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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Dad fills the car's gas tank when it is about 1/2 empty. Later, he fills the tank when it is about 3/4 empty. He bought a total of 18 1/2 gallons of gas on those two days. How many gallons does the tank hold?
Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
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solve the question math
Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
Answer:
16(2z-3) or GCF: 16
Step-by-step explanation:
32z-48 has a GFC of 16
16(2z-3)
Answer:
$16(2z-3)
Step-by-step explanation:
Prime factorization:
32: 2*2*2*2*2
48: 2*2*2*2*3
Notice any similarities:
2*2*2*2=16
$32z-$48 = $16(2z-3)
Solve for the roots in simplest form using the quadratic formula:
2x²-28x= -116
in november's math meet, the little monsters of beast academy solved $\frac{1}{5}$ of the problems. in march's math meet, they solved $\frac 23$ of the problems. (there might be different numbers of problems asked in november and march.) in total, the little monsters solved $13$ of $30$ problems over both math meets. how many problems were asked at march's math meet?
The little monsters solved 15 problems in March's Math meet
Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.
In March's math meet, they solved 2/3 of the problems.
In total, the little monsters solved 13 of 30 problems over both math meets.
Let, the number of problems in November be n,
and the number of problems in March be m
According to the question,
n + m = 30 as, the total problems be 30
Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems
n + m = 30 ... (1)
n/5 + 2m/3 = 13 ... (2)
On simplifying Eq (2) becomes
3n + 10m = 195 ... (2)
On multiplying Eq (1) by 3, we get
3n + 3m = 90
3n + 10m = 195
On subtracting, we get
- 7m = - 105
m = 105/7
m = 15
So, the problems asked in March's Math meet be 15.
Hence, 15 problems were asked at March's Math meet.
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A triangle has vertices A(−1,2)
, B(2,5)
, and C(3,−4)
. If the image resulting from a rotation has vertices A'(−2,−1)
, B'(−5,2)
, and C'(4,3)
, write the rule that describes the rotation:
Answer: [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
90 degree counter-clockwise rotation around the origin.
===================================================
Explanation:
Focus on A(-1,2) and A'(-2,-1)
The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"
In other words, we've gone from (x,y) to (y,x) to (-y,x)
Representing this with arrows looks like:
[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]
or in short
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
which represents a 90 degree counter-clockwise rotation around the origin.
-----------------------------------
Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]
Sure enough, it works for point B.
Lastly, let's check if it works for point C.
We should go from C(3,-4) to C'(4,3).
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]
All points have been confirmed.
the sum of the number of factors of n and n2 is 34. how many such distinct numbers such that n<150 exist?
The total 18 numbers such that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34
Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.
Factors in total (2+1)*(1+1)=6
It will have 2- 4 times and 3-2 times for 122.
15 total factors of 5*3
Situation 1: N = xy
attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.
Regarding N-x-2 and Y-3 timings.
There are a total of (2+1)*(3+1)=12 factors.
Situation 2
Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.
Consequently, 17+1 = 18 factors in total.
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a dart board is a regular octagon divided into regions as shown. suppose that a dart thrown at the board is equally likely to land anywhere on the board. what is the probability that the dart lands within the center square?
The probability that the dart lands in centre is = √2-1.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
Let the side of octagon be rexterior angle of octagon = 360/8 = 45So interior angle = 180 -45 = 135So all the triangles will have 45-90-45 combinationsc sides of triangles = r/2√r/2 Calculate the total area of octagon and the area of central squareProbability = area of square /area of octagon = r2/(r2+r2+22√+r2)r2/(r2+r2+22+r2)= 1/(2+22√)take 2 common and multiply and divide byhence,The probability that the dart lands in centre is = √2-1.
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A baseball diamond is a square that measures 90ft on each side. Write and expression for the distance from 2nd base to home plate in square root form using a^2+b^2=c^2, then give the answer rounded to the nearest tenth
If a baseball diamond is a square that measures 90ft on each side. The expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)² and the distance is 127ft.
