First, we need to calculate the volume of the package and the volume of the box
Package
[tex]V_P=6\times7\times2=84in^2[/tex]Box
[tex]V_B=9\times9\times3=243in^3[/tex]we need to subtract the volume of the package from the volume of the box
[tex]V=V_B-V_P=243-84=159in^3[/tex]159 in^3 of packing peanuts will fill into the box
Find the nth term of this quadratic sequence
4. 7, 12, 19, 28. . . .
Answer:
[tex]a_n=n^2 + 3[/tex]
Step-by-step explanation:
To find the nth term of a quadratic sequence, we need to determine the quadratic function that generates the sequence.
Given quadratic sequence:
4, 7, 12, 19, 28, ...
Begin by calculating the first differences between consecutive terms:
[tex]4 \underset{+3}{\longrightarrow}7 \underset{+5}{\longrightarrow} 12\underset{+7}{\longrightarrow} 19\underset{+9}{\longrightarrow} 28[/tex]
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
[tex]3\underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7\underset{+2}{\longrightarrow}9[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is 2, the coefficient of the n² term is 1.
Now we need to compare n² with the given sequence (where n is the position of the term in the sequence).
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}n&1&2&3&4&5\\\cline{1-6}n^2&1&4&9&16&25\\\cline{1-6}\sf operation&+3&+3&+3&+3&+3\\\cline{1-6}\sf sequence&4&7&12&19&28\\\cline{1-6}\end{array}[/tex]
We can clearly see that the algebraic operation that takes n² to the terms of the sequence is add 3.
Therefore, the expression to find the the nth term of the given quadratic sequence is:
[tex]\boxed{a_n=n^2 +3}[/tex]
Can you find the slope and type the correct code? Please remember to type in ALL
CAPS with no spaces.
Puzzle #2
1: Find the slope:
XO-2
-1
79339
Your answer
-3
3 Find the slope:
2: Find the slope:
(-1, 5), (2, -7)
& Find the slope:
Y
00 00 00 0X
8
8
8
8
97233
1
4
answer choices
C:
mau
A=
B=
m
undefined m=6
D: - E
F:
m²3m=-6 m = 3
G=
H=
m = -4|m=4
I:
A
m=0
Type the 4-
letter code into
the answer
box. All CAPS.
no spaces.
Et
Answer:
The answer is -4 as the correct slope for Find the slope:
(-1, 5), (2, -7)
Step-by-step explanation:
Given the information in the image below, find the measure of angle N. Explain how you arrived at this answer. Be sure to use key terms such at “isosceles triangle,” vertical angles,” and “congruent,” etc. You should at least have four sentences.
In the triangle LMN angle N is 76 degree.
Given,
In the question:
There is two isosceles triangle in the figure:
Triangle JKL and Triangle LMN
Angle J = 64 degree
To find the angle Angle N
Now, According to the question:
The triangle is isosceles.
<J = 64 degrees
All triangles have 180
<JLK = 180 - 64 - 64
Angle JLK = 52degree.
Angle JLK = MLN = 52 degree (Vertical opposite angle )
M is the left over from the 2 equal angles.
N = 180 - <M - < MLN
N = 180 - 52 - 52
N = 76 degree
Hence, In the triangle LMN angle N is 76 degree.
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let f(x)=-5-10x and g(x)=1/5x+1. Fine f(g(x))
Answer:
I hope I did it right
Lines AB and CD (if shown) are straight lines. Find x .
By using properties of angles, it is obtained that
x = 20°,
What is an Angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Here,
[tex]m\angle DOB =m\angle DOE +m\angle EOB[/tex] [ Addition of two angles]
[tex]m\angle DOB =90+x[/tex] [ Substitution]
[tex]m\angle AOC = m\angle DOB[/tex] [Vertically opposite angle]
[tex]110 = 90 + x[/tex] [ Substitution]
[tex]x = 20^{\circ}[/tex] [Algebra]
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Find the slope of the line that passes through (-92, 21) and (-93, 35).
