Finding the numeric value of the regression line, it is found that the electric bill in a month with temperature of 48 degrees is of $157.59.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
In the context of this problem, the function is given as follows:
y = 227.19 - 1.45x.
Which y giving the electric bill for a month of temperature x degrees.
The temperature is of 48 degrees, hence to find the electric bill, the lone instance of x in the function is replaced by 48, hence:
y = 227.19 - 1.45(48) = $157.59.
Hence the electric bill in a month with temperature of 48 degrees is of $157.59.
What is the missing information?The regression line is missing in this problem, as is defined as follows:
y = 227.19 - 1.45x.
In which:
y is the electric bill.x is the monthly temperature.The problem asks for the electric bill in a month with temperature of 48 degrees.
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can u please help me on b guys ty
Answer:
circle is 22
Triangle is 34
Step-by-step explanation:
22 + 22 + 22 = 66
22 + 34 + 34 = 90
Take 90 - 22 = 68
Divide 68 by 2 to get 34
Timmy has stamps. He wants to organize them on pages that hold stamps each. He has pages. Does Timmy have enough pages to organize all his stamps?
Using division we can infer that 50 pages will not be enough.
Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number.
Multiplication, subtraction , and addition make up the remaining operations. The division with remainder, also known as Euclidean division, of two natural numbers produces an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that is left over, when it is impossible to allocate any more full chunks of the size of the second number during the computation of the quotient after the division.Timmy has 810 stamps.
Now each page can hold 16 stamps and he has 50 pages.
Now we will divide 810 by 16 to calculate the number of pages required to put all the stamps.
∴ 810 ÷ 16 = 50 remainder 10.
Therefore after completing the 50 pages there are 10 stamps left.
Hence from division we can infer that 50 pages will not be enough.
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Timmy has 810 stamps. He wants to organize them on pages that hold 16 stamps each. He has 50 pages. Does Timmy have enough pages to organize all his stamps?
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7, 5, 2, 1
For the sequence above:
i.) Find the general term
ii.) Find the next three terms
iii.) Hence- find the 25th term
The sequence 7, 5, 2, 1, then the
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
The sequence is,
⇒ 7, 5, 2, 1
[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]
( i ) . The general term,
Let us assume general term = d
We can use this formula,
d = [tex]a_{n+1} -a_{n}[/tex]
where,
[tex]a_{n+1} = 5\\a_{n} = 7[/tex]
d = 7 - 5
d = 2
So,
The general term d = 2
( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]
We can use this formula,
[tex]a_{n+1} =a_{n} +d[/tex]
[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]
[tex]a_{5} = 1+2\\a_{5} = 3[/tex]
[tex]a_{6} = 3+2\\a_{6} = 5[/tex]
[tex]a_{7} = 5+2\\a_{7} = 7[/tex]
So,
The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term
We can find nth term,
We can use this formula,
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n} = 7+(n-1)2[/tex]
[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]
Then, 25th term is,
We can substitute n = 25
[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]
So,
The 25th term [tex]a_{25}[/tex] = 55
Therefore,
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
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Line E passes through the points (-3, 4) and (2, 7). What is the slope of a line perpendicular to line E?
The slope of a line perpendicular to line E is -(5/3).
How do you calculate slope of a perpendicular line?By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m₂ = -1/m₁ if the slope of the provided line is m₁ and the slope of a perpendicular line is m₂.Given:
Line E passes through the points (-3, 4) and (2, 7).
Slope of line E = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{7-4}{2-(-3)}[/tex]
= [tex]\frac{3}{5}[/tex]
So, the slope of a line perpendicular to line E will be the negative reciprocal of the slope of line E i.e. -(5/3).
Therefore, the slope of a line perpendicular to line E is -(5/3).
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the
unit cost is given by the function C(x)=0.5x²-180x+25,885. What is the minimum unit cost?
Do not round your answer.
Answe(0.5x²-180x+25,885= 47,925.25
Step-by-step explanation:
x=1
Work clothes costing $25.95, $23.95, $26.50, $39.95, and $41.25.
six tickets to a movie cost 76.50 what constant of proportional relates the number of tickets and total cost
Based on the number of movies, $12.75 is the constant of proportionality per movie
How to determine the constant of proportionality?The given parameters are
Number of the movie tickets = 6
Cost of the movie tickets = 76.50
The constant of proportionality of the movie tickets is calculated as
Constant of proportionality = Cost of the movie tickets/Number of the movie tickets
Substitute the known values in the above equation
So, we have
Constant of proportionality = 76.50/6
Evaluate the quotient
So, we have
Constant of proportionality = 12.75
Hence, the constant of proportionality per movie is $12.75
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Answer:
Step-by-step explanation:
$12.75
Zander downloads a combination of 30
games and songs. He downloads 8
more songs than games. The equation g+(8+g)=30
can be solved to determine g
, the number of games Zander downloaded. How many games and songs did Zander download?
