The total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².
What is geometric progression?A geometric progression is the series of numbers such that the ratio of any two consecutive numbers of the series is the same.
If we look closely at the problem we will understand that on each of the square boxes the number of pennies will get double from the previous one therefore, we can say that it is forming a geometric progression where the first term of the sequence is 1, while the common ratio is of 2. thus,
The total number of pennies on Rows 1-4 (the first 32 squares) is the sum of the geometric progression for the first 32, terms, therefore,
[tex]S_n = a_1(\dfrac{r^n-1}{r-1})[/tex]
Now, as we know that the first term of the series is 1, while the common ratio(r) is 2, and the number of terms(n=32). Thus, the sum can be written as,
[tex]S_n = a_1(\dfrac{r^n-1}{r-1})\\\\S_n = 1(\dfrac{2^{32}-1}{2-1})\\\\S_n = 4,294,967,295[/tex]
The number can also be written as,
[tex]S_n = 4,294,967,295\\\\S_n = 2^{32}[/tex]
Hence, the total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².
Learn more about Geometric progression:
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Answer:
A: 2^32 – 1
Step-by-step explanation:
Nolan drives 15 miles in 30 minutes. If he drove three hours in total at the same rate,
how far did he go?
Before you try that problem, answer the question below.
How many minutes did Nolan drive in total?
Order he distance traveled from least to greatest
30 kph for 4 hours
5 kph for 10 hours
15 kph for 2 hours
35 kph for 1 hour
Answer:
15 for 2 = 30km
35 for 1 = 35km
5 for 10 = 50km
30 for 4 = 120km
Step-by-step explanation:
formula is
distance = speed x time
Can you help with my math work please
Answer:
A. pen 0.75, pencil 0.50
Step-by-step explanation:
there is 4 of each that means you have to multiply by 4so
0.75 × 4 = 3
0.50 × 4 = 2
add them up equal 5
Answer:
The correct option is A. Pen $0.75; pencil, $0.50
Find the geometric mean of 4 and 49
Can someone please help me with this ty!
please help fast i have 30 mins
Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
Choose two equations that can be used to find the height, h, of the tree. what is the equation
Answer:
the answer is... Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
Choose two equations that can be used to find the height, h, of the tree.
Step-by-step explanation:
hope it helps
The two equations that can be used to find the height are as follows:
12 / 4 = h /5
5 / 4 = h / 12
What is Similar Triangles?Similar triangles are not necessarily the same in size. Corresponding angles of similar triangles are congruent. The sides of similar triangle are a ratio of each other.
here, we have,
Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
The tree cast a shadow of 12 ft.
Let's establish the proportion base on similar triangles. The height of the tree is h.
Therefore,
h / 12 = 5 / 4
Therefore,
h / 12 = 5 / 4
cross multiply
4h = 60
divide both sides by 4
h = 60 / 4
h = 15 ft
Therefore, the two equations that can be used to find the height are as follows:
12 / 4 = h /5
5 / 4 = h / 12
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given that €1 =£0.75
a how much is €530 in £
b £1 =€
Answer:
a) £397.50
b) £1 ≈ €1.33
Given:
€1 = £0.75
To find out:
a)
€530 = £0.75 × 530
€530 = £397.50
b)
Since £397.50 = €530:
£1 = €530 ÷ 397.5
£1 = €1.33333333333
£1 ≈ €1.33
7 5/10 - 2 2/11 estimate the difference. HELP.
Answer:
605/110
Step-by-step explanation:
75*11/110
-
22*10/110
=605/110
A cube has an edge length of 14 feet. What is its volume, in cubic feet?