Answer:
slope = - 14
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )
m = [tex]\frac{35-21}{-93-(-92)}[/tex] = [tex]\frac{14}{-93+92}[/tex] = [tex]\frac{14}{-1}[/tex] = - 14
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
The value of equation is x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".
Given,
In the question:
The equation is :
2[tex]x^{2}[/tex] – 7 = 9
To solve the above equation and explain which method to solve the equation?
Now, According to the question:
2[tex]x^{2}[/tex] – 7 = 9
2[tex]x^{2}[/tex] = 9 + 7
2[tex]x^{2}[/tex] = 16
[tex]x^{2}[/tex] = 8
x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex]
{There is no one- time item}
The method is used for solving equation is the "Direct keeping Method"
Hence, The value of equation is x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".
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Answer:
Use the square root property of equality.
There is no x term.
Add and divide to isolate x^2.
Step-by-step explanation:
Abigail buys 12 bottles of grapefruit juice at the corner store for a total cost of $12.48. If each bottle costs the same amount, how much is 19 bottles of juice?
The cost of 19 bottles of juice is $19.76.
What is cost per-unit rate?The "Unit Price" tells us the cost per litre, per kilogram, per pound, etc, of what we want to buy.
Given that, Abigail buys 12 bottles of grapefruit juice at the corner store for a total cost of $12.48 and each bottle costs the same amount,
Cost of one bottle = 12.48/12 = $1.04
Cost of 19 bottles = $1.04*19 = 19.76
Hence, The cost of 19 bottles of juice is $19.76.
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Jay wants to make a bike ramp a draw the following sketch what is the surface area of the ramp
We find the surface area of the figure by dividing the figure into smaller ones. This is:
Area 1, rectangle:
[tex]A=\text{length}\times width=2.2\times1.6=3.52[/tex]Area 2, triangle:
[tex]A=\frac{base\times height}{2}=\frac{2\times0.9}{2}=0.9[/tex]Area 3, rectangle:
[tex]A=1.6\times0.9=1.44[/tex]Area 4, triangle:
[tex]A=\frac{2\times0.9}{2}=0.9[/tex]Area 5, rectangle:
[tex]A=2\times1.6=3.2[/tex]Therefore, the surface area of the ramp is:
[tex]A=A1+A2+A3+A4+A5[/tex]Substitute the corresponding values:
[tex]A=3.52+0.9+1.44+0.9+3.2=9.96[/tex]Answer: 9.96 m^2
Camila invested $4,400 in an account that is earning an interest rate 90% every year. Camilla wants to create an exponential equation that allows her to track the interest earned over time, M(t).
Given:
Principal Amount, P = $4,400
Interest rate, r = 90%
Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.
This is a Compound interest problem.
To find create an exponential equation, apply the formula below:
[tex]I=P(1+r)^t-P[/tex]WHere:
P is the principal amount = $4,400
r is the rate = 90% = 0.90
t is the time (number of years)
Input values into the equation above:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Therefore, the exponential equation that allows her to track the interest earned over time is:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Plugging the value for the number of years for t, you will get the interest earned over time, t.
ANSWRER:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]3x - 5 = Px – 6
Which values l,when substituted for p in the given equation,result in a linear equation with only one solution
Answer:
Any value other than 3 will work.
4. Marcella has 4 fewer male cousins than female cousins. Let f represent the number of femalecousins. Write an expression for the number of boy cousins.
Since f is the number of female cousins and the number of male cousins is 4 less than the number of female cousins, we can write the following expression to represent the number of male cousins:
[tex]f-4[/tex]For example, if the number of female cousins is 7, we can use this value (f = 7) in the expression above to find the number of male cousins:
[tex]7-4=3[/tex]So if the number of female cousins is 7, the number of male cousins is 3.
Therefore the expression for the number of boy cousins is f - 4.
A six sided die is rolled and a coin is tossed. Find Plodd and T).11/121/41/2
You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:
[tex]P(O\cap T)[/tex]Where
"O" represents the event " rolling an odd number"
"T" represents the event "tossing a coin and obtaining tail"
The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:
[tex]P(O\cap T)=P(O)\cdot P(T)[/tex]So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)
-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:
[tex]\begin{gathered} P(N\text{)}=\frac{\text{favorable outcomes}}{total} \\ P(N)=\frac{1}{6} \end{gathered}[/tex]The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}
Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:
[tex]\begin{gathered} P(O)=\frac{\text{favorable outcomes}}{total} \\ P(O)=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]So, the probability of rolling an odd number is P(O)=1/2
-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.
