Answer:
Total Surface Area
= 384 sq ft
Step-by-step explanation:
To find Total Surface Area, add up the areas of all the sides of the shape. A square based pyramid has five sides, a square bottom and four triangular sides. Luckily all four sides are the same, so just one calculation for these.
Area of square base is given.
A = 144 sq ft
Since the base is a square the length of the side of the square is 12, because 12×12 is 144.
The side of the square base is the base of the triangular side.
Area of a triangle:
A = 1/2•b•h
A = 1/2(12)(10)
A = 60
The area of one triangular face is 60. There are four of these.
A = 4(60)
A = 240
This is the area of all the triangular faces.
Add them all up.
A (TOTAL)
= 144+240
= 384 sq ft
In the third month of a study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month?
A. an = 83 + 1.5(n – 1)
B. an = 83 + 1.5(n + 1)
C. an = 86 + 2(n – 1)
D. an = 86 + 2(n + 1)
The rule for the height of the tree during the nth month will be an = 83 + 1.5(n – 1). The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in the third month of the study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall.
For option A satisfy the equation for n = 3 and n = 7,
an = 83 + 1.5(n – 1)
a₃ = 83 + 1.5(3 – 1)
a₃ = 83 + 3
a₃ =86
a₇ = 83 + 1.5(7– 1)
a₃ = 83 + ( 1.5 x 6 )
a₃ = 83 + 9
a₃ = 92
Therefore, the rule for the height of the tree during the nth month will be an = 83 + 1.5(n – 1). The correct option is A.
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Suppose that Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the
sum of the dice is 8 and B be the event that Eitan rolls doubles. Using the sample space of possible outcomes
below, answer each of the following questions,
What is P(A), the probability that the sum of the dice is 8?
What is P(B), the probability that Eitan rolls doubles?
What is P(A and B), the probability that the sum of the dice is 8 and Eitan rolls doubles?
Are events A and B independent?
Choose 1 answer:
A Yes, events A and B are independent events.
No, events A and B are not independent events.
Given : Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. A be the event that the sum of the dice is 8 and B be the event that Eitan rolls doubles
To find : probability of event A , event B , Event A or B , Event A & B
Solution:
Six Sides Dice has { 1 , 2 , 3 , 4 , 5 ,6 }
4 Sides Dice has = { 1 , 2 , 3 , 4 }
Total possible outcome = 6 * 4 = 24
n(S) = 24
A = Sum of Dice = 8
(4 , 4) , ( 5 , 3) , ( 6 , 2)
n(A) = 3
B = Double ( means same number on each Dice )
B = ( 1 , 1) , ( 2, 2) , ( 3 , 3) , ( 4, 4)
n(B) = 4
A U B = ( 1 , 1) , ( 2, 2) , ( 3 , 3) , ( 4, 4) ( 5 , 3) , ( 6 , 2)
n (A U B ) = { 6 }
A ∩ B = { 4 , 4}
n(A ∩ B) = 1
Probability of Event A = 3/24 = 1/8
probability of Event B = 4/24 = 1/6
Probability of Event A or B = 6/24 = 1/4
Probability of Event A and B = 1/24
Learn more:
You are given one 6 sided dice and an 8 sided dice. The 8 sided die
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You roll a fair 666-sided die. What is ext{P(roll greater than 4})P(roll ...
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Katie lives in the Florida Keys. She loves
to dive and take pictures of marine life.
During her last dive, she used her depth
gauge to change her position relative
to sea level by -4.5 feet to reach her
goal, -12 feet. Let x represent her
initial position. Write and solve an
equation to find x.
Today when the dwarf planet Ceres is furthest from Earth, it is 564 million km away. 233 days from now, it will be at its closest average distance of 264 million km away. Using this information, formulate a sinusoidal function that models Ceres's distance from Earth.
Answer:
currently 464,833,060 kilometers, equivalent to 3.107217 Astronomical Units. Light takes 25 minutes
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
Answer:f θ =2sin θ + square root of 3.
