Answer:1
Step-by-step explanation: it’s always at the end of a linear equation
A bouncy ball is dropped such that the height of its first bounce is 6 feet and each successive bounce is 72% of the previous bounce's height. What would be the height of the 6th bounce of the ball? Round to the nearest tenth (if necessary).
Answer:1.2
Step-by-step explanation:
The height of the 6th bounce of the ball will be 1.2 feet.
What is geometric sequence?
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
[tex]T_{n} =ar^{n-1}[/tex]
Where,
[tex]T_{n}[/tex] is the nth term.
r is the common ratio
a is the first term
According to the given question.
During the first bounce, height of the ball from the ground, a = 6 feet
And, the each successive bounce is 72% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
= 72% of 6
= [tex]\frac{72}{100} (6)[/tex]
= 0.72 × 6
= 4.32 feet
During the third bounce, the height of ball from the ground
= 72% of 4.32
= [tex]\frac{72}{100} (4.32)[/tex]
= 3.11 feet
Like this we will obtain a geometric sequence 6, 4.32, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.72
Therefore,
The sixth term of the geometric sequence is given by
[tex]T_{6} = 6(0.72)^{6-1}[/tex]
[tex]T_{6} =6(0.72)^{5}[/tex]
[tex]T_{6} = 6 (0.193)[/tex]
[tex]T_{6} = 1.16 feet[/tex]
[tex]T_{6} = 1.2[/tex] feet
Hence, the height of the 6th bounce of the ball will be 1.2 feet.
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What is the product? [ 5 -2 -6 2] x [ -1 -1 ]
Answer:
118
Step-by-step explanation:
Distribute 5 through the parentheses
-5 - 5 - 2(-1 - 1) - 62(-1 - 1)
distribute -2 through the parentheses
-5 - 5 + 2 + 2 -62(-1-1)
distribute -62 through the parentheses
-5 - 5 + 2 + 2 + 62 + 62
calculate the sum & differences
118
Answer:
[ -3 4 ]
Step-by-step explanation:
The graph below shows the number of paintballs a machine launches, y, in x seconds
Answer:
64/4
Have an amazing day!
Find AB. PLEASE HELP ASAP!!!
Answer: i believe its 15
Step-by-step explanation:
it continues to go down by seven (if this is wrong I´m so sorry )
A bag contains 20 red marbles, 8 white marbles, and 2 gray marbles. You randomly pick out a marble, record its color, and put it back in the bag. You repeat this process 120 times. How many white or gray marbles do you expect to get?
please answer soon!!
Answer:
10
Step-by-step explanation:
What is the weight on Earth of a girl with a mass of 30 Kg? The acceleration due to gravity on Earth is 9.8 m/ s 2.
ex
Answer: If, on earth, your mass is 30kg, then your weight is m*g which is mass (30kg) times Earth gravity (9.8m/s^2) = 294 N.
Step-by-step explanation:
The weight of a girl would be 294 N on Earth with a mass of 30 Kg.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
The weight on Earth of a girl would be the product of the mass and acceleration due to gravity on Earth
So the required solution would be:
⇒ weight = mass × acceleration due to gravity on Earth
⇒ weight = 30 × 9.8
⇒ weight = 294 N.
Hence, the weight of a girl would be 294 N on Earth with a mass of 30 Kg.
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8 divided by 1 4/5 in either fraction form or just number
Answer:
4.44444444444 or 40/9
Step-by-step explanation:
i searched it up
8 divided by 1 4/5 in fraction form will be 40 / 9. Then the faction number 40 / 9 in the decimal form will be 4.4444.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The mixed fraction number is converted into a faction number.
⇒ 1 4/5
⇒ 1 + 4/5
⇒ (5 + 4) / 5
⇒ 9/5
Then the quotient of the numbers 8 and 9/5 will be given as,
⇒ 8 / (9/5)
⇒ 8 x 5 / 9
⇒ 40 / 9
The faction number 40 / 9 in the decimal form will be 4.4444.
More about the Algebra link is given below.
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A bag of rare spice that weighs 3/4 pounds will be split equally among 36 people. How much spice will each person get?
Answer:
Each person will get 1/48 of a pound of spice
Answer:
1/48 pound
Step-by-step explanation:
You have to do 3/4 divided by 36, so you get
[tex]\frac{3}{4} / 36 = \frac{3}{4} * \frac{1}{36} = \frac{1}{48}[/tex]
if
[tex]a - \frac{1}{a} = 9 find \: the \: value \: of \: {a}^{3} - \frac{1}{ {a}^{3} } [/tex]
Write an equation for the line that passes through (−10,3) and whose slope is undefined. Give an answer in standard form.
Answer:
y=-10x+3
Step-by-step explanation:
The slope is -10
[tex]601893654x59765=[/tex]
Answer:
3.5972174e+13 could i get brainliest please?
Step-by-step explanation:
What is the slope of the line that passes through the points (4, 7) and (5,8)?
Write your answer in simplest form.