Answer:
V=2744ft³ is the answer
Answer:
2,744 cubic feet
Step-by-step explanation:
You only need a single measurement, then you multiply it by itself and by itself again, equivalent to raising it to the power of 3. Finally, adjust the unit to its cubic equivalent. in this case Volume = (Edge of the cube) 3 so 14 x 14 x 14 is 2,744
Please find the perimeter and area of these shapes
Answer:
ABC shaded area = 36[tex]\pi[/tex] - 72 cm²
ABC shaded area perimeter = [tex]6\pi +12\sqrt{2}[/tex] cm
ABCD area = [tex]\dfrac52 \pi[/tex] cm²
ABCD perimeter = [tex]3\pi +2[/tex] cm
Step-by-step explanation:
Shape ABC
Assuming you want the area and perimeter of the shaded part of the shape only...
Area
Area of a sector = [tex]\dfrac12r^2\theta[/tex] (where r is the radius and [tex]\theta[/tex]
⇒ area of a sector = [tex]\dfrac12 \times 12^2\times \dfrac{\pi}{2} =36\pi \ \textsf{cm}^2[/tex]
Area of triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 12 x 12 = 72 cm²
Therefore, area of shaded area = area of sector - area of triangle
⇒ area = 36[tex]\pi[/tex] - 72 cm²
Perimeter
Arc length = [tex]r\theta[/tex] (where r is the radius and [tex]\theta[/tex]
⇒ arc length = [tex]12\times\dfrac12\pi =6\pi \ \textsf{cm}[/tex]
Hypotenuse of triangle = [tex]\sqrt{a^2+b^2}[/tex] (where a and b are the legs of the right triangle)
⇒ hypotenuse = [tex]\sqrt{12^2+12^2} =12\sqrt{2}[/tex] cm
Therefore, perimeter = arc length + hypotenuse
⇒ perimeter = [tex]6\pi +12\sqrt{2}[/tex] cm
Shape ABCD
Area
Area of a semicircle = [tex]\dfrac12 \pi r^2[/tex] (where r is the radius)
⇒ area of large semicircle ABC = [tex]\dfrac12 \times \pi \times 2^2=2\pi \ \textsf{cm}^2[/tex]
⇒ area of small semicircle AD = [tex]\dfrac12 \times \pi \times 1^2=\dfrac12\pi \ \textsf{cm}^2[/tex]
⇒ area of shape ABCD = [tex]\dfrac12 \pi + 2 \pi=\dfrac52 \pi \ \textsf{cm}^2[/tex]
Perimeter
1/2 circumference = [tex]\pi r[/tex]
⇒ perimeter = [tex]2\pi +2+\pi=3 \pi+2 \ \textsf{cm}[/tex]
I don't know this. Can someone please help me. I am in 7th grade.
Answer:
590 or 589.89
Step-by-step explanation:
Hope this helps!
Answer:
1380.25
Step-by-step explanation:
So to solve this problem, you find the outside circle and subtract it from the inside circle.
So, lets find the basic values
Radius of inside circle = diameter of the inside circle / 2
= 27.6
= 13.8
Radius of outside part = 11.3
So the area of the outside circle is
A = pi r^2
= pi (11.3 + 13.8)^2
= 630.01
= 1978.23
And the area of the inside circle is
A = pi r^2
= pi (13.8)^2
= 190.44
= 597.98
To find the shaded part, we subtract the outer circle with the inner circle
1978.23 - 597.98 = 1380.25
The area of the shaded region is 1380.25
What is the perimeter of the triangle?
Maritar has a
triangluar garden 17% of it in plantel corrests, what
area is planted with carrots...
Answer:
WRONG SUBJECT
Step-by-step explanation:
YOU'RE QUESTIOON WAS DELETED FOR THE WRONG SUBJECT
which equation shows x2+6x-6=0
Answer :0.75
Step-by-step explanation:
2x+6x-6=0
2x+6x=6
8x=6
x=6/8
x=0.75
HOPE IT HELPS .... MARK ME BRAINLIEST
What is the area of a triangle with vertices at (−4, −6), (1, −6), and (1, 2)?
Answer:
The answer is (1,2) I'm pretty sure that is the answer if it is not please tell me I'll check.
which of the following lists of ordered pairs is a function?
