The rule that represents the height of the ball after each bounce is;
H(n) = 400(0.8)^(n - 1)
Geometric Sequence Progression
From online sources, we have that;
After first bounce, height = 400 m
After 2nd bounce, height = 320 m
After 3rd bounce, height = 256 m
Formula for the nth term of a geometric sequence is;
T_n = ar^(n - 1)
First term is 400m
Since second term is 320, then common ratio is;
r = 320/400
r = 0.8
Thus, the 6th bounce which is the 6th term will be;
T_6 = 400 * 0.8^(6 - 1)
T_6 = 131 m
Read more about geometric sequence at; https://brainly.com/question/21688964
Which vocabulary word best describes what has been circled in this expression?'
7x +4y -3x +2
variables
coeffidents
constants
terms
Answer:
If the 7 4 and the -3 are circled then it's coefficient. I have the same vocab quiz lol
I buy
packet of bread rolls costing £1.50 for each packet
2 bottle of ketchup costing £1.60 for each bottle
3 packets of sausages
I pay with a £10 note.
I get 50p change.
How much does 1 packet of sausages cost?
Step-by-step explanation:
are you having problems with something if so message
helppppppp thxxx need this asap
If u+8=5 and v -3=-2 whats the value of u and v
Answer:
[tex]{ \tt{u + 8 = 5}} \\ { \tt{u = 5 - 8}} \\ { \underline{ \underline{ \tt{ \: u = {}^{ - }3 \: }}}}[/tex]
[tex]{ \tt{v - 3 = - 2}} \\ { \tt{v = - 2 + 3}} \\ { \underline{ \underline{ \tt{ \: \: v = 1 \: \: }}}}[/tex]
43, 52, 56, 47, 53, 60, 45, 40, 52, 48, 50
Find the median and mode of the following data.
Answer:
median = 50
mode = 52
Step-by-step explanation:
Answer:
Median: 50
Mode: 52
Step-by-step explanation:
To find the median, you arrange all of the numbers in order and find the number in the middle.If the number of values is an even number, the median will be the average of the two middle numbers.
The mode is the number that occurs the most in a set of data.
In a class of 50 students, the number of students who offer accounting is twice as the number who offer economic. 10 students offer neither of the two subject and 5 students offer both subjects.How many student offer economic and illustrate the information on the venn diagram
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month? Credit New Car APR (%) Used Car APR (%) 5.40 Excellent 5.65 6.35 Good 5.95 16.30 6.90 Average 17.60 Fair 7.55 9.80 10.0 Poor
Using simple interest, it is found that $97.06 of interest is accrued after the first month.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of interest after t years in is modeled by:
[tex]I(t) = Prt[/tex]
In which:
P is the principal.r is the interest rate, as a decimal.In this problem, first we have to find the total price of purchase of the car, which is $19,725.00 plus 4.75% sales tax, hence:
[tex](1 + 0.0475) \times 19725 = 1.0475(19725) = 20662[/tex]
Then:
Considering a down payment of $2,175, the principal is of P = 20662 - 2175 = 18487.New car and average credit rating, hence the interest rate is of 6.30%, that is, r = 0.063.We want the interest earned after one month, considering the time is measured in years, we have that [tex]t = \frac{1}{12}[/tex].Then:
[tex]I\left(\frac{1}{12}\right) = 18487(0.063)\frac{1}{12} = 97.06[/tex]
$97.06 of interest is accrued after the first month.
You can learn more about simple interest at https://brainly.com/question/25296782
Write the equation of the line in fully simplified slope-intercept form.
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 2/3x + 5 (-3, 8)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2/3 and passes through (-3 , 8)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{8})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{\cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-8=\cfrac{2}{3}(x+3)\implies y-8=\cfrac{2}{3}x+2\implies y=\cfrac{2}{3}x+10[/tex]
There are 12 months in a year.
Use the drop-down menus to help write the equation that can be used to find the number of months, , given the number of years, .
Answer:
12 months=1 years
24 months=2 years
36 months=3 years
(click choose and pin the photo please) so that i can see options
hope it helps you
make me brainliest plz
I need help with this quick
Plz show all the work plz
Answer:
Step-by-step explanation:
Teresa bought n packs of pencils. Each pack has 12 pencils. Write an equation to represent the total number of pencils c that Teresa bought.