For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:
[tex]\begin{gathered} P(T)=\frac{\text{favorable outcomes}}{total} \\ P(T)=\frac{1}{2} \end{gathered}[/tex]The probability of tossing a coin and obtaining a tail is P(T)=1/2
Once calculated the individual probabilities you can determine the asked probability:
[tex]P(O\cap T)=P(O)\cdot P(T)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]What is the average rate of change of the exponential function g(x)=2^x-1 between x=3 and x=7?
The average rate of change over the interval x = 3 and x = 7 is 30
How to determine the average rate of changeThe average rate of change of a function, graph, table or ordered pair is simply the slope of the relation
The equation is given as
g(x) = 2ˣ - 1
The interval is given as:
x = 3 and x = 7
Start by calculating g(3) and g(7)
So, we have
g(3) = 2³ - 1 = 7
g(7) = 2⁷ - 1 = 127
So, the average rate over these intervals is calculated as:
Average rate = [g(b) - g(a)]/[b - a]
This gives
Average rate = [g(7) - g(3)]/[7 - 3]
Substitute known values
Average rate = [127 - 7]/[7 - 3]
Simplify
Average rate = 120/4
Average rate = 30
Hence, the average rate of change is 30
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Suppose the linear regression line y=-0.3x+11.2 predicts the time, in minutes, it takes you to finish an obstacles course after training for x days. About how much time would it take you to finish the course after training for 5 days.
SOLUTION
From the equation, to find the time in minutes which is y, we plugging 5 (from 5 days) for x into the equation, we have
[tex]\begin{gathered} y=-0.3x+11.2 \\ y=-0.3(5)+11.2 \\ y=-1.5+11.2 \\ y=9.7\text{ minutes } \end{gathered}[/tex]Hence the answer is option B
The population of a town in Texas is modeled by the function f(x)=16,007(1.031)x. If the initial population (that is, the population when x=0) was measured January 1, 2014, what will the population be on January 1, 2030? Round your answer to the nearest whole number, if necessary.
From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.
This means
[tex]\begin{gathered} Yr1=2015-2014 \\ Yr2=2016-2014 \\ Yr3=2017-2014 \end{gathered}[/tex]This trend would be used until we get to January 1, 2030, when we would calculate as follows;
[tex]Yr16=2030-2014[/tex]Note that the years count from Jan 1 to Jan 1.
The function that models the yearly growth is;
[tex]f(x)=16007(1.031)^x[/tex]Using the first year, 2014 which is year zero, the result would remain 16,007. That is;
[tex]\begin{gathered} f(0)=16007(1.031)^0 \\ f(0)=16007\times1 \end{gathered}[/tex]For the 16th year, which is year 2030, we woud now have the following;
[tex]\begin{gathered} f(16)=16007(1.031)^{16} \\ f(16)=16007(1.629816253511204) \\ f(16)=26,088.4687699\ldots \end{gathered}[/tex]Rounded to the nearest whole number, this figure becomes;
ANSWER:
[tex]\text{Population}\approx26,088[/tex]1. What is the general formula for calculating the volume of a uniform shape?
A 4500 square foot roll of plastic wrap costs $23.95. If 120 square feet is need for a party game, what is the monetary value of that 120 square foot piece of plastic wrap? Interpret the answer.
120 square feet of plastic wrap costs $0.64.
64 square feet of plastic wrap costs 1.20.
Plastic wrap costs $0.64 per square foot.
$0.64 is the cost of plastic wrap.
