + 6x² + 8x
Describe how the given equation represent a transformation of the function f(x)
A function that transforms one function or graph into another, typically related function or graph is referred to as a function in mathematics.
For instance, when a quadratic graph is translated, the vertex and axis of symmetry are moved, but the parabola's general form remains the same.
What is the translational equation?
The translation equation or formula is written as g(x) = f(x+k) + C.
Replace "x" in a function with "x-h" to translate it horizontally.
The graph's left or right shift is determined by the value of the variable "h."
Since h = -4 in our example, the graph moves 4 units to the left.
Add 'k' to the end of a function to translate it vertically.
f(x+k) + C.
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1 month bet Rented 3 movies and 2 videos games for a total of $21 the next month she rented 8 movies and four game for a total of $49 find the rental cost for each movie and each video game
Let "m" represent the cost of one movie rent and "v" represent the cost of one videogame rent.
One month she rented 3 movies and 2 videogames for a total of $21, you can express the total cost for this month as:
[tex]3m+2v=21[/tex]Another month she rented 8 movies and 4 video games for a total of $49, you can express the rental costs for this month as follows:
[tex]8m+4v=49[/tex]These expressions form an equation system. To solve it, the first step is to write one of the equations in terms of one of the variables, for example, write the first equation for "v"
[tex]\begin{gathered} 3m+2v=21 \\ 3m-3m+2v=21-3m \\ 2v=21-3m \\ \frac{2v}{2}=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}m \end{gathered}[/tex]Next, replace the expression obtained for "v" into the second equation and solve for "m"
[tex]\begin{gathered} 8m+4v=49 \\ 8m+4(\frac{21}{2}-\frac{3}{2}m)=49 \end{gathered}[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 8m+4\cdot\frac{21}{2}-4\cdot\frac{3}{2}m=49 \\ 8m+42-6m=49 \end{gathered}[/tex]-Order the like terms together and simplify them:
[tex]\begin{gathered} 8m-6m+42=49 \\ 2m+42=49 \end{gathered}[/tex]-Pass 42 to the right side of the equation by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 2m+42-42=49-42 \\ 2m=7 \end{gathered}[/tex]-Divide both sides by 2 to determine the value of m:
[tex]\begin{gathered} \frac{2m}{2}=\frac{7}{2} \\ m=\frac{7}{2}\approx3.5 \end{gathered}[/tex]-Replace the value obtained for "m" on the expression for "v" to determine the rental cost of one video game:
[tex]\begin{gathered} v=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}\cdot\frac{7}{2} \\ v=\frac{21}{2}-\frac{21}{4} \\ v=\frac{21}{4}\approx5.25 \end{gathered}[/tex]The rental cost for the movies is m=$3.50/movie and the rental cost for the videogames is v=$5.25/video game
The graph below shows the relationship between the number of hours and thenumber of miles jogged.Y161514131211109Miles8322356HoursBased on the information in the graph, what is the unit rate in miles per hour?How did u get the unit rate
Since the graph shows a proportional relationship, in order to find the unit rate in miles per hour, we just need to choose a point in the graph and divide the number of miles by the number of hours.
Looking at the graph, we can choose the point (2.5, 8), so we have:
[tex]\text{unit rate}=\frac{8\text{ miles}}{2.5\text{ hours}}=3.2\text{ miles/hour}[/tex]So the unit rate is 3.2 miles per hour.
solve for x: In(x+2)= -5
The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]Find the Slope and the Y-Intercept of the line with the given equation
Answer: Slope is -4/5 and Y-int is 6
Step-by-step explanation: From the y=mx+b you can see the m is -4/5 and the b is 6. So in this case the slope would be -4/5 and y int would be 6
How do you write – 7.83 as a fraction into simples form?
7.83 can be written as a fraction in simplified form as [tex]7 \frac{80}{100}[/tex].
A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole. Here, we'll explain the steps involved in converting 7.83 decimal numbers to fraction form and mixed numbers. In order to convert 7.83 to a fraction, do the following:
Write the decimal number split by one first as follows:
7.83/1
Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 = 100, removing the decimal point.
7.83 × 100/1 × 100 = 783/100
We can also express 7.83 as a mixed number because the improper fraction is caused by the numerator being bigger than the denominator; as a result, 783/100 is equal to:
[tex]7 \frac{80}{100}[/tex]
Therefore, 7.83 is 783/100 as a fraction, and its mixed number form is [tex]7 \frac{80}{100}[/tex].