Answer:
1
Step-by-step explanation:
Use the coordinates of the points to determine the slope
slope = Δy/Δx = (8-7)/(5-4) = 1
A 1 : 6
B 1 : 3
C 2:1
D 3:1
Answer:
B)1:3
plz mark as brainliest
Acellus
Find all the missing elements:
B
C
a
B = 32°
C = 125°
a = 7
Α'
b C
A = [?]° b = [ ] c = [ ]
Enter
Answer:
A = 23°
B = 9.5
C = 14.7
Step-by-step explanation:
Right Answers :)
The missing values are:
A = 23°
b = 9.5
c = 14.72
What is obtuse triangle?"It is a triangle whose one of the angles measure greater than 90° and other two acute angles."
What is law of sines?"The ratio of the length of a side of a triangle to the sine of the angle opposite to that side is the same for all sides and angles in a given triangle."
For given question,
We have been given an obtuse triangle ABC.
Here, ∠B = 32°
∠C = 125°
We know that the sum of all angles of a triangle is 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠A + 32° + 125° =180°
⇒ ∠A = 23°
Using the law of sines to triangle ABC,
[tex]\Rightarrow \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} \\\\\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} =\frac{c}{sin125^{\circ}}[/tex]
Consider,
[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{b}{0.53} \\\\\Rightarrow 7\times 0.53=b\times 0.39\\\\\Rightarrow b = 9.5[/tex]
Now we find the length of the side AB.
[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{c}{sin125^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{c}{0.82} \\\\\Rightarrow 7\times 0.82=c\times 0.39\\\\\Rightarrow c = 14.72[/tex]
Therefore, the missing values are:
A = 23°
b = 9.5
c = 14.72
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Daniel's age is 15% of
Sarah's. Luke's age is 75% of
Sarah's and 300% of Daniel's.
When they added their ages,
the total was 141. How old is
Rachel?
Answer:
27 years oldStep-by-step explanation:
Full question isDaniel's age is 15% of Sara's. Luke's age is 75% of Sara's and Rachel's is 300% of Daniel's. When they added their ages, the total was 141. How old is Rachel? SolutionDaniel = d, Sara = s, Luke = l, Rachel = r
We get below relations:
d = 0.15sl = 0.75sr = 3d ⇒ r = 3*0.15s ⇒ r = 0.45sSum of ages:
d + s + l + r = 141Substitute and solve for s:
0.15s + s + 0.75s + 0.45s = 1412.35s = 141s = 141/2.35s = 60Rachel's age is:
r = 0.45*60 = 27Greg has a 15 foot ladder. He needed to clean his gutters which are 12 feet high from the ground. How far away does Greg need to place the ladder from the base of the house to reach the gutters
Answer:
Base = 81 feet
Step-by-step explanation:
Given that,
Length of the ladder = 15 foot
Greg needed to clean his gutters which are 12 feet high from the ground.
We need to find how far away does Greg need to place the ladder from the base of the house to reach the gutters. Let it is b.
Here, hypotenuse = 15 feet, height = 12 feet and base = b
We can use Pythagoras theorem to find b.
[tex]b^2+h^2=H^2\\\\b^2=H^2-h^2\\\\b^2=15^2-12^2\\\\b^2=225-144\\\\b=81\ \text{feet}[/tex]
So, the ladder should be placed at a distance of 81 feet from the base of the house to reach the gutters.
A vehicle moves along a straight road. The vehicle's position is given by f(t), where t is measured in seconds since the vehicle starts moving. During the first 10 seconds of the motion, the vehicle's acceleration is proportional to the cube root of the time since the start. Which of the following differential equations describes this relationship, where k is a positive constant?
a. df/dt= k3√t
b. df/dt= k3√f
c. d^2f/dt^2= k3√t
d. d^2f/dt^2= k3√f
Answer:
C. [tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]
Step-by-step explanation:
Physically speaking, the acceleration is equal to the second derivative of the position of the vehicle in time. After a careful reading to the statement, we construct the following ordinary differential equation:
[tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]k[/tex] - Proportionality constant, measured in meters per second up to 7/3.
Therefore, the correct answer is C.
The differential equation that models the situation is:
[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]
Which is option C.
The position is the integral of the acceleration, with is the integral of the acceleration, hence, the relation between the position and the acceleration is:
[tex]\frac{d^2f}{dt^2}[/tex]
The acceleration is proportional to the cube root of the time since the start, hence:
[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]
In which k is the constant of proportionality.
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15 POINTSSS
An = 15 +3 (n-1)
term # l value of An
1 l ______
5 l ______
10 l ______
20 l ______
complete the table for each given sequence.
Adding linear expressions
(-4x+6) + (x-5)
Answer:
Step-by-step explanation:
Like terms have same variables. Combine like terms.
2) (-4x + 6) + (x - 5) = -4x + 6 + x - 5
= -4x + x + 6 - 5
= -3x + 1
4) (-2x + 10) + (-8x - 1) = -2x + 10 - 8x - 1
= - 2x - 8x + 10 - 1
= - 10x + 9
6) (8x + 9) + (-6x - 1) = 8x + 9 - 6x - 1
= 8x - 6x + 9 - 1
= 2x + 8
Solve each system using SUBSTITUTION. Remember to check!