Step-by-step explanation: I think this is right
NO LINKS!! Use the cylinder shown to mark each statement as true or false. Rewrite and correct any false statements.
Problem 9
Answer: FalseReason:
The height of the cylinder is 2.5 ft. It's misleading because the cylinder is tipped onto its side, so it appears that 4 ft is the height. The height of any cylinder is always perpendicular to the circular base. It might help to rotate the paper so that the circular base is horizontal.
==============================================================
Problem 10
Answer: FalseReason:
The diameter of the base is 4 feet, which divides in half to 2 feet and it's the radius of the circle.
Area = pi*(radius)^2 = pi(2)^2 = 4pi
So the area expression should be either pi(2^2) or pi(4) or 4pi
==============================================================
Problem 11
Answer: TrueReason:
V = pi*r^2*h
V = 3.14*2^2*2.5
V = 31.4 cubic feet
This volume is approximate since pi = 3.14 is approximate.
Beth is going to paint her dog's house
this weekend. If her dog's house is
24cm long, 20cm wide and 15cm tall,
how much paint Will Beth need to
buy?
If a permutation is chosen at random what is the probability that it begins with at least two A's
Answer:
Starting with AT LEAST 2 A's means starting with 3 A's, or starting with 2 A's with some different letter third.
P(AAA...) = (3/9)(2/8)(1/7) = 1/84
Step-by-step explanation:
The ABC brand hand sanitizer is sold at four stores. table below: The bottle size and cost are shown in the Store Size (millilitres) Price Andrea's Store 600 $650.00 Sandra's Store 540 $550.00 Cynthia's Store 480 $530.00 Janet's Store 400 $450.00 Which store has the lowest price per millilitre? a) Andrea's Store b) Sandra's Store c) Cynthia's Store d) Janet's Store
Answer:
can you post the question but more clear I didn't understand
Step-by-step explanation:
post it again I didn't understand
In a city election, two people ran against each other to be the next mayor. Candidate 1 received 24,000votes and candidate 2 received 80,000
.
Answer:
What is the question You are just stateing facts?
Step-by-step explanation:
saved: 12:19 PM
Week 1
Week 2
Week 3
Total
Lettuce
$5.48
?
$3.55
$12.00
Apples
$3.57
$ 2.12
$4.44
?
Chicken
$8.12
$10.13
?
$20.45
Enter his total cost for lettuce, apples, and chicken during Week 2.
$
Answer:
15.22
Step-by-step explanation:
You add the amount for lettuce on week 1 and week 3. then you subtract the total for lettuce from that number to get lettuce for week 2. After that just add the lettuce, apples, and chicken in the week two section and thats your answer
(80 + 240 times 3) ÷ 20
Solve the equation
1. P= 17 and t=25
2. T= 15 and a=9
3. P=10 and < A=50°
4. A=13 AND < A=37°
5. T=20 and < P=66°
Step-by-step explanation:
MARK A BRAIN LESS
CARRY ON LEARNING
which is greater 0.209 or 0.21
Answer:
0.21
Explanation:
210 hundredths is larger than 209 hundredths.
Answer:
0.21 because .210 is more than .209
A trapezoid has sides of length 11 inches, 1.5 inches, 11 inches, and 19.1 inches. What is the perimeter?
Answer:
The Perimeter of the trapezoid = 42.6 inches
Step-by-step explanation:
______
Formula:
let a , b , c , d be consecutively the lengths of the sides of the trapezoid
then
The Perimeter of the trapezoid = a + b + c + d
___________________________________
Suppose a = 11 , b = 1.5 , c = 11 , d = 19.1
therefore,
The Perimeter of the trapezoid = a + b + c + d
= 11 + 1.5 + 11 + 19.1
= 42.6
Ryan's mother recorded how many donuts he has eaten over the past few months. cake donuts 3 chocolate frosted donuts 48 maple donuts 7 cream-filled donuts 12 glazed donuts 20 Considering this data, how many of the next 45 donuts Ryan eats would you expect to be cream-filled donuts?