Zander Downloaded _ games and _ songs
Would someone help me please and thank you
Zander downloaded a total of 19 Songs and 8 Games.
In the given question, it is stated that Zander's downloads had a combination of 30 games and songs in which he downloaded 8 songs more than games. The equation representing the given situation is g + (8 + g) = 30. Here, g represents Games, and (g+8) represents songs.
Now, to find out the number of games and songs, we need to calculate the value of g by the equation.
=> g + (8 + g) = 30
=> 2g + 8 = 30
=> 2g = 22
=> g = 11
We get value of g = 11, So, downloaded games will be 11 and songs will be 19
Hence, the number of Games and Songs will be 11 and 19 respectively.
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you know x is a number less than 4. Select all the inequalities that must be true
The inequality is (3,∞) < x < 4.
What is an inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given Data
x is a number less than 4
x<4
Numbers which are less than 4 are 3 to infinity
So,
The inequality is:
(3,∞) < x < 4
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please help asap. due monday
if I am correct that is the solution.
Jenna is making knit hats for Christmas presents.
Each hat requires her to use 1 1/3 yards of yarn. If she has 30 yards of yarn, how many hats can she make?
This problem is asking me to determine?
Write the equation you will be using to solve.
Answer:
22 hats
Step-by-step explanation:
30÷1 1/3=22.5
The question is implying how many completed hats she can make, and since half a hat is not completed, she can only make 22 completed hats.
Simplify the expression.
the expression negative five eighths times k minus 8 plus the expression 2 plus one third times k
A: 7 over 24 times k plus negative 6
B: negative 4 over 11 times k plus negative 10
C: negative 7 over 24 times k plus negative 6
D: negative 23 over 24 times k plus negative 10
Answer: C
Step-by-step explanation:
- 5/8k -8 + 2 + 1/3k
-5/8 = -15/24
1/3 = 8/24
-15/24k -8 + 2 + 8/24
-7/24k -6
Which line matches the equation?
Answer:
23) D
24) A
25) C
26) B
Step-by-step explanation:
23)
4x + 4y = -8 Let's find the intercepts. The x intercept is when y = 0 and the y intercept is when x = 0
Let y = 0
4x + 4y = -8
4x = -8
x = -2
(-2,0)
4x + 4y = -8
Let x = 0
4y = -8
y = -2
(0,-2)
We are looking for the line that goes through the points (-2,0) and (0,-2) That is line D.
24)
3x -2y = -6
Let y = 0
3x = -6
x = -2
(-2,0)
Let x = 0
-2y =-6
y = 3
(0,3)
We are looking for the line that goes through the points (-2,0) and (0,3). That is line A.
25)
x + 2y = 2
Let y = 0
x = 2
(2,0)
Let x = 0
2y = 2
y = 1
(0,1)
We are looking for the line that goes through the points (2,0) and (0,1). That is line C
26)
3x - y = 3
Let y = 0
3x = 3
x= 1
(1,0)
Let x = 0
-y = 3
y= -3
(0, -3)
we are looking for the line that goes through the points (1,0) and (0, -3) which is line B
Answer: 23. D 24. A 25. C 26. B
Step-by-step explanation:
y=mx+b
The intersection of the straight line with the y-axis equals b
23.
4x+4y=-8
Divide both parts of the equation by 4:
x+y=-2
x+y-x=-2-x
y=-x-2
⇒b=-2 (D)
24.
3x-2y=-6
3x-2y+2y=-6+2y
3x=2y-6
3x+6=2y-6+6
3x+6=2y
Divide both parts of the equation by 2:
1,5x+3=y
⇒ b=3 (A)
25.
x+2y=2
x+2y-x=2-x
2y=-x+2
Divide both parts of the equation by 2:
y=-0.5x+1
⇒ b=1 (C)
26.
3x-y=3
3x-y+y=3+y
3x=y+3
3x-3=y+3-3
3x-3=y
⇒ b=-3 (B)
Please answer the question
The four students; Michal, Hypatia, clodoveo and Jamal's attempt to explain the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is incorrect
Simplification of expressionThis means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.
3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³
Using PEMDAS
P = parenthesisE = ExponentM = multiplicationD = divisionA = additionS = SubtractionCorrect workings:
3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³
3 - 5 × (1 × 2)² - 1 + 2(-1)³
= 3 - 5 × (2)² - 1 + 2(-1)
= 3 - 5 × (4) - 1 - 2
= 3 - 20 - 3
= - 20
Michal made the mistake of writing 2 instead of 20 Hypatia made the mistake of doing 3 - 5 first instead of opening the parenthesis according to PEMDASClodoveo's mistake was finding the cube of -1 to be 1 instead of -1Jamal's mistake was missing the 2 in 2(-1)³In conclusion, the correct simplification of the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is -20
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When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6/216. What is the probability that the three numbers do not all match?