Answer:
c = 12n
Step-by-step explanation:
Ten less than the quotient of a number and-6 is -2
Answer:
(n÷-6)-10 = -2
n = -48
Step-by-step explanation:
let 'n' = number
(n÷-6)-10 = -2
[tex]\frac{n}{-6}[/tex] - [tex]\frac{60}{6}[/tex] = -2
[tex]\frac{(-n-60)}{6}[/tex] = -2
multiply each side by 6 to get:
-n-60 = -12
-n = 48
n = -48
Guys I need your help !!!
Answer:
hope this helps you
a lot
have a great day..
Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil? *
Answer:
5 months
Step-by-step explanation:
120 * 10m = 150 * 4m
subtract 4m to 10m
120 * 6m = 150
subtract 120 to 150
6m = 30
divide 6 to 30
30 / 6 = 5
5 months
. You are mailing a gift box that is 18 inches by 8 inches by 12 inches. You
want to put it in a larger box and surround it with foam packing. The larger
box is 20 inches by 12 inches by 15 inches. How many cubic inches are
there for the foam packing?
Cubic inches of first box = 18 x 8 x 12 = 1,728 cubic inches
Cubic inches of larger box = 20 x 12 x 15 = 3,600 cubic inches.
Cubic inches for packing foam = 3600 - 1728 = 1,872 cubic inches
Answer: 1,872 cubic inches
8a+3b=7 solve for b I dont know it.
Answer:
[tex] b = \dfrac{7 - 8a}{3} [/tex]
Step-by-step explanation:
[tex] 8a + 3b = 7 [/tex]
[tex] 3b = 7 - 8a [/tex]
[tex] b = \dfrac{7 - 8a}{3} [/tex]
Answer:
b = [tex]\frac{7-8a}{3}[/tex]
Step-by-step explanation:
8a + 3b = 7 ( subtract 8a from both sides )
3b = 7 - 8a ( isolate b by dividing both sides by 3 )
b = [tex]\frac{7-8a}{3}[/tex]
Solve. −2x 3. 25=0. 5x 4. 75 x=−0. 6 x=−1 x=−3. 2 I don't know.
Answer:
x=-0.6
Step-by-step explanation:
What is the lateral surface area of the square pyramid represented by this net?
Answer:
340 ft²
Step-by-step explanation:
From the diagram, we can see that the shape is made up of a square and 4 triangles. (We know it's a square as its width equals its length).
First, find the area of the square.
Area of a square = width x length = 10 x 10 = 100 ft²
All the triangles are the same, so we need to find the area of one of the triangles and multiply it by 4.
Area of a triangle = 1/2 x base x height = 1/2 x 10 x 12 = 60 ft²
So the total area of all 4 triangles = 4 x 60 = 240 ft²
Therefore the total surface area = 100 + 240 = 340 ft²
Answer:
340 ft²
Step-by-step explanation:
The surface area of a shape is basically the area of its faces.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
1. First, Let's find the area of the triangles. To find the area of a triangle, we need to multiply the height and the base and then divide the product by 2.
[tex]\rightarrow \text{Area of triangle} = \dfrac{12 \times 10}{2}[/tex]
Now, let's find the area of the triangle by simplifying the RHS.
[tex]\rightarrow \text{Area of triangle} = 6 \times 10[/tex]
[tex]\rightarrow \text{Area of triangle} = 60 \ \text{ft}^{2}[/tex]
Since there are four triangles, we need to further multiply the area of the triangle by 4 to find the area of four triangles.
[tex]\rightarrow \text{Area of four triangles} = 4(60)[/tex]
[tex]\rightarrow \text{Area of four triangles} = 240 \ \text{ft}^{2}[/tex]
2. Now, let's find the area of the square. To find the area of the square, we need to square the side length.
[tex]\rightarrow \text{Side length} = 10 \ \text{ft}[/tex]
[tex]\rightarrow \text{Area of square} = 10^{2}[/tex]
[tex]\rightarrow \text{Area of square} = 100 \ \text{ft}^{2}[/tex]
3. Lastly, let's find the surface area. To find the surface area of the figure, we need to sum up the area of the triangles and the area of the square.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 240 + 100}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 340 \text{ft}}^{2} }[/tex]
Sandra bought 4 pounds of sweet potatos for $6.12 what is the cost per pound of sweet potatoes
Answer:
$1.53 per pound
Step-by-step explanation:
if she bought 4 pounds for 6.12 dollars then you can divide 6.12 by 4 to get the answer for one pound of potatoes and 6.12/4 = 1.53
Hope this helps! :)
NEED HELP ASAP
Find f(-2) for f(x) = 2(4)^x
Answer:
A.) [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
f(-2) means plug in -2 in for x for the equation f(x), therefore,
f(-2) = [tex]2(4)^x = 2(4)^{-2} = \frac{1}{8}[/tex]
(Givng Good Points!)