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find the image Matrix that represents the rotation of the polygon then graph the polygon and its image
SOLUTION
[tex]\text{The image matrix at 90}^o\text{ rotation is derived using the formula }[/tex][tex]\begin{gathered} \begin{bmatrix}{\cos \theta} & -\sin \theta & {} \\ \sin \theta & {\cos \theta} & {} \\ {} & {} & {}\end{bmatrix}\text{ where }\theta\text{ is 90}^{} \\ \text{This becomes the matrix of } \\ \begin{bmatrix}{0} & {-1} & {} \\ {} & {} & {} \\ {1} & {0} & {}\end{bmatrix}\text{ }\times\text{ }\begin{bmatrix}{2} & {4} & {6}{}{} \\ {2} & {5} & {1}\end{bmatrix}\text{ = }\begin{bmatrix}{0-2} & {0-5} & {0-1}{}{} \\ {2+0} & {4+0} & {6+0}\end{bmatrix}\text{ = } \\ \\ \begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \\ \\ \text{Therefore, the image matrix is }\begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \end{gathered}[/tex]The graph is shown below
Find the real solutions, if any, of the following equation. Use the quadratic formula.
EXPLANATION
Given the equation 6x^2 = 5x
We can apply the following procedure :
Subtracting -5x to both sides:
[tex]6x^2-5x=0[/tex]Apply exponent rule:
[tex]a^{(b+c)}=a^ba^c[/tex][tex]x^2=\times[/tex][tex]=6\times-5x[/tex]Factor out common term x:
[tex]x\mleft(6x-5\mright)=0[/tex][tex]\mathrm{Using\: the\: Zero\: Factor\: Principle\colon\quad \: If}\: ab=0\: \mathrm{then}\: a=0\: \mathrm{or}\: b=0[/tex][tex]x=0\quad \mathrm{or}\quad \: 6x-5=0[/tex][tex]\mathrm{Add\: }5\mathrm{\: to\: both\: sides}\text{ from 6x -5=0}[/tex][tex]6x-5+5=0+5[/tex][tex]Simplify\colon[/tex][tex]6x=5[/tex][tex]\mathrm{Divide\: both\: sides\: by\: }6[/tex][tex]\frac{6x}{6}=\frac{5}{6}[/tex][tex]Simplify\colon[/tex][tex]x=\frac{5}{6}[/tex][tex]\mathrm{The\: solutions\: to\: the\: quadratic\: equation\: are\colon}[/tex][tex]x=0,\: x=\frac{5}{6}[/tex]Hence, the solution set is as follows:
{0 , 5/6}
help mee pleasee!!
thank you <3
The equation would be y = 20.1x + 359 which represents an estimate of the number of individuals employed as medical assistants in the year.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
We have to determine the slope of the line :
⇒ m = (y₂ - y₁)/(x₂ -x₁ )
⇒ m = (560 - 359)/(10-0)
⇒ m = 20.1
This represents new assistants per year
So y-intercept of 359, your equation becomes
⇒ y = 20.1x + 359
Using the above equation, estimate the number of individuals employed as medical assistants in the year.
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Can you please help me out with a question
There are 360 degrees in a circle.
We can write:
[tex]Arc\text{LAM}+Arc\text{MBL}=360\degree[/tex]Given, Arc LAM = 256°, we can find Arc MBL:
[tex]\begin{gathered} Arc\text{LAM}+Arc\text{MBL}=360\degree \\ 256+\text{ArcMBL}=360 \\ \text{ArcMBL}=360-256 \\ \text{ArcMBL}=104 \end{gathered}[/tex]The central angle that subtends Arc MBL also measures 104 degrees.
[tex]\angle\text{MPL}=104\degree[/tex]We also know,
[tex]\angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL}[/tex]Angle MPB and Angle BPL are equal, so we have:
[tex]\begin{gathered} \angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL} \\ 104=2\angle\text{BPL} \\ \angle\text{BPL}=\frac{104}{2} \\ \therefore\angle\text{BPL}=52\degree \end{gathered}[/tex]Now,
Arc LB subtends the central angle BPL, so they are same in measure.