If your answer is a repeating decimal, type the repeated portion of the decimal only once.
For example:
for you only type in 3.6
for you only type in 0.45
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Find the amount in a continuously compounded account for the given conditions.
Principle: $5000
Annual Interest Rate: 6.9%
Time: 30 years
Round to the nearest cent and do not include the $ symbol.
Answer:
A= 5000 e
A= 39,624.12
Step-by-step explanation:
Answer:
no round to the nearest cant and do no
80p as a fraction of £3
simplest form
Answer:
Step-by-step explanation:
4/15
Based on the concept of fraction, 80p is equivalent to 4p/15p as a fraction of £3.
What is a fraction?Fraction is a term that is used to describe the portion or part of the whole thing.
Generally, the term fraction represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator.
In this case, to find the fraction of 80p as a fraction of £3, we divide 80p by £3.
Since there are 100 pence in 1 pound the fraction can be expressed as 80p/£3.
To simplify the fraction divide both the numerator and the denominator by 10:
80p/£3 = 8p/30p
Simplifying further both the numerator and the denominator can be divided by 2:
8p/30p = 4p/15p
Therefore, in this case, it is concluded that 80p is equivalent to 4p/15p as a fraction of £3.
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help please, geometry.
Answer:
400
Step-by-step explanation:
the volume of a pyramid with a square base is [tex]\frac{lwh}{3}[/tex] so the volume is 12*10*10 divided by 3, which is 1200/3, or 400
Question 5 only need help asap
The number of runs that Jack must score will be 90.
How to calculate the value?It should be noted that the mean score from 8 matches is 45. Therefore, the total score will be:
= 8 × 45
= 360
When the coach says that he must increase the mean to 50 in the next match, the total score will be:
= 50 × 9
= 450
Therefore, the number of points that must be scored will be:
= 450 - 360
= 90
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Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 13 and hypotenuse labeled 16
square root of 425
square root of 3
square root of 29
square root of 87
hypotenuse = 16
perpendicular = 13
base= ?
By using pythogoras theroem :
H² = P² + B²
16² = 13² + B²
256 = 169 + B²
B² = 256 -169
=87
B² = 87
B = √87
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Answer: The correct answer is D - square root of 87
Step-by-step explanation: I took the test and I got it right.
Have a good day/night :)
the sum of 2 numbers is 96. the larger number is 9 less than 4 times the smaller. find boh nmbers.
The sum of 2 numbers is 96, this can be expressed as
[tex]x+y=96[/tex]The larger number is 9 less than 4 times the smaller, this can be expressed as
[tex]x=4y-9[/tex]Now, we replace the second equation in the first one
[tex]\begin{gathered} 4y-9+y=96 \\ 5y=96+9 \\ y=\frac{105}{5} \\ y=21 \end{gathered}[/tex]We use this number to find x.
[tex]x=4\cdot21-9=84-9=75[/tex]Hence, the numbers are 75 and 21.Ayana's favorite brownie recipe calls for
1
2
of a cup of flour for every
1
3
of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
cups of flour
Answer:
4/5 cup
Step-by-step explanation:
Answer: 1 1/2
Step-by-step explanation:
1/2 divided 1/3 = 3/2 = 1 1/2
1/2 divided 1/3
= 1/2 x 3/1
1 × 3
2 × 1
= 3/2
= 1 1/2
two packages of strawberries are sold for $10. how much could you buy with $25?
F.) 3
G.) 4
H.) 5
J.) 6
K.) 7
Answer:
G.) 4
Step-by-step explanation:
If you get two packs of strawberries for $10, with another $10 you could get another two packs. 2+2=4, and 10+10=20. So you could get 4 packs with with $20.
The length of Rectangle A is 5 inches more than its width. The perimeter of Rectangle B is 17. The difference between the perimeters of the rectangles is less than 9. What are the possible integer values for the width of Rectangle A? 1in. 2in. 3in. 4in.5in. 6in. 7in. 8in.
Answer:
Step-by-step explanation:
Let L and W be the length and width of a triangle.
Rectangle perimeter (Px) = 2L + 2W, where x is triangle a or b.
Rectangle A: La = 5Wa [The length of Rectangle A is 5 inches more than its width.]
Perimeter Rectangle A: Pa = 2La + 2Wa
Substitute L = 5Wa:
Pa = 2La + 2Wa
Pa = 5Wa + 2Wa
Pa = 7Wa
Perimeter Rectangle B: Pb = 17 [The perimeter of Rectangle B is 17]
Pb = 17
Difference between Pa and Pb: Is it < 9?
See the attached table. The perimeters of rectangle A are computed for each of the answer options that define the width. Length (rectangle A) is 5 inches more than the width. The perimeter is 2*Length + 2*Width, and shown as Pa.