Answer:
A (Only A)
Step-by-step explanation:
the X position can NOT repeat itself at all. In A it does not do that but in the rest it does
in B there is a 2,5 and a 2,2 (Repeating X)
in C there is a -1,4 and a -1, 7 (Repeating X)
in D there is a 3,1 and a 3,2 (Repeating X)
Answer:
A
Step-by-step explanation:
A function is a set of coordinate points that has a separate point for the x axis in every pair.
In order to find a function, just look at the first number in every parentheses and see if there are any multiples
Answer A has -2, 2, -3, and 3
Answer B has 2, 3, 4, and 2
Answer C has 0, -1, 1, and -1
Answer D has 1, 2, 3, and 3
Answer A is the only one that doesn't have repeating x points
Please give brainliest if I helped! :)
Normal Samantha is using ribbon to make bows to be sold at a school fundraiser. She has 83.2 meters of ribbon. She needs 1.28 meters of ribbon for each bow. How many bows she can make?
The answer would be 65
hope that helps :b
Answer:
83.2 meters ÷ 1.28 meters = 65 bows
(5x-25)(x+4)=0
What’s the answer
Answer:
x = - 4, x = 5
Step-by-step explanation:
(5x - 25)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
5x - 25 = 0 ⇒ 5x = 25 ⇒ x = 5
Answer:
x = - 4, x = 5
Step-by-step explanation:
(5x - 25)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
5x - 25 = 0 ⇒ 5x = 25 ⇒ x = 5
Hence, the correct answer is x=-4, x=5
A 6-pack of dish towels costs $21.36. What is the unit price?
Answer:
$3.56
Step-by-step explanation:
Divide 21.36 by 6 and you get 3.56
Answer:
d = $3.56
Step-by-step explanation:
d = the cost of each towel
6d = 21.36
/6 /6
d = $3.56
Check your answer:
6d = 21.36
6(3.56) = 21.36
21.36 = 21.36
Hope this helps!
There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
Answer:
1/3 x 3/11 = 3/33 or 0.09, or 9 percent
Step-by-step explanation:
Answer:
16/144
4/12 × 4/12 = 16/144
4x0.75
Expian pls
4x0.75
4/0.65
Answer:
3
Step-by-step explanation:
0.75 out of 1 for 4 is 3
for 4
0.25 is 1
0.5 is 2
0.75 is 3
1 is 4
4/0.65 = 2.15 (not 100% on this one)
If y = x3 + x,
find the value of y when x=-2
Answer:
y=-8
Step-by-step explanation:
if x=-2 -2*3= -6, -6+-2=-8
Answer:
-8
Step-by-step explanation:
-2 times 3 is -6, and -6 plus -2 equals -8
What would the answer be
NEED ANSWER ASAP AND MARKING BRANLIEST
The given quadratic equation forms a parabola when graphed, a U-shaped line.
To find the minimum value of y, we could find the y-coordinate of the vertex.
What is the vertex?The vertex represents the maximum or minimum point on a parabola. It tells us the optimal y-value of the function and the x-value at which it occurs.
For the given quadratic, [tex]y=x^2+6x+7[/tex] the optimal y-value, or the y-coordinate of the vertex, will be a minimum. The [tex]x^2[/tex] value is positive, meaning the parabola will open upwards. (Please see below for an image representation).
Different Ways to Approach the ProblemThere are multiple ways to approach this question.
One way is to rearrange the equation, which is currently in standard form, to vertex form.
Standard form for a quadratic: [tex]y=ax^2+bx+c[/tex]Vertex form for a quadratic: [tex]y=a(x-h)^2+k[/tex] where (h,k) is the vertexAnother way is to factor the equation to first find the x-intercepts of the graph, find the x-coordinate of the vertex, then at the end, plug the x-coordinate into the equation to find the minimum y-value.
The second strategy is a bit redundant for this type of question, so we can go about solving it by using the first method.
