Answer:
Step-by-step explanation:
From the information given:
Neighbourhood A = 30 homes and the number increases by 20% each year
Neighbourhood B = 45 homes, and each year 3 new homes are built.
A.
The function representing the numbers of homes in Neighbourhood A and B are as follows:
For neighbourhood A: f(x) = [tex]\mathbf{30 \times (1.2)^x}[/tex]
For neighbourhood B: f(x) = 45 + 3x
B.
After five years;
Neighbourhood A has = [tex]\mathbf{30 \times (1.2)^x}[/tex]
Neighbourhood A = [tex]\mathbf{30 \times (1.2)^5}[/tex]
Neighbourhood A = 74.65 homes
Neighbourhood B: = 45 + 3(5)
Neighbourhood B: = 45 + 15
Neighbourhood B: = 60 homes
C.
To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.
i.e.
[tex]\mathbf{30 \times (1.2)^x= 45 + 3x}[/tex]
[tex]\mathbf{ (1.2)^x= \dfrac{45 + 3x}{30}}[/tex]
[tex]\mathbf{ (0.4)^x= \dfrac{15 + x}{10}}[/tex]
x = 3.3
Thus, after 3.3 years, the number of homes will be the same.
The length of a day on Earth is 24 hours. The length of a day on Mercury is 58 2/3 times the length of a day on earth. The length of a day on Mercury in hours is
Answer:
Roughly about 1,407.
Step-by-step explanation:
Simply multiply 24 times 58 2/3
The 58 2/3 times 24 will be equal to the 1408 hours thus the length of the day on Mercury will be 1408 hours.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than 1.
As per the given,
The length of a day on Mercury is 58 2/3 times the length of a day on earth.
58 2/3 = 58 + 2/3 = 176/3
176/3 times 24 will be,
176/3 × 24 = 1408 hours.
Hence "The 58 2/3 times 24 will be equal to the 1408 hours thus the length of the day on Mercury will be 1408 hours".
For more information about multiplication,
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Can you please solve? And if anyone can please explain how to do this, thank you so much!
Answer:
15
Step-by-step explanation:
Both angles can add up to 180, so what I did was 7t-6 plus 5t+6=180. From there, I combined both positive 6 and negative 6 to which they cancel out. All that leaves is 7t+5t, which is 12t. Finally leaving 12t=180, so divided both sides by 12 to remove the 12 from 12t. 180/12=15. I think this is correct, but I am not sure. Please do check
Answer:
15
Step-by-step explanation:
ig my question was deleted lol
What is the mixed number in decimal form? 4 23/100 *
Ughhh
Answer:
4.23
Step-by-step explanation:
First, you need to write this mixed number into an improper fraction, which would be 423/100. Then all you need to do is divide 423 by 100 to get 4.23.
Help please help pre Algebra
Answer:
none is a solution...the solution.is -3
Round to the nearest tenth: 0.087
Answer:
0.1
Step-by-step explanation:
When rounding, look at whether or not the number is less than 5, or greater than or equal to 5.
If it is greater than 5, you will round up to the next number.
In this number, 8 is greater than 5. This means to the nearest tenth, it will be rounded to 0.1
Answer:
0.1
Step-by-step explanation:
0.087
The number to the right of the decimal is always the tenth's place. To the left of the decimal is the one's place 8 is a high number, so you are rounding up because 5 or higher is always a high number. If it was a low number, you round down because a low number is 4 and under.
Hope this helps
Same has 3 apples Carly has 8 how many apples do Sam Carly have together
p- 6= -5 what is the answer (NEED HELP)
Answer:
P=1
Step-by-step explanation:
1-6=-5
A line of symmetry for the figure is shown in red. Find the coordinates of point A. (Photo attached)
Answer:
a. Coordinate of A (-4,-1)
b. Coordinate of A (4,4)
c. Coordinate of A (-2,2)
Find the midpoint M of the line segment joining the points R = (-3,-7) and S = (1, -1).