Monetary value of 120 square foot piece of plastic wrap is $0.64
Direct variation means when ratio of two variable say cost and item always remains same.
example if cost of 2 pen is $1
then it will cost $2 for 4 pens
Given :
A 4500 square foot roll of plastic wrap costs $23.95
we have to find cost of 120 square foot roll of plastic for party game
Cost of 4500 square foot roll = $23.95
Cost of 1 square foot roll = [tex]\frac{23.95}{4500}[/tex]
= $0.00532
Cost of 120 square foot long roll = cost of 1 square foot roll × 120
= 0.00532 × 120
=0.63833
rounding off
$0.64 is cost of 120 square foot long plastic roll
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How many pennies do you save on the twenty-third day?
Solution:
Given:
[tex]\begin{gathered} Day1=1penny \\ Day2=2pennies \\ Day3=4pennies \\ Day4=8pennies \end{gathered}[/tex]An exponential function is of the form:
[tex]y=ab^x[/tex]To get the exponential function for the relation;
[tex]\begin{gathered} For\text{ day 1:} \\ 1=ab^1.........................(1) \\ For\text{ day 2:} \\ 2=ab^2.........................(2) \\ For\text{ day 3:} \\ 4=ab^3 \\ \\ \\ \\ Hence,\text{ equation \lparen2\rparen divided by equation \lparen1\rparen;} \\ \frac{2}{1}=\frac{ab^2}{ab} \\ 2=b \\ b=2 \\ \\ Substituting\text{ b into equation \lparen1\rparen;} \\ ab=1 \\ a(2)=1 \\ 2a=1 \\ a=\frac{1}{2} \\ \\ \\ \\ Hence,\text{ the function is;} \\ y=\frac{1}{2}(2^x) \end{gathered}[/tex]Part A:
Relating this to the parameters given:
The exponential function that models the problem is;
[tex]f(t)=\frac{1}{2}(2^t)[/tex]Part B:
On the twenty-third day,
[tex]\begin{gathered} when\text{ }t=23,\text{ the pennies saved will be;} \\ \\ f(t)=\frac{1}{2}(2^{23}) \\ f(t)=\frac{2^{23}}{2} \\ f(t)=4,194,304\text{ pennies} \end{gathered}[/tex]Therefore, he would have saved 4,194,304 pennies on the twenty-third day.
Can you just tell me if I did it right thank you.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the given equation
[tex]y=x^2[/tex]STEP 2: Complete the table
[tex]\begin{gathered} y=x^2 \\ \text{When x=x} \\ y=x^2 \\ \text{When x=}0 \\ y=0^2=0 \\ \text{When x=1} \\ y=1^2=1 \\ \text{When x=2} \\ y=2^2=4 \end{gathered}[/tex]Hence, the table for the equation will be:
your home feels cold to you at 60 f. you turn up the heat in order to raise the temperature by 15 degrees. what will the resulting temperature be
Answer:
45f.
Step-by-step explanation:
home is 60f.cold
we turn heat in order to raise the temprature by15
and 60minus 15 is 50
Answer:
75f
Step-by-step explanation:
since you raise the temperature you need to add those 2numbers together so 60+15=75f degrees
ch/#/test-player II 100% There is 1 teacher for every 18 students on a school trip. How many teachers are there if 72 students go on the school trip? Move values to create a proportion that can be used to solve the problem. 6 18 36 72
Let x be the number of teachers that go on the school trip
1 : 18 = x : 72
1/18 = x/72
cross-multiply
18x = 72
Divide both-side of the equation by 18
x = 4
Therefore, 4 teachers went on the school trip
Padma is covering the top of her square pyramid with gold foil. If there is no overlap, how much foil will she need?Round to the nearest cm2
Answer: She will need 1239 cm^3 of foil
Explanation:
Surface area of square pyramid = base area of square + area of 4 triangular faces
Area of square base = l^2
where
l is the length of each side of the square base
From the information given,
l = 8
Area of square base = 8^2 = 64
Area of each triangular face = 1/2 x base x height
We would find the height of each face by applying Pythagorean theorem to the right triangle formed below. It is ex[ressed as
hypotenuse^2 = one leg^2 + other leg^2
hypotenuse = 10
one leg = 4
other leg = h
4^2 + h^2 = 10^2
36 + h^2 = 100
h^2 = 100 - 36 = 64
h = √64
h = 8
base = 8
Area of 4 triangular faces 4 x 1/2 x 8 x 8 = 128
Surface area of square base pyramid = 128 + 64 = 192 in^2
We would convert 192 in^2 cm^2
Recall,
1 inch^2 = 6,4516 cm^2
192 inch^2 = 192 x 6.4516
= 1239 cm^2
She will need 1239 cm^3 of foil
The price of a go kart that Rafael wants to buy is $2,589 when the go kart goes on sale next month, the price will be $2,119. Which is the best estimate of the amount of money that Rafael will save if he waits to buy the go kart next month?
