The length of the base edge of the given square pyramid is 3.67 feet.
What is the Surface Area?
The sum of all an item's faces makes up the surface area of a three-dimensional object. When wrapping, painting, and finally creating things to get the finest possible design, we apply the idea of surface areas of various items in real life.
What is a Square Pyramid?
In geometry, a pyramid with a square base and four lateral sides is referred to as a square pyramid.A polyhedron with a base and three or more triangle faces that meet above the base is called a pyramid (the apex). A pentahedron is a three-dimensional structure with a total of five faces, such as a square pyramid. The Great Pyramid of Giza is one of the most well-known examples of a pyramid like this in real life.Steps to Calculate the Base Edge Length of Square Pyramid
The formula for surface area of square pyramid is given by, [tex]SA=a^{2} +2a\sqrt{\frac{a^{2} }{4}+h^{2} }[/tex], -----(1)
where [tex]a[/tex] is the length of the base edge and [tex]h[/tex] is the square pyramid height.
In the question, it is given that the surface area of the square pyramid is 96 square feet.
The height of the square pyramid is two-thirds of the base edge length.
[tex]\implies h=\frac{2a}{3}[/tex] ------(2)
Now substituting the given values in (1), we get
[tex]96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+(\frac{2a}{3} )^{2} }\\\implies 96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+\frac{4a^{2} }{9} }[/tex]
Simplifying, we get
[tex]96=a^{2} +2a\times 0.834a^{2} \\\implies 96=a^{2} +1.668a^{3} \\\implies 1.668a^{3}+a^{2} -96=0[/tex]
Finally, we get the value of [tex]a=3.67[/tex] feet.
Therefore, the base edge length of the given square pyramid is 3.67 feet.
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a fast-food restaurant offers 6 different burgers, 5 different side orders, 8 different flavor drinks, and 9 different flavors of ice cream. in how many ways can a combo containing 2 burgers, 2 different sides, 3 different flavor drinks, and 3 ice cream flavors be made? a) 36 b) 705,600 c) 404,040 d) 165 e) 2,160 f) none of the above.
Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made = 529,200
What are combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.Where:n – the total number of elements in a setk – the number of selected objects (the order of the objects is not important)! – factorialacc to our question-
A fast-food restaurant offers 6 different burgers, 6 different side orders, 7 different flavor drinks, and 9 different flavors of ice cream .choose 2 burgers from 6 different burger = choose 3 different sides from 6 different side orders = choose 2 flavor drinks from 7 different flavor drinks = choose 3 ice cream from 9 different flavors of ice cream = Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made=15*21*20*84529,200hence,Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made = 529,200
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the ratio of 15 and square of m? This question is on Get More Math
The ratio of 15 and square of m is 15/m².
What is a ratio?A ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities. This ultimately implies that, a ratio can be expressed as a quotient.
What is quotient?In Mathematics, quotient can be defined as a mathematical expression that is simply used to represent the division of a numerical value by another numerical value or variable.
In this scenario, the numerical value 15 would be the numerator while the variable m would be the denominator, and it should be expressed as follows:
Ratio = 15/m²
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The magnitude and direction of two forces acting on an object are 70 pounds, S76°E, and 120 pounds, N80°E, respectively. Find the magnitude, to the nearest
hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.
The magnitude is approximately
pounds.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
The magnitude is approximately 186 pounds.
What is meant by magnitude?A mathematical object's magnitude, often known as its size, is a quality that indicates whether it is bigger or smaller than other things of the same sort. Formally speaking, an object's magnitude represents the ordered (or ranked) outcome of the class of objects it belongs to.
We have to assume that the notation starts South and then moves 76 degrees East.
The 70-pound force is going at an angle down and to the right.
The down one is negative and the right one is positive.
We have to use the vectors as the hypotenuse of a rectangle.
70 cos(76) = vertical = 16.93 down
70 sin(76) = horizontal = 67.92 right
120 cos(80) = vertical = 20.83 up
120 sin(80) = horizontal =118.17 right
We have to add up all the values vertically and horizontally, and we get
-16.93 + 20.83 =3.9 up
67.92 + 118.17= 186.09 right
Here, the magnitude is the hypotenuse.
sqrt(15.21+34629.49) =186.13 pounds.
Direction is cos⁻¹(3.9/186.13) = 88.802
Remember this is North then 88.802 degrees East
Therefore, the magnitude is approximately 186 pounds.
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3y - x - (4x - 5y)/10 - 7y+2x/4
Which of the following is(are) the solution(s) to |5x + 2| = 8 ?