2) y = –2x – 1
y = 3x – 16
Answer:
[tex]\left \{ {{x=3} \atop {y=-7}} \right.[/tex]
Step-by-step explanation:
We can directly substitute y of the first equation to the second equation.
-2x - 1 = 3x - 16
5x = 15
x = 3
Substituting back to any of the two equations, we get y = -2(3)-1 = -7. If you check with the second equation, y = 3(3)-16 = -7 as well.
Therefore [tex]\left \{ {{x=3} \atop {y=-7}} \right.[/tex].
what is the meaning of the following data? 101, 143, 132, 155, 166
Answer:
it depends on what you're doing
what's the name of the topic
Mariam is going to see a movie and is taking her 3 kids. Each movie ticket costs $12
and there are an assortment of snacks available to purchase for $3 each. How much
total money would Mariam have to pay for her family if she were to buy 6 snacks for
everybody to share? How much would Mariam have to pay if she bought x snacks for
everybody to share?
Answer:
a) $66
b) $48 + $3x
Step-by-step explanation:
4(12)=48
3(6)=18
48+18=66
---------------
4(12)=48
Each snack is $3, so is the bought x snacks, it would be $3x
She would pay $48 on movie tickets and $18 on snacks which would be a grand total of $66. If she bought x amount of snacks the equation would be 3x+48
Step-by-step explanation:
Please help me with my homework!
Linda used a number line to simplify an expression. Which expression did Linda simplify based on the number line?
A. -9+1
B. -1-9
C. -1+(-8)
D. -1-(-8)
There are 96 diners in a restaurant. If 3/8 of the diner are children, what fraction of
the diners are adults? How many adults is that?
Does Mario Kart have a secret agenda? Is it promoting capitalism, socialism, or communism?
help! asap i’ll mark you brainliest please.
Let X, denote the weight of a randomly selected prepackaged one-pound bag of carrots. Of course, one pound bags of carrots won't weigh exactly one pound. In fact, history suggests that Xi is normally distributed with a mean of 1.18 pounds and a standard deviation of 0.07 pound. Now, let W denote the weight of randomly selected prepackaged three-pound bag of carrots. Three pound bags of carrots won't weigh exactly three pounds either. In fact, history suggests that Wis normally distributed with a mean of 3.22 pounds and a standard deviation of 0.09 pound. Selecting bags at random, what is the probability that the sum of three one-pound bags exceeds the weight of one three-pound bag?
Answer:
0.9830 = 98.30% probability that the sum of three one-pound bags exceeds the weight of one three-pound bag
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Three one pound bags:
3 one pound mags, which have mean 1.18 and standard deviation of 0.07. The mean is 1.18 multiplied by 3, and the standard deviation will be 0.07 multiplied by the square root of 3. So
[tex]\mu_{1} = 3*1.18 = 3.54[/tex]
[tex]\sigma_{1} = 0.07\sqrt{3} = 0.1212[/tex]
Three pound bags:
Mean 3.22, standard deviation 0.09. So
[tex]\mu_{2} = 3.22, \sigma_{2} = 0.09[/tex]
What is the probability that the sum of three one-pound bags exceeds the weight of one three-pound bag?
Here, we work with the subtraction of the normal variables. The mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances. So
[tex]\mu = \mu_{1} - \mu_{2} = 3.54 - 3.22 = 0.32[/tex]
[tex]\sigma = \sqrt{\sigma_{1}^2 + \sigma_{2}^2} = \sqrt{0.1212^2+0.09^2} = 0.151[/tex]
This is the probability of the subtraction being positive, that is, 1 subtracted by the pvalue of Z when X = 0. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 0.32}{0.151}[/tex]
[tex]Z = -2.12[/tex]
[tex]Z = -2.12[/tex] has a pvalue of 0.0170
1 - 0.0170 = 0.9830
0.9830 = 98.30% probability that the sum of three one-pound bags exceeds the weight of one three-pound bag
Jill orders t-shirts on Amazon. Each shirt costs $15.00 including tax. A one-time shipping fee of $3.25 is added to the cost of the order. The total cost of Jill's order is $78.25. How many t-shirts did Jill order
Answer:
5 shirts
Step-by-step explanation:
78.25- 3.25 = 75
75/ 15 = 5
Reindeer are fed 2 cups of corn for every 3 cups of grain. If you have 12 cups of corn, how many cups of grain need to be added?
S cups
1 cup
9 cups
13 cups
Which is an equation of a direct proportion
Answer:
The equation of a direct proportion is: y=8x
So, the correct option is Option A.
Step-by-step explanation:
We need to find equation of direct proportion.
If y varies directly with x then:
[tex]y\:\alpha \:x\\y=kx[/tex]
Where k is constant of proportionality
So, Now Looking at all the options and comparing it with the general equation of direct proportion [tex]y=kx[/tex]
We get the correct option: y=8x
All other options are not according to direct equation
The equation of a direct proportion is: y=8x
So, the correct option is Option A.