Current price of go-kart = $2,589
Price of go-kart next month = $2,119
If Rafael decides to buy the go-kart next month,
He will save $2,589 - $2,119 = $470
By definition of estimation
Estimation is an approximate calculation or judgment of the value, number, quantity, or extent of something
Approximating to the nearest hundred
$470 = $500
Therefore, Rafael will save an estimate of $500 if he wants to buy the go-kart next month
As I am completely new to thisPlease, explain thoroughly on how to solve A step by step explanation on how to solve *in the simplest way possible would be amazing, thanks in advance
ANSWER:
D. 44
STEP-BY-STEP EXPLANATION:
The percentage of a number is calculated by multiplying the percentage number in its decimal form by the number whose percentage is to be calculated.
A percentage number is converted to a decimal by dividing that number by 100, so it would finally look like this:
[tex]\begin{gathered} p=1100\cdot\frac{4}{100} \\ \\ p=44 \end{gathered}[/tex]So the correct answer is D. 44
Which phrase represents this expression?
(62−42)×3
We can represent the expression (62−42)×3 in phrase as "three times the difference of 62 and 42".
In the given question we have to write a phrase that represent a given expression.
The given expression is (62−42)×3.
We can phrase a given expression by writing expression in to words. We write epression in to word according to the given expression.
As we can see that we subrating 62 by 42
So we can write it as difference of 62 and 42.
Then we multiplying with 3. So the expression in phrase is;
"three times the difference of 62 and 42"
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Towns K and L are shown on a map.
a) Work out the actual distance
between towns K and L.
b) A third town, M, is 150 km due
South of town K.
Mark M on the map with X.
c) Measure the bearing of town L
from town K.
A)The actual distance between towns K and L is 10 cm .
B) The bearing of town L from town k is 117 degree
What is mean by actual distance?The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.
The following list includes four distance metrics that are maybe the most often employed in machine learning: the Hamming Distance. Distance in Euclid. New York City distance
The distance a number is from 0 on the number line is its absolute value. Because -7 is 7 units away from 0, its absolute value is 7. Because it is 5 units away from 0, the number 5 has an absolute value of 5. Any number that is less than zero is considered to be negative.
Given ,
A)The actual distance between towns K and L is 10 cm .
B) check the photo of my work
C) The bearing of town L from town k is 117 degree
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For the function f(x) = 2|5x + 7– 1, evaluate f(-4).
To evaluate f(x) at x = -4 we substiitute x in the equation with -4. Doing this gives
[tex]f(-4)=2|5(-4)+7|-1[/tex][tex]f(-4)=2|-20+7|-1[/tex][tex]\begin{gathered} f(-4)=2|-13|-1 \\ f(-4)=2\cdot13-1 \end{gathered}[/tex][tex]f(-4)=25[/tex]which is our answer!
What is the value of this expression when x = 8 and y = 2?
9+y^2⋅x−y^3
Enter your answer in the box.
Answer:
The answer will
be 0
Step-by-step explanation:
=9+4×8-8
=13×0
=0
In a survey of 164 pet owners, 61 said they own a dog, and 66 said they own a cat. 11 said they own both a dog and a cat. How many owned neither a cat nor a dog?
The given information is:
- They surveied 164 pet owners
- 61 own a dog
- 66 own a cat
- 11 own both a dog and a cat
We have to find how many owned neither a cat nor a dog.
We can represent this survey in the following diagram:
To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:
[tex]\begin{gathered} People\text{ who own neither a dog nor a cat}=164-61-66-11 \\ P=26 \end{gathered}[/tex]The people who own neither a dog nor a cat are 26.