Answer:
[tex] \huge{ \bold{ \boxed{ \tt{( - 1 \: , - 4)}}}}[/tex]
Step-by-step explanation:
Let the point R ( - 3 , - 7 ) be ( x1 , y1 ) and S ( 1 , -1 ) be ( x2 , y2 ).
[tex] \text{Finding \: the \: midpoint} : [/tex]
[tex] \boxed{ \sf{midpoint = ( \frac{x1 + x2}{2 } \: , \frac{y1 + y2}{2} )}}[/tex]
[tex] \sf{➳midpoint = ( \frac{ - 3 + 1}{2} \:, \frac{ - 7 + ( - 1)}{2} })[/tex]
[tex] \text{Remember} : [/tex]
( + ) * ( - ) = ( - )( - ) * ( + ) = ( - )( + ) * ( + ) = ( + )( - ) * ( - ) = ( + )[tex] \sf{➳midpoint = ( \frac{ - 3 + 1}{2} \: , \frac{ - 7 - 1}{2} )}[/tex]
[tex] \text{Remember} : [/tex]
The positive integers are always added and posses the positive ( + ) sign.The negative numbers are always added but posses the negative sign ( - ).The negative and positive integers are always subtracted but posses the sign of the bigger integer.[tex] \sf{➳midpoint = ( \frac{ - 2}{2} \: , \frac{ - 8}{2} )}[/tex]
[tex] \sf{➳midpoint = ( - 1 \:, - 4})[/tex]
[tex] \text{Hope \: I \: helped!}[/tex]
[tex] \text{Best \: regards!}[/tex]
[tex] \text{TheAnimeGirl}[/tex]
A friend asks to borrow $250 for 100 days and agrees to pay 36.5% annual simple interest. How much interest will you earn? Assume that one year has 365 days
Answer:
$25
Step-by-step explanation:
We express the interest rate r in decimal form, so we have r=36.5%=36.5100=0.365. We express the time t in years, so we have t=100365. The principal is P=250, so the interest is I=Prt=(250)(0.365)(100365)=$25. The interest earned is $25.
Find the slope of the line that passes between the points (4, 3/8) and (6, 7/8)
Answer:
1/4
Step-by-step explanation:
We have two points, so we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 7/8 - 3/8 ) / ( 6-4)
= ( 4/8) /2
= 1/2 / 2
= 1/4
Solve r-x+2y = 1 for y
Answer:
y=(1-r+x)/2
Step-by-step explanation:
(r-x)+2*y=12*y=1-(r-x)y=(1-r+x)/2A shirt cost 160$ last week. The price of a shirt has increased 48$ this week. What was percentage increase in price?
Answer:
30%
Step-by-step explanation:
% = increase/original * 100%
= 48$/160$ * 100%.
= 48/160 * 100%
= 30%
Answer:
30%
Step-by-step explanation:
percentage=increased marks / marks before increased*100
=48/160*100
=30%
therefore the percentage increase in price is 30%
I hope this will help u
Best of luck
-6y - 3 = 3 - 6y. Pls solve
5. Translate this sentence into an equation. 23 more than Hector's savings is 75. Use the
variable h to represent Hector's savings.
Answer:
h+23=75
Step-by-step explanation:
This is true because x is basically h, and if its more then you add.