Answer:
x = -2 ; x = 6/5
Step-by-step explanation:
5x + 2 >=0
5x >= -2
5/5 x >= -2/5
x >= -2/5
if x >= -2/5
5x +2 = 8
5x = 8 -2
5x = 6
5/5 x = 6/5
x = 6/5
if x < -2/5
-5x -2 = 8
-5x = 8+2
-5x = 10
-5/-5 x = 10/-5
x = -2
A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer: $2738.02
Step-by-step explanation:
1) (3000x0.97) = 2910 } Year 1
2) (2910x0.97) = 2822.7 } Year 2
3) (2822.7x0.97) = 2738.019 } Year 3
A recipe requires 4 1/2 cups of milk for every 2/3 of a cup of flour. What is the ratio of cups of milk to one cup of flour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
PLEASE HELP!!!
a) 4 x -3 x 2 =
b) -2 x 5 x -4 =
c) -3 x -1 x -6 =
Answer:
a) 4 x -3 x 2 = -24
b) -2 x 5 x -4 = 40
c) -3 x -1 x -6 = -18
Answer:
a.4 x -3 x 2 =
use the rules for multiplication
-(4×3×2)
-(12×2)
=2
----------------------------------
b. -2 x 5 x -4 =
note:
-2×5(-4)
multiplying an even number of negative terms makes the product positive.
-2×5= 10
10×-4
=40
----------------------------------
C. -3 x -1 x -6 =
note:
multiplying an odd number of negative terms makes the product negative.
-(3×1×6)
=-18
Let a function of 2 variables be defined by f (a,b) =ab - (a-b) what is the value of f (8,9)
By using function, it can be calculated that
The value of f(8, 9) is 73
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the function is
f(a, b) = ab - (a - b)
f(8, 9) = 8 [tex]\times[/tex] 9 - (8 - 9)
f(8, 9) = 72 + 1
f(8, 9) = 73
So the value of f(8, 9) is 73
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Which is the order from least to greatest of the following
4/3, 0.8, 1/5, 30%?
A. 4/3, 0.8, 1/5, 30%
B. 30%, 4/3, 0.8, 1/5
C. 1/5, 4/3, 30%, 0.8
D. 1/5, 30%, 0.8, 4/3
Which is the order from least to greatest of the following
A. 4/3, 0.8, 1/5, 30%
1.33 , 0.8 , 0.2 , 0.3
B. 30%, 4/3, 0.8, 1/5
0.3 , 1.33 , 0.8 , 0.2
C. 1/5, 4/3, 30%, 0.8
0.2 , 1.33 , 0.3 , 0.8
D. 1/5, 30%, 0.8, 4/3
0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ?1/3
Oy + 2 = (x+3)
Oy -2=(x-3)
Oy+ 3 = (x + 2)
Oy-3=(x-2)
The equation which passes through (3,2) and slope 1/3 is:
y - 2 = 1/3 (x - 3)
Given, we have:
slope (m) = 1/3
Point = (3,2) = (x₁,y₁)
we are asked to determine the point slope form :
we know that:
point slope form:
y-y₁ = m(x-x₁)
substitute the above values in the formula:
y - 2 = 1/3 (x - 3)
Hence the correct option is B.
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can someone make a systems of equations word problem using (2, -2)? i included the equation
The word problem including the given equation is mentioned below.
Given, a system of equations
x + y = 0
2x - y = 6
We have to make a word problem using the given system of equations.
Ram and Rahul are two friends and both attempt a test of 10 marks. Now, Ram prepared for the test whereas Rahul didn't prepared for the test and marked the wrong answers in the test. If negative marking is allowed in the test and it is given that, sum of the marks of both the students is zero. Also, twice the marks of Ram is 6 less than the marks of Rahul.
Find the marks of both the students.
Hence, the word problem including the given equation is mentioned above.
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What is the difference in average speed between two cars, one that traveled 160
kilometers in 5 hours, and the other that traveled 140 kilometers in the same
amount of time?
(Average speed = total distance + total time)
32 kilometers per hour
28 kilometers per hour
( 4 kilometers per hour
60 kilometers per hour
The difference in average speed between two cars is 4 kilometers per hour . Average speed of cars are 32 kilometers per hour and 28 kilometers per hour. The average speed is the total distance traveled by the object in a particular time interval.
How To calculate average speed ?The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.
Both can be measured and quantified since they are physical quantities. Both phrases refer to moving bodies alone; they do not refer to static bodies.
Average speed of first car = total distance / total time
= 160/ 5 = 32
Average speed of second car = total distance / total time
= 140/ 5 = 28
The difference in average speed between two cars = 32 -28= 4
4 kilometers per hour is the difference
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Which statement is true about 67?
A. its a prime number
B. its a composite number
C. its neither prime or composite
Answer:
a. its a prime number cuz as far as ik 67 has one factor 67x1
Answer:
Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself
Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn. Can Theo mow the lawn in 2 hours if he continue to mow at the same rate?
Yes, he can mow the lawn in 2 hours.
What is work done?We can define the work done as, a work done in a given period of time.
Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn
In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn
Therefore, in 8/5 hours he is mowing 7/9 part of lawn
In 1 hour = 7/9*5/8 = 35/72
In 2 hours = 35/72*2 = 35/36 ≈ 1
Hence, Yes, he can mow the lawn in 2 hours.
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rachel and robert run on a circular track. rachel runs counterclockwise and completes a lap every 9090 seconds, and robert runs clockwise and completes a lap every 8080 seconds. both start from the same line at the same time. at some random time between 1010 minutes and 1111 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. what is the probability that both rachel and robert are in the picture?
The probability that both Rachel and Robert are in the picture is 3/16.
The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.
Given that
Rachel and Robert both begin at the same point
Rachel completes a lap every 90 seconds.
Robert completes a lap every 80 seconds.
The photographer captures 1/4th of the track, centered on the starting line.
As a result, the photo captures 1/8th of the track on either side of the starting line.
The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.
Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.
Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.
Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).
Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.
i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.
Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}
= {90/8}/60
= 3/16
Therefore the probability that both Rachel and Robert are in the picture is 3/16
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According to this rate shown in this graph, after 12 minutes the coffee is about 110 degrees. After one hour (60 minutes), what do you think the temperature would be?
After one hour (60 minutes, the value of the temperature is 550 degrees.
What is temperature?Temperature is the degree of hotness and coldness that a body contains.
In this case, after graph, after 12 minutes the coffee is about 110 degrees. The temperature per minute will be:
= 110 / 12
= 9.167° per minute.
Therefore, the temperature after 1 hour which is 60 minutes will be:
= Time × Rate
= 60 × 9.167°
= 550°
The temperature is 550°.
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Given that U={a,b,c,d,e,f} and X={a,b,c,d}, Y={c,d,e} and Z={b,d,f} , Find (XUY)U(XUZ)
A and B are two sets, and the set formula is given as n(AB) = n(A) + n(B) - n(AB), where n(AB) denotes the number of elements present in either A or B, and n(AB) is the number of elements present in both A and B.
How do you solve sets?Drawing Venn diagrams, as seen below, is the simplest method for solving set issues.
The total number of elements in any set A or B is n(AB).
The total number of elements in sets A and B is n(AB).
n(AB) is equal to n(A) + n(B) - n(AB)
U={a,b,c,d,e,f}
X={a,b,c,d},
Y={c,d,e}
Z={b,d,f}
(XUY) = (a,b,c,d,e)
(XUZ) =(a,b,c,d,f)
(XUY)U(XUZ) = (a,b,c,d,e,f)
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Which pairs of triangles are similar? check all that apply. â–³abc ~ â–³def â–³def ~ â–³ghi â–³ghi ~ â–³abc â–³ghi ~ â–³jkl â–³jkl ~ â–³abc
The similar pairs of triangles are given as follows:
DEF and HGI.JKL and ABC:What are similar triangles?Similar triangles are two triangles that have the same angle measures.
For these triangles, considering the relations between angles such as sine/cosine/tangent, or the law of sines, the side lengths have to be proportional.
Considering the need for proportional side lengths, the similar triangles in this problem are given as follows:
DEG and HGI: as the proportion between the side lengths of each triangle is of 1.5.JKL and ABC: as the proportion between the side lengths of each triangle is of 0.5.The other triangles are not similar as there are no proportional relationships that can be established from the side lengths of these triangles.
Missing InformationThe problem is given by the image at the end of the answer.
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Linda' chool play tarted at 9:05 AM. It lated 1 hour and 45 minute. What time did the play end?
In given word problem ending time of the play is 10.50 AM.
What is word problem?
A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.
Here starting time of play = 9:05 AM
It took 1 hour 45 minutes to end the play. Then ,
=> 9 hour 05 minutes
1 hour 45 minutes +
=> 10 hour 50 minutes.
Hence ending time of the play is 10.50 AM.
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Select the correct answer. Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(7) = -1 C. g(0) = 2 D. g(-4) = -11
The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.
Which of the statements could be true for the function g?It follows from the task content that the statement which could be true about the function g is to be identified.
Since the given function instances are; g(0) = -2 and g(-9) = 6.
Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.
Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.
This is so because, 0 is in the domain of the function and 2 is in the range of the function.
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,160) and (6,240) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make each minute = 40
In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.
Also, we have been given two points (4,160) and (6,240)
We need to find the number of soda bottles the machine can make each minute.
i.e., we need to find the slope of line passing through points (4,160) and (6,240)
Using the formula of slope,
m = (240 - 160) / (6 - 4)
m = 80/2
m = 40
Therefore, the number of soda bottles the machine can make each minute = 40
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a government agency wished to estimate the proportion of drivers aged 16-24 who have been involved in a traffic accident within the last year. the agency wished to make the estimate within one percentage point and at 90% confidence. find the minimum sample size required, using the information that, several years ago, the proportion was 0.12.