Mark deopsits $500 into a bank account. He gets a 3% interest rate. How much money will Mark earn in interest over 5 years?
$150
$750
$75
$10
Simple interest formula :
total = starting amount x (1 + ( interest rate x time))
total = 500 x (1 + (.03 x5))
Total = 575
Interest = 575-500 = 75
answer: $75
3E. Given square ABCD, with point P on side AB , point Q on side BC, point R on side CD, and point S on side DA as shown. Additionally, P is 2/3 of the way from A to B, Q is 2/3 of the way from B to C, R is 2/3 of the way from C to D, and S is 2/3 of the way from D to A. Compute the ratio of the area of square PQRS to the area of square ABCD. Write your answer as a fraction in lowest terms.
The length of the sides of the square PQRS is a fraction of the
length of the sides of square ABCD.
Correct response:
The ratio, of area of square PQRS to the area of square ABCD is; 5:9Which is the method used to find the ratio of the areas?Let x represent the side length of the square, ABCD we have;
Area of the square, ABCD is A = x²
Side length, s, of the inscribed square, PQRS, is given as follows;
[tex]s = \displaystyle \sqrt{ \left(\frac{2}{3} \cdot x \right)^2 + \left(\dfrac{1}{2} \cdot x\right)^2 } = \frac{\sqrt{5} }{3} \cdot x[/tex][tex]Area \ of \ the \ inscribed \ square\ = s^2 = \left(\dfrac{\sqrt{3} }{3} \cdot x \right)^2 = \mathbf{\dfrac{5}{9} \cdot x^2}[/tex]
[tex]Ratio \ of \ area \ of \ square \ PQRS \ to \ square \ ABCD = \dfrac{\dfrac{5}{9} \cdot x^2 }{x^2} = \mathbf{ \dfrac{5}{9}}[/tex]
The ratio of the area of the square PQRS to the square ABCD is 5:9Learn more about finding the area of geometric shapes here:
https://brainly.com/question/316492
PLEASE HELP 100 POINTS AND BRAINLIEST
Answer:
C
.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
(6-6)
select all of the equations that represent a nonlinear function
A. y= 3x(square)+9x+6
B. y=3x-10
c. y=2x+9x
d. y=x(3x+10)
e.y=x/3+10
Answer:
a. y = 3x² + 9x +6
d. y = x(3x + 10)
Step-by-step explanation:
Most equations that have a squared variable are going to be nonlinear.
If you distribute the x in the d equation you get this: y = 3x² + 10x
Choices b, c, and e are going to be linear because there is only one variable, and those variables do not have exponents.
Find the area of a square with a diagonal of 28cm (step by step)
if line r bisects DG at point E, and if DE= 2z +2 and DG = 5z-7, then find DG
Answer:
DG = 48
Step-by-step explanation:
if line r bisects DG at point E, then point E is midpoint of DG
so DG = 2DE
5z - 7 = 2(2z + 2)
5z - 7 = 4z + 4
5z - 4z = 4 + 7
z = 11
DG = 5z - 7 = 5(11) - 7 = 55 - 7 = 48
Simplify : √3 + √27 - 12/√3 + 6/√3
Answer:
2√3
Step-by-step explanation:
The volume of a rectangular prism is 36 cubic feet. Select three choices which could be the dimensions of the prism.
Answer:
Well we don't have the choices to choose from so I will just list some
36x1x1
18x2x1
3x6x2
3x3x4
2x2x9
6x6x1
3x12x1
Step-by-step explanation:
anything that multiples together to get 36
Hope this helps if you need more let me know! :)
1x factors of 36
1x1x36
1x2x18
1x3x12
1x4x9
1x6x6
2X factors of 18
2x1x18
2x2x9
2x3x6
3 times factors of 12
3x1x12
3x2x6
3x3x4
4 times factors of 9
4x1x9
4x3x3
6 times factors of 6
6x1x6
6x2x3
there are some repeats but that should be most of the choices
Ryan has 4 cups of grape juice, and Kelsey has 7 cups of lemonade. They want to combine what they have to make punch. How many 1/2 cup servings of punch can they make?
What is the math problem?
Answer:
22 servings
Step-by-step explanation:
4+7=11 cups
11 divided by 1/2=22