How to find the distance?Using the Pythagoreans theorem formula
c= √ a²+b²
Where:
c = length of hypotenuse
a and b = length of the sides of the right triangle
Let plug in the formula
c =√ (90)² + (90)²
c =√ 8100 +8100
c =√16200
c = 127.3
c = 127 ft (Approximately)
Therefore the distance is 127ft.
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Area and Circumference of Circles
All circles have the same ratio of circumference to (fill in the blank)
constant . Using this ratio, an exact formula was determined for the distance around a circle: (fill in the blank)
Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.
Perimeter is the distance around a circle.
Circumference of circle [tex]C = \pi d[/tex].
Perimeter of circle [tex]= 2 \pi r[/tex]
What is circle ?
A circle is a spherical shape without boundaries or edges.
A circle is a closed, curved object with two dimensions in geometry.
Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.
For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].
Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.
Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.
So it was proved.
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Suppose m<4 =108 find m<5 and m<7
m ∠5 and m ∠7 is 72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or π (in radians).
How to find angle ?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
m ∠4 = 108°
m ∠5 = m ∠1
m ∠1 is in same line of m ∠4
So
m ∠1 = 180 - m ∠4
m ∠1 = 180 - 108
m ∠1 = 72 °
So m ∠5 = 72 °
m ∠7 is opposite to m ∠5 , opposite angles will be equal
Therefor m ∠7 = 72 °
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Find the value of x.
79
118°
109
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Find the value of x ?y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
answer is B
x = 108 and y = 109
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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.
Find the value of x ?Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
Therefore the value of x and y is x = 108 and y = 109
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7. A bag of marbles contains 3 green, 7 red, 2 white
and 8 black marbles. If a marble is randomly
chosen, what is the probability that the marble will
NOT be green or white?
a. 25%
b. 50%
C. 60%
d. 75%
e. 80%
Answer: 50%
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
There are 20 marbles, so each 1 has a chance of 5% If you were to choose randomly 75% of the time you will get either red or black and 25% you will get green or white
7
Oliver makes a plan to be healthier, starting with exercising more often. He signs up for a karate class, thinking this will be a cool way to get active.After three weeks, Oliver finds himself dreading karate class. He would much rather stay home and play RPG with his friends. Since Oliver has already made the decision, what is the BEST path for him to take?
It a because i told the tese
It take Jada 20 minute to walk to chool. It take Andre 80% a long to walk to chool. How long doe it take Andre to walk to chool?
Andre takes 36 minutes to walk to the school.
Given, It take Jada 20 minutes to walks to school.
It takes Andre 80% a long to walk to school.
As, Andre takes 80% more to walk to school
So, the time Andre takes = 20×180/100
the time Andre takes = 2×18
the time Andre takes = 36 minutes
Hence, Andre takes 36 minutes to walk to the school.
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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
when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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Round 837 to 1 significant figure
Answer:
800
Step-by-step explanation:
we gotta go with the highest value to round since it’s only one sig fig
In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800.
How do round any digit?To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep as it is and if it is 5 or greater than 5 then we will round up.
In order to round to 1 significance the remaining digit will mark as zero
As per the given,
837 Here, 1 significant figure is 8.
The ramainging digit = 3 and 7
Put 0 instant of 3 and 7
837 → 800
Hence "In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800".
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79 ala decena mas cercana
Answer:
80
Step-by-step explanation:
Solve for x:-
[tex]\sf -10 + x + 4 - 5 = 7x - 5[/tex]
Answer:
x = -1
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ -10 + x + 4 - 5 = 7x - 5
Then the value of x will be,
→ -10 + x + 4 - 5 = 7x - 5
→ -11 + x = 7x - 5
→ 7x - x = -11 + 5
→ 6x = -6
→ x = -6/6
→ [ x = -1 ]
Hence, the value of x is -1.
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
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Answer:
Step-by-step explanation:
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
What is proportionality?
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
survey of 397 children given at a local elementary school showed that 175 like chocolate ice cream 225 like pistachio ice cream, and 97 do not like chocolate or pistachio ice cream. how many children like at most one kind of ice cream mentioned in the survey?