The required minimum sample size is 2875
Given that,
A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.
From the standard normal table, the z-critical value at 90% confidence is 1.65.
The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.
n = (Zc / E )² x P(1-P)
= (1.65 2x0.12(1 - 0.12)0.01
= 2874.96 ~ 2875
Hence, 2875 is the necessary number of samples, minimum.
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Divide [tex]4\frac{2}{15}[/tex] by 3.1.
[tex]\fbox{1.333333}[/tex]
[tex]4\frac{2}{15} \div3.1[/tex]
Simplify:
[tex]4\frac{2}{15} \div3.1[/tex]
[tex]=1.333333[/tex]
let's firstly convert the mixed fraction to improper fraction and the decimal one to a fraction.
[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]
Find the error in the calculations below, if there is one:
Line (1): 4x³ + 2x² − 6x +3
Line (2): = 2x²(2x + 1) − 3(2x + 1)
Line (3): = 2x²(2x + 1) + ( − 3)(2x + 1)
Line (4): = (2x² − 3)(2x + 1)
Line 1 4x³ + 2x² − 6x +3 is having error.
Line 1.
4x³ + 2x² − 6x +3
Line 2.
= 2x²(2x + 1) − 3(2x + 1)
= 4x³ + 2x² - 6x - 3
Line 3.
= 2x²(2x + 1) + ( − 3)(2x + 1)
= 4x³ + 2x² - 6x - 3
Line 4.
= (2x² − 3)(2x + 1)
= 4x³ + 2x² - 6x - 3
expect line 1 remaining all three are equal.
Therefore Line 1 4x³ + 2x² − 6x +3 is having error.
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the population of a town increased from 3450 in 2006 to 5700 in 2012. find the absolute and relative (percent) increase. absolute increase: relative increase:
Answer:
The absolute difference is 1050
The relative percentage is 32.3076%
Step-by-step explanation:
We are given
The population of a town increased from 3,250 in 2008 to 4,300 in 2010
In 2008:
In 2010:
Absolute difference:
we know that
absolute difference =
absolute difference =
absolute difference is 1050
Relative increase:
we know that
Relative percentage is
now, we can plug values
=32.3076
So, the relative percentage is 32.3076%
Y+4=2(x-7)
In standard form
Answer:
2x-y=18
Step-by-step explanation:
y + 4 = 2(x - 7) (open brackets)
y + 4 = 2x - 14 (re arrange)
4 + 14 = 2x - y
2x - y = 18
pls help? i dont know any of this
Answer:
Round to the nearest tenth.
a. 0.54 + 0.278 = 0.5 +0.3 = 0.8
b. 2.65 + 28. 17= 2.70 + 28.20 = 30.9
c. 3.09 + 2.41 + 9.86 = 3.10+ 2.40 + 9.90= 15.4
d. 15.234 + 1.37 + 0.76 = 15.20 + 1.3 + 0.8 = 17.30
e. 39.18 + 2.48+ 0.84 = 39.20 + 2.5 + 0.8 = 42.5
Round to the nearest whole number.
f. 4.112 + 3.89 = 4 + 4 = 8
g. 23.14 + 7.6 + 3.67 = 23 + 8 + 4= 35
h. 53.2 + 3.08 + 27.51 = 53 + 3+ 28 = 84
i. 11.08 + 17.28 + 92.6 = 11 + 17 + 93 = 121
j. 24.08+ 7.9 + 3.06 = 24 + 8 + 3 = 35
Step-by-step explanation:
Hopefully it's right!!!
Dan spends
3
4
of his wages on rent and
1
8
on food. If he makes £240 per week, how much money does he have left?
The money left with Dan is £30 .
In the question ,
it is given that
the amount of money earned by Dan in a week is = £240 .
amount of money spent by Dan on rent is = 3/4 wage
amount of money spent by Dan on food is = 1/8 of wage
So ,
the total amount spent = amount spent on food + amount spent on rent
Substituting the values ,
we get ,
= 3/4 + 1/8 = 7/8 of his wage = (7/8)*240
= 210
so , total amount spent is £210 .
Amount left = amount earned - amount spent
= 240 - 210
= 30
Therefore ,The money left with Dan is £30 .
The given question is incomplete , the complete question is
Dan spends 3/4 of his wages on rent and 1/8 on food. If he makes £240 per week, how much money does he have left?
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I need to know the answer
Step-by-step explanation:
The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5. That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f. For example, if x = 2, the point (2, 20) is on the graph of f but the point (2, 16) is on the graph of p (so it lies under the point (2, 20).
The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of f and it is reflected over the x-axis. The negative coefficient -1 is doing that. The values of the function p(x) are opposite sign to values of f(x).
The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of p lie farther away from the x-axis than points on the graph of f(x).