Finding the Vertex of this Parabola[tex]y=x^2+6x+7[/tex]
First, we can group [tex]x^2[/tex] and [tex]6x[/tex] by using a set of parentheses:
[tex]y=(x^2+6x)+7[/tex]
Then, we can complete the square:
[tex]y=(x^2+6x+(\dfrac{6}{2})^2)^2+7-(\dfrac{6}{2})^2[/tex]
[tex]y=(x^2+6x+9)^2+7-9\\\\y=(x^2+6x+9)^2-2[/tex]
Apply the rule [tex]a^2+2ab+b^2=(a+b)^2[/tex]:
[tex]y=(x+3)^2-2[/tex]
Therefore, the vertex of the quadratic is (-3,-2).
This makes the minimum y-value -2. The x-value at which this occurs is -3.
Answer:The minimum y-value -2. The x-value at which this occurs is -3.
PLEASE HELP ME PLEASE HELP ME I NEED HELP ON SIX PLEASE ANSWER ME AND DONT SEND LINKS THAT DONT WORK!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Pudge sold 8 tickets, Christi sold 19
tickets, Ace sold 38 tickets
Step-by-step explanation:
x = Pudge
3x - 5 Christi
2(3x-5) = Ace
Let x, 3x - 5 and 2(3x-5) be the tickets
x + (3x- 5) +2(3x - 5) = 65
Combine like terms
x+ (3x - 5) + 6x - 10 = 65
4x -5+6x - 10 = 65
10x - 5-10 = 65
Transpose -5 and -10 and change their
signs
10x = 65 +5+ 10
Add
10x = 80
Divide both sides by 10
10x/10x = 80/10
x =8
Pudge sold 8 tickets.
Evaluate x as 8
3x-5
3(8)-5
24-5 19
Christi sold 19 tickets.
2(3x-5)
2(3(3)- 5)
2(24- 5)
2(19)= 38
Ace sold 38 tickets.
Checking:
x+ (3x - 5) +2(3x - 5) = 65
8+(3(8)-5) +2(3(8) - 5) = 65
8 +19 +38 = 65
65 =65
Exit Ticket: Solve the triangle.
Solve the following problem. Round to one decimal place if
necessary. If your answer is correct you will see an image
appear on your screen.
T
.
Х
35
45°
Х
The value of x from the figure is 35√2
SOH CAH TOA identityFrom the given figur, we have the following parameters
figure
Opposite = 35
Angle = 45 degrees
Required
Hypotenuse = x
USing the theorem
Sin 45 = 35/x
x = 35/sin45
x = 35√2
Hence the value of x from the figure is 35√2
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what is 4.87 x 7.23 (show ur work with a pic)
How many eighth graders chose History as their favorite subject. Round answer to the nearest whole number.
19%
22%
27%
33%
The percentage of eighth-graders that chose History as their favorite subject is 19%
Percentages and proportionFrom the given table, we have the following parameters
Total students in the 8th grade = 124 students
Total number of 8th graders that chose history = 11 + 12
Total number of 8th graders that chose history = 23
Required percentage = 23/124 * 100
Required percentage = 19%
Hence the percentage of eighth-graders that chose History as their favorite subject is 19%
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A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 10^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 21^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance between points A and B and the boat is an illustration of elevation and distance
The distance from point A to point B is 346 feet
How to calculate the distance ABThe height of the lighthouse is given as:
h = 113
The distance between point A and the base of the lighthouse is calculated using the following tangent ratio
[tex]\tan(10) = \frac{113}{A}[/tex]
Make A, the subject
[tex]A = \frac{113}{\tan(10)}[/tex]
[tex]A = 640.85[/tex]
The distance between point B and the base of the lighthouse is calculated using the following tangent ratio
[tex]\tan(21) = \frac{113}{B}[/tex]
Make B, the subject
[tex]B= \frac{113}{\tan(21)}[/tex]
[tex]B= 294.38[/tex]
The distance AB, is then calculated as:
[tex]AB = A - B[/tex]
[tex]AB = 640.85 - 294.38[/tex]
[tex]AB = 346.47[/tex]
Approximate
[tex]AB = 346[/tex]
Hence, the distance from point A to point B is 346 feet
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