297 children like at most one kind of ice cream.
Total number of children = 397
Let C and P be the number of children like chocolate and pistachio ice cream respectively.
n(C) = 175
n(P) = 225
The number of student do not like chocolate or pistachio ice cream is,
n(P' and C') = 97
n(P or C)' = 97, by De Moivre's theorem
n(P or C) = 397-97 = 300
n(P) + n(C) - n(P and C) = 300
175 + 225 - n(P and C) = 300
400 - n(P and C) = 300
n(P and C) = 100
So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297
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b. Which of these products has the same value as 4(12)? Select all that apply.
A.
8(6)
B.
76
C.
316
D.
12(4)
E.
124
Answer:
A and D
Step-by-step explanation:
8(6) means 8x6 so that's 48
and 12(4) is the same as 4(12) so that should be simple enough
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
6, (2, 8) 7, (2,10)
The equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
We know that the equation of a line with gradient m and y-intercept is:
y = mx + c.
We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
We know the point-slope form of equation of line,
(y - y1) = m(x - x1)
For m = 6 and (x1, y1) = (2, 8)
(y - 8) = 6(x - 2)
y - 8 = 6x - 12
y = 6x - 4
For m = 7 and (x1, y1) = (2, 10)
(y - 10) = 7(x - 2)
y - 10 = 7x - 14
y = 7x - 4
Therefore, the equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
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David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
What is the distance between (-5,-6),(-9,-4)
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
Describe in words where cube root of 24 would be plotted on a number line.
100 points and brainliest
Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.
Step-by-step explanation:
in 1950, the world population was 2560 million people. in 1960, the population was 3040 million people. assume that world population grows in constant relative proportion. (a) what is the relative growth rate, k? [3p] (b) use the model to predict the population in 2020.
(i) Relative growth rate, k = 48 million people/ year
(ii) Population in 2020 is given by 5920 million people.
Given that in 1950, the population of world was 2560 million.
In 1960, the population of world was 3040 million people.
Also it is mentioned that, world population grows in constant relative proportion.
So, the difference between time = 1960 – 1950 = 10 years
The growth in population = 3040 mil – 2560 mil = 480 million
So the relative growth rate of population is = 480/10 = 48 million/year
Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.
Then the mathematical model is,
N = 2560 + kt
So for 2020, t = 2020-1950 = 70
k = 48
So, N = 2560+48*70 = 5920
So the population in 2020 is 5920 million people.
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the mpg (miles per gallon) of a certain compact car is normally distributed with a mean of 31 and a standard deviation of 1.2. what is the probability that the mpg for a randomly selected compact car would be more than 30?
The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.
Given data;
A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.
We need to get the probability that the mpg for a randomly selected compact car would be more than 30.
Therefore;
Mean = μ = 31
Standard deviation = σ = 1.2
Let;
P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)
= P(Z > -0.833)
= 0.797
Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.
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super bowl xlvi was played between the new york giants and the new england patriots in indianapolis. due to a decade-long rivalry between the patriots and the city's own team, the colts, most indianapolis residents were rooting heartily for the giants. suppose that 90% of indianapolis residents wanted the giants to beat the patriot. what is the probability that, of a sample of 100 indianapolis residents, at least 15% were rooting for the patriots in super bowl xlvi?
The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
By using the normal distribution method, a mean u and standard deviation σ,
The ratio of people who wants the Giants to eat patriots is p = 0.90,
The assumed sample size denoted by n is 100,
and their distribution's mean is u = 0.90,
by using the standard deviation formula is
σ = √(p(1 - p) ÷ n),
σ = √(0.90(1 - 0.90) ÷ 100),
σ = 0.03,
we get that the standard deviation is σ = 0.03
Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match Super Bowl XLVI is
P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))
The significant value of X,
X - u ÷ σ = Z
we get,
P(X > 0.75) = (Z<5)-1
P(X < 0.75) = 1.293 - 1
P(X < 0.75) = 0.293
By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
To learn more about the probability normal distribution method:
https://brainly.com/question/21688399
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