Answer:
6
out of the total donuts (90), Ryan ate 12 cream filled donuts. 45 is half of that, therefore he should eat half the cream filled donuts
log(x + 2) – logx =log(2x – 1) - log(3x – 12)
First note that any solution must belong to all of the intervals
x + 2 > 0 ⇒ x > -2
x > 0
2x - 1 > 0 ⇒ x > 1/2
3x - 12 > 0 ⇒ x > 4
so x must be larger than 4.
Recall that log(a) - log(b) = log(a/b). So we can rewrite
log(x + 2) - log(x) = log(2x - 1) - log(3x - 12)
log((x + 2)/x) = log((2x - 1)/(3x - 12))
Take the antilogarithm/exponential of both sides (note that the base of the logarithm doesn't matter here):
exp[log((x + 2)/x)] = exp[log((2x - 1)/(3x - 12))]
(x + 2)/x = (2x - 1)/(3x - 12)
Eliminate the fractions:
x (3x - 12) • (x + 2)/x = x (3x - 12) • (2x - 1)/(3x - 12)
(3x - 12) (x + 2) = x (2x - 1)
Expand both sides, collect terms and factorize to solve for x :
3x² - 6x - 24 = 2x² - x
x² - 5x - 24 = 0
(x - 8) (x + 3) = 0
x - 8 = 0 or x + 3 = 0
x = 8 or x = -3
Identify the trinomial that is not a perfect square.
A. 64x2 + 48x + 9
B. 25x2 + 70x + 49
C. 100x2 + 60x + 9
D. 121x2 + 100x + 25
Answer:
Option D, [tex]121x^2 + 100x + 25[/tex]
Step-by-step explanation:
Step 1: Determine the one that is not a perfect square
Factor Option A
[tex]64x^2 + 48 + 9[/tex]
[tex](8x + 3)(8x + 3)[/tex]
[tex](8x + 3)^2[/tex]
Factor Option B
[tex]25x^2 + 70x + 49[/tex]
[tex](5x + 7)(5x + 7)[/tex]
[tex](5x + 7)^2[/tex]
Factor Option C
[tex]100x^2 + 60x + 9[/tex]
[tex](10x + 3)(10x + 3)[/tex]
[tex](10x + 3)^2[/tex]
Factor Option D
[tex]121x^2 + 100x + 25[/tex]
Cannot factor this equation with rational number
Answer: Option D, [tex]121x^2 + 100x + 25[/tex]
Drag the tiles to the correct boxes to complete the pairs.
Consider the functions below.
f(x) = 12 - 61 – 27
g(t) = 1 - 9
Match the expressions to the correct function combinations.
( + 5)()
(1.9)(*)
(5-8)(=)
13 – 15.12 + 271 + 243
>
2 - 71 - 18
>
22 – 50 – 36
I + 3
Answer:
answer attached
Step-by-step explanation:
just solve them out
The expressions to the correct function combination is (f. g)(x).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
f(x) = 12 - 61 – 27
g(t) = 1 - 9
Now,
To match the expressions to the correct function combinations, you can substitute the values of f(x) and g(t) into the expressions and simplify. For example:
( + 5)() = (f(x) + 5)(g(t))
( + 5)() = ((12 - 6x - 27) + 5)(1 - 9t)
( + 5)() = (17 - 6x)(1 - 9t)
( + 5)() = 17 - 153t - 6x + 54xt
Therefore, by the given equation the answer will be (f. g)(x).
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Rajani has a bag that contains strawberry chews, cherry chews, and lime chews. She performs an experiment. Rajani randomly removes a chew from the bag, records the result, and returns the chew to the bag. Rajani performs the experiment 38 times. The results are shown below: A strawberry chew was selected 23 times. A cherry chew was selected 4 times. A lime chew was selected 11 times. Based on these results, express the probability that the next chew Rajani removes from the bag will be strawberry or cherry as a fraction in simplest form.