Thus,
[tex]\text{ArcLB}=52\degree[/tex](C) 0.845 ÷ 5 I need help explaining the answer
The given expression is
[tex]\frac{0.845}{5}[/tex]As long division, we solve it as follows
So, the answer is 0.169.Observe that we have to add a zero first in the quotient in order to transform 0.845 into 845, then we divide it by 5 as a normal long division.
What is the sum of the two odd numerals following 26 in the following sequence?
2,3,5,6,7,9,10,11,13…
The two odd numbers are 11 and 15. The sum of the odd numbers in the sequence will be 26.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that,
The sequence is,
2,3,5,6,7,9,10,11,13…
As we know the given series is an arithmetic progression with a common difference is 2.
The sequence is further obtained as,
2,3,5,6,7,9,10,11,13, 15
From the given condition the sum of the numerals has to be 26.After applying a lot of addition to the sequence we get only two odd numbers 11 and 15 which will give the sum of 26 as,
= 11 + 15
=26
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Andy Lee is the punter for the San Francisco 49ers. He had a stellar 2011 season with an average punt length of 50.9 yards with a standard deviation of 3.5. His punt distance follows a normal distribution. Andy Lee's first punt of the season was 66 yards. what is the z-score for this punt?A. -2.4B. 2.4C. 4.3D.5.5
The z-score of a normal distribution is defined by
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x\text{ is the score we want to find } \\ \mu\text{ is the mean value of the distribution} \\ \sigma\text{ is the standard deviation of the distribution} \end{gathered}[/tex]Then, using the formula for the z-score in our problem we have
[tex]Z=\frac{66-50.9}{3.5}=\frac{15.1}{3.5}=4.3[/tex]Then the z score for that punt is 4.3.
Find the 20% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
Lengths of Longest 3-Point Kick for NCAA Division 1-A Football
29 30 35 37 38 40 40 43 44 45
47 48 49 49 50 53 55 55 58 59
Using the methodology of Trimmed Mean to the tune of 20%, the result derived is given as 45.5. See further explantion below.
What is Trimmed Mean?A truncated mean (another name for Trimmed Mean), like the mean and median, is a statistical measure of central tendency.
It entails calculating the mean after deleting specified sections of a probability distribution or sample at the high and low ends, often an equal proportion of both.
In the above instance, since the instruction is to trim 20% of 20 observations is 4.
Hence, 2 observations from the start and 2 from the rear will be removed. This leaves us with:
35 37 38 40 40 43 44 45 47 48 49 49 50 53 55 55. (Note that the observations must be arranged from low to high)
Hence the Trimmed Mean = (35 + 37 + 38 + 40 + 40 + 43 + 44 + 45 + 47 48 + 49 + 49 + 50 + 53 + 55 + 55)/ 16
= 728/16
=45.5
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A scale drawing for a restaurant is shown below. In the drawing, 2 I'm represents 3 m. Assuming the dinning hall is rectangular, find the area of the real dining hall
To solve this question, follow the steps below.
Step 01: Find the real measures of the dining hall.
The measure of the drawing is 2cm x 6cm.
Given: 2cm = 3m.
Then, 6cm = 2cm + 2cm + 2cm = 3m + 3m + 3m = 9m
The real measure of the dining hall is 3m x 9m.
Step 02: Find the area of the dining hall.
The dining hall is a rectangle and the area (A) of a rectangle is:
[tex]A=l*h[/tex]Where l and h are the sides of the rectangle.
Then, the area of the dining hall is:
[tex]\begin{gathered} A=3*9 \\ A=27m^2 \end{gathered}[/tex]Answer: The area of the dining hall is 27 m².
If P = (-1, 0, 1, 2, 4} and Q = (4, 5, 6}, find Pu Q.O (-1, 0, 1, 2, 4, 5, 6}Of0 (4)O (-1, 0,1, 2, 4}
Statement Problem: If;
[tex]P=\mleft\lbrace-1,0,1,2,4\mright\rbrace,Q=\mleft\lbrace4,5,6\mright\rbrace[/tex]Find;
[tex]P\cup Q[/tex]Solution:
The union of two sets is a set containing all elements that are in the two sets.
The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Thus, the union of set P and set Q is;
[tex]P\cup Q=\mleft\lbrace-1,0,1,2,4,5,6\mright\rbrace[/tex]