Paired t-test Application (Part 1)An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than allowed by environmental regulations. They measure water temperatures at the cooling system input and the cooling system output for several different days in several different seasons. A data file containing these measurements is Fin_PTA.csvPreview the document. Do a statistical analysis on this data to determine if the temperature change between the input and output of the cooling system is different than 6 degrees. What does your analysis indicate
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
Part 1
The correct option is B
Part 11
The correct option is H
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
Generally the sample mean for the input temperature is mathematically represented as
[tex]\= x _1 = \frac{\sum x_i}{n}[/tex]
[tex]\= x _1 = \frac{57.6 + 68.9 \cdots +60.4 }{15}[/tex]
[tex]\= x _1 = 62.57 [/tex]
Generally the sample mean for the output temperature is mathematically represented as
[tex]\= x _2 = \frac{\sum x_i}{n}[/tex]
[tex]\= x _2 = \frac{65.1 + 74.4 \cdots +67.3 }{15}[/tex]
[tex]\= x _2 = 55.97 [/tex]
Generally the difference between the mean of the input temperature and that of the output temperature is
[tex]d = \= x_1 - \= x_2[/tex]
=> [tex]d = 62.57 - 55.97 [/tex]
=> [tex]d = 6.6[/tex]
Generally the standard deviation of the difference between the input temperature and the output temperature is mathematically represented as
[tex]s_d = \sqrt {\frac{1}{n-1 } \sum [d_i - d]^2}[/tex]
=> [tex]s_d = \sqrt{\frac{[(57.6 - 65.1) - 6.6]^2+[(68.9 - 74.4) - 6.6]^2+ \cdots +[(68.1 - 74.7) - 6.6]^2 }{15-1} }[/tex]
=> [tex]s_d = 1.732 [/tex]
The null hypothesis is [tex]H_o : \mu_1 -\mu_2 = 6[/tex]
The alternative hypothesis is [tex]H_a : \mu _1 - \mu_2\ne 6[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{d - 6}{ \frac{s_d}{ \sqrt{n} } }[/tex]
[tex]t = \frac{6.6- 6}{ \frac{1.732}{ \sqrt{15} } }[/tex]
[tex]t = 1.342[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 1.342)[/tex]
From the student t distribution table( reference - danielsoper(dot)com(slash)statcalc(slash)calculator) at a degree of freedom of df = n-1 = 15-1 = 14
[tex]P(t > 1.342) = t_{1.342 , 14} = 0.100478[/tex]
So
[tex]p-value = 2 * 0.100478)[/tex]
[tex]p-value = 0.201[/tex]
From the values obtained we see that the [tex]p-value > \alpha[/tex] hence the decision rule is fail to reject the null hypothesis
The conclusion is
The cooling system changes the temperature of the water by 6 degrees.
What is the approximate length of minor arc XZ
Answer:
3.7
Step-by-step explanation:
2r(pi)(∅/360)
2*3*(pi)*(70/360)
6*(pi)*(0.19444...)
3.665191429188092
3.7
What is the volume?
7 cm
5 cm
8 cm
cubic centimeters
Answer:
280 cm
or 280cm^2
Step-by-step explanation:
Answer: 280 cm^3
Step-by-step explanation: Multiply 7 x 5 x 8 = 280
There are 22 students in a 6th grade class. For the class field trip, they went to the local museum. Admission to the museum was $7 a person. After going to the museum, they went to the art festival. Admission to the art festival was $4 a person. Each student paid $12 for the field trip and the bus. What is the total amount of money the teacher collected from the students?
Answer:
$264
Step-by-step explanation:
There is some useless information that you need to ignore. The only important numbers is 22 students that each paid $12, so multiply them together to get $264.
Answer:
528
Step-by-step explanation:
12*2=24
24*22=528
URGENT SOLVE
13 - 2n = 19
Answer:
n=−3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
13−2n=19
13+−2n=19
−2n+13=19
Step 2: Subtract 13 from both sides.
−2n+13−13=19−13
−2n=6
Step 3: Divide both sides by -2.
−2n/−2=6/−2
[tex]13 - 2n = 19[/tex]
Subtract sides -13
[tex]13 - 13 - 2n = 19 - 13[/tex]
[tex] - 2n = 6[/tex]
Divided sides by -2
[tex] \frac{ - 2}{ - 2}n = \frac{ 6}{ - 2} \\ [/tex]
[tex]n = - 3[/tex]
Done....♥️♥️♥️♥️♥️
A firm makes bulldozers (B), cranes (C) and tractors (T) at two locations, New York City (NYC) and Los Angeles (LA). The matrices below show the number of each item made in each location for the months of January (J) and February (F).