Answer:
[tex]\frac{27}{38}[/tex]
Step-by-step explanation:
P (Srawberry or Cherry)
= [tex]\frac{23 + 4}{38}[/tex]
= [tex]\frac{27}{38}[/tex]
I hope this help out.
The tubing was 146 feet long if each piece of tubing was cut so that it was 6 feet long how many six-foot pieces could be made from the tubing
Based on the histogram, how many items cost less than $3.00 per pound?
here are the option I already eliminated one
A. 1
B. 3
C. 7
What is the interquartile range of the data represented in the box plot below??
A.30
B.50
C.60
D.70
Option A: 30.
Step-by-step explanation:
Hope this helped.
Geometry. please help. image is attached. will give brainliest
Answer:
B (x= 14/3 , y= -5/3)
Step-by-step explanation:
A (x= 6, y= 1) and C (x= 2, y = -7)
On x-axis between A and C are 6 -2 = 4 units
On y-axis between A and C are 1 + 7 = 8 units
AB = (1/3) BC
Divide the distance between AC in 3 pieces
On x-axis will have 4/3 units on each piece
On y-axis will have 8/3 units on each piece
Now move away from A the 1/3 distance
A (x= 6, y= 1)
B (x= 6 -(4/3) , y= 1 -(8/3))
B (x= (18- 4)/3) , y= (3-8)/3))
B (x= 14/3 , y= -5/3)
In a certain Algebra 2 class of 21 students, 12 of them play basketball and 14 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
The probability that a student is chosen randomly from the class plays both basketball and baseball is 4/21
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcomeIf the total number of people in the class is 21 students, hence the total outcome is 21Get the number of students that plays both basketball and baseball
n(U) = n(B)only + n(Ba)only + n(BnBa) + n(BuBa)'
21 = 6-x + 14-x + x + 5
21 = 25 -x
x = 25 - 21
x = 4
Hence 4 students play both basketball and baseball
Pr(basketball and baseball) = 4/21
Hence the probability that a student chosen randomly from the class plays both basketball and baseball is 4/21
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To feed his plants logan creates a mixture that requires 3/8 cup of plant food for every gallon of water. If he uses 10 1/2 gallons of. Water what is the total amount of. Plant food he needa
Answer:
[tex]3\ \frac{15}{16}[/tex]
Step-by-step explanation:
The mixture requires 3/8 cup of plant food for every gallon of water
Then it requires (10 1/2)×(3/8) cup of plant food for 10 1/2 gallons of water
Now we have to calculate (10 1/2)×(3/8)
[tex]10\ \frac{1}{2} \ =\ \frac{10\times 2}{2} +\frac{1}{2} \ =\frac{20+1}{2} =\frac{21}{2}[/tex]
[tex]\frac{21}{2} \times \frac{3}{8} =\frac{63}{16} =3\ \frac{15}{16}[/tex]
then he needs :
[tex]\frac{63}{16}\ \ \text (cup\ of\ plant\ food)[/tex]
Using each digit once, list all the
3-digit numbers that can be made
From 1, 4, and 7.
Answer:
1,4,7 1,74. 4,7,1 ,4,1,7 ,7,4,1
Reflect the given triangle over
the line y=x.
3
-3
6
3
3
3
3
B!
-3
3
[?] [
[ ] [
Answer:
[tex]\left[\begin{array}{ccc}-3&3&3\\3&6&3\end{array}\right][/tex]
Step-by-step explanation:
Reflection over the line y=x is described by the transformation ...
(x, y) ⇒ (y, x)
The corresponding transformation matrix is ...
[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]
When this left-multiplies the given coordinate matrix, the result is the one shown above.
Find the exact value of the trigonometric expression when
sin(u) = − /13 and cos(v) = − 4/5. (Both u and v are in Quadrant III.)
tan(u+v)
Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)
Pleasse I need help Asap!!!!
Help Pleaseeee
Answer:
33
Step-by-step explanation:
simply replace x with 7!
7^2 = 49
49-16=33