The perimeter of rectangle b is 17, shown as Pb on the table. The last column of the table is the absolute value of the difference of Pa and Pb. If it is less than 9, the cell is green (it is a possible integer value for the width of rectangle A), Red mean it does not meet the "less than 9" requirement, One cell has the difference as 9. The problem states "less than 9," so it does not meet the requirement.
Divide. Express your answer in scientific notation.
7.2x 10-4
3x10-3
7.2x10-4
3x10^-3
(Use scientific notation. Use the multiplication symbol in the math palette as needed.
The value of 7.2 × 10^-4 divided by 3 × 10^-3 when expressed in scientific notation is 2.4 × 10^-7.
What is scientific notation?It should be noted that scientific notation is simply used to illustrate the numbers that are either too large or too small. It is denoted as a × 10ⁿ.
It should be noted that the exponents will be added. Therefore, 7.2 × 10^-4 divided by 3 × 10^-3 will be:
= 7.2 × 10^-4 / 3 × 10^-3
= 2.4 × 10^-7.
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You have a $25 calling card. Calls made using the card within the United States cost $.10 per minute while calls made from the US to France cost $.25 per minute. a. Write an inequality that relates the number of minutes ‘x’ you can use for calls within the U.S. and the number of minutes ‘y’ you can use for calls from the U.S. to France.
The inequality that represents the number of minutes of calls made in the United States and in France, can be presented as follows:
The inequality that represents the duration of calls that can be made in the United States: 0 ≤ x ≤ 250The inequality that represents the number of minutes of calls that can be made in France using the calling card is: 0 ≤ y ≤ 100What is an inequality in mathematics?An inequality expresses the relationship between two or more values that are not equal.
The value of the calling card = $25
The cost of calls made in the United States = $0.10
Cost of calls made in France = $0.25
The number of minutes that can be used for calls in the U.S. = x
The number of minutes that can be used for making calls in France = y
The duration of calls that can be made in the United states is therefore:
[tex]x_{max} = \dfrac{\$25}{\$0.10} = 250[/tex]
The inequality that represents the number of calls that can be made in the United States is therefore: 0 ≤ x ≤ 250
The duration of calls that can be made in France with the $25 calling card is therefore: [tex]y_{max}=\dfrac{\$25}{\$0.25} = 100[/tex]
The inequality that represents the number of minutes the calling card can be used in making calls in France is: 0 ≤ y ≤ 100
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Solve the inequality 1/4 (x-20)<-6 or -6x+5≤-1. Write your solution in algebraic form, interval notation, and graphed on a number line.
The solution of the given inequality is:
x ≥ 1.
And the graph on the number line can be seen in the image at the end.
How to solve and graph the inequality?
The inequality we want to solve and graph is:
-6x + 5 ≤-1
To solve this, we need to start by isolating the variable x in one of the sides, we will get:
-6x + 5 ≤-1
-6x ≤-1 - 5
-6x ≤ -6
Now we can divide both sides by -6 to get:
x ≥ 1.
Then the graph will be like the one below. You need to have a closed dot on x = 1 (because that is a solution to the inequality) and then shade all the region to the right of x = 1, because x also can be larger than 1.
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A plumber have an estimate for the renovation of a kitchen. Her hourly pay is $26 per hour and the plumbing parts will cost $80 flat. If her total estimate is $366, how many hours does she expect this job to take?
I need to show work too so please help!! thank you!
Answer:
11 hours
Step-by-step explanation:
let x represent the hours worked
26(x) + 80 = 366
26(x)=366-80
26(x)=286
x=11
.˙. the plumber worked 11 hours
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Less than or equal to (≤).Less than (<).Greater than or equal to (≥).Greater than (>).In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:
Let w represent the number of weeks.
Translating the word problem into an algebraic equation, we have;
Volunteering hours = 52 hours.Remainder of her volunteer hours = 3w hours.Total time to graduate (at least) = 90 volunteer hours.Next, we would combine the above parameters to form an algebraic equation as follows:
52 + 3w ≥ 90
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Complete Question:
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
answer choices
A. 52w + 30w ≥ 90
B. 52w + 30w ≤ 90
C. 52 + 3w ≤ 90
D. 52 + 3w ≥ 90
A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. what is the slope in the situation?
A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. then the slope in the situation is 2
How do you find the slope of a line?
We need to find the ratio of the difference between the y-coordinates and x-coordinates of the two points, that form the line. The resulted value is the slope of the line. It shows the rise of the line along the y-axis over the run along x-axis.
since seed planted 1 inch deep then y1 = -1 and initial x1 =0
the plant grow an average of 3 inches every 2 weeks then y2 =3 and x2=2
putting in the formula
slope= y2 -y1 /x2 -x1
= 3-(-1)/2-0
= 4/2
=2
thus the slope in this situation is 2
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