B C T
J = NYC 144 474 274
LA 598 572 302
B C T
F = NYC 424 492 546
LA 596 530 164
Required:
Suppose the production for March of all products at all locations was the average of the January and February production. Write an expression using the matrices J and F for the March production matrix M.
Answer:
The expression is
[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ C \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{284}&{483}&{410}\\{597}&{551}&{233}{2}}\\\end{array}\right][/tex]
Step-by-step explanation:
From the question we are told that
The number of each items made in the month of January[J] is
[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ C \ \ \ \ \ \ T\\J = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{144}&{474 }&{274}\\{598}&{572}&{302}\\\end{array}\right][/tex]
The number of each items made in the month of February[F] is
[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ C \ \ \ \ \ \ T\\J = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{ 424}&{492}&{546}\\{596 }&{530}&{164}\\\end{array}\right][/tex]
Generally given that the production for March of all products at all locations was the average of the January and February production then the number of each items made in the month of March[M] is
[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ \ \ \ \ \ \ \ C \ \ \ \ \ \ \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{\frac{144 +424}{2}}&{\frac{474 +492}{2}}&{\frac{274 +546}{2}}\\{\frac{598 +596}{2}}&{\frac{572 +530}{2}}&{\frac{302+164}{2}}\\\end{array}\right][/tex]
=> [tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ C \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{284}&{483}&{410}\\{597}&{551}&{233}{2}}\\\end{array}\right][/tex]
at the bank , mr smith changes a e5 note for 20p pieces . how many 20 pieces does he have
Answer:
it should be 25
Step-by-step explanation:
£500 = 500p
500 ÷ 20 = 25
*BRAINLIEST* What values are equal to the inequality?
Answer:
A.-9
C.5
D.7
Explanation:
Take every number and put it in the spot of x and multiply every number by themselves like 9x9 or 5x5. Then see if it is equal too or less than 81. If it is equal too or less than 81 then it is correct.
Could I please have BRAINLIEST?
What is the answer to thissss???
Step-by-step explanation:
This is the furthest I could get.
If you want to write it as a result with no powers, let me know and I will write it.
Please help me, thank you
Problem 1
Answer: C) No solution
---------------------------
Explanation:
We have z = -4 and 4z = -4 at the same time. Solving 4z = -4 leads to z = -1
So in effect we have z = -4 and z = -1 at the same time, but this is a contradiction. A variable can only hold one number at a time.
======================================================
Problem 2
Answer: C) Infinitely many solutions
---------------------------
Explanation:
The two equations are equivalent. You can prove as such by isolating 2y in the first equation.
5x = 8-2y
5x+2y = 8
2y = 8-5x
2y = -5x+8
-5x+8 = 2y
This shows the first equation is equivalent to the second, and vice versa. They both graph the same line. Any point along the line is a solution. So that's why there are infinitely many of them.
======================================================
Problem 3
Answer: Choice A) [tex]-6 < y \le 3[/tex]
---------------------------
Explanation:
The range is the set of the possible y values. We're concerned with every y coordinate of each (x,y) solution. So we only focus on the shaded region.
The dashed line means we exclude the boundary. It's an electric fence we cannot touch. So y > -6 or -6 < y describes part of the range
The other part is [tex]y \le 3[/tex] since y = 3 is the when the highest point occurs.
So writing [tex]-6 < y \le 3[/tex] describes all possible y values of each (x,y) solution in the shaded region.
At her birthday party, Ms. Willow would not give her age directly. She said, 'If you add the year of my birth to this year, subtract the year of my 80th birthday and the year of my 30th birthday, and then add my present age, the result is 42.'
Ms. Willow's birth year = x
This year = 2020
80th birth year = x + 80
30th birth year = x + 30
Present age = 2020 - x
(x + 2020) - (x + 80 + x + 30) + (2020 - x) = 42
Simplify the right side.
-2x + 3930 = 42
Subtract 3930 from both sides.
-2x = -3888
Divide both sides by -2
x = 1944
1944 is Ms. Willow's birthday year.
As stated previously, her present age is 2020 - x, which equals 78
Ms. Willow is 78 years old
Here we want to interpret a word problem and transform it into an equation that we can solve.
We will find that her current age is 76.
First, let's define variables:
Her birth year = x
This year = 2021 (naturally this depends on the year we are on)
80th birth year = x + 80
30th birth year = x + 30
Then the actual age is the difference between the current year and the year when she was born:
Age = 2021 - x
What she says is:
"If you add the year of my birth to this year, subtract the year of my 80th birthday and the year of my 30th birthday, and then add my present age, the result is 42."
(x + 2021) - (x + 80 + x + 30) + (2021 - x) = 42
Now we can solve this for x:
x + 2021 - x - 80 - x - 30 + 2021 - x = 42
(x - x - x - x) + 2021 - 80 - 30 + 2021 = 42
-2*x + 3932 = 42
3932 - 42 = 2*x
3890 = 2*x
3890/2 = x = 1945
The current age is:
age = 2021 - x = 2021 - 1945 = 76
Her current age is 76.
If you want to learn more, you can read:
https://brainly.com/question/24595783
Arrange the fraction in asending and desending order 4/5 , 2/15 , 2/30
Answer:
See below
Step-by-step explanation:
Given fractions
4/5, 2/15, 2/30To arrange the fractions we need to bring them to common denominator
LCM(5,15,30) = 304/5 = 24/302/15 = 4/302/30In ascending order
2/30, 4/30, 24/30Reverse order
24/30, 4/30, 2/30Square root 3 to the power of 4 -6 to the power of 2
Answer:
-27
Step-by-step explanation:
[tex]( \sqrt{3} )^{4} - {6}^{2} \\ \\ = {3}^{2} - {6}^{2} \\ \\ = (3 + 6)(3 - 6) \\ \\ = 9( - 3) \\ \\ = - 27[/tex]
Find 5 solutions to the question.
Y=-1.5x+2
Answer:
☆< 《HOPE IT WILL HELP YOU》>☆
Step-by-step explanation:
Y=1.5x+2
(x=1)y=1.5 (1) +2
y=1.5+2
y=3.5
(x=2)y=1.5(2)+2
y=3+2
y=5
(x=3)y=1.5 (3)+2
y=4.5+2
y=6.5
(x=4)y=1.5 (4)+2
y=6+2
y=8
(x=5)y=1.5 (5)+2
y=7.5+2
y=9.5
please mark my ans as BRAIN LISTData were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax^3, where a is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables?
A - Taking the cube of y
B - Taking the cube root of y
C - Taking the cube root of both y and x
D - Taking the log of y
E - Taking the log of both y and x
Answer:
B - Taking the cube root of y
Step-by-step explanation:
Data provided in the question
y = ax^3
Based on the above information
Now we take the cube root of y
So, it would be calculated below:
y1/3 = a1/3 × x
So
As it can seen by the above equation there is a linear relationship between the cube root of y and x
Therefore, the correct option is B.
Hence, all the other options are wrong
Linearity is the concept used to describe linear relationships between variables.
The appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x
The function is given as:
[tex]\mathbf{y = ax^3}[/tex]
The function is a power function (i.e. cube of x)
To create linearity between power function, we simply take the logarithms of both variables
So, we have:
[tex]\mathbf{\log(y) = a\log(x^3)}[/tex]
Apply law of logarithm
[tex]\mathbf{\log(y) = 3a\log(x)}[/tex]
Hence, the appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x
Read more about linearity between variables at:
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