Using linear functions, it is found that it will take 7 hours for Michael to deliver as many newspapers as Franklin.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear functions that give the amounts for Franklin and Michael after h hours are given by:
F(h) = 26 + 9h.M(h) = 5 + 12h.They will be equal when:
F(h) = M(h)
Hence:
26 + 9h = 5 + 12h
3h = 21
h = 7
It will take 7 hours for Michael to deliver as many newspapers as Franklin.
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Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Part A: The amount of ice cream increases as the temperature increases. Part B: the slope is 2 and the y-intercept will be 5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Part A: The relationship between the temperature of the city and the number of ice cream cones sold.
From the graph, the dots on the graph increase in the up-right direction.
Thus, The amount of ice cream increases as the temperature increases.
Part B: The line of best fit
First, if we draw a line through the points
we select any 2 points on the line:
( p,q) and (x,y) as (15, 35) and (0, 5).
The slope (m) is:
[tex]m = \dfrac{y-q}{x-p}[/tex]
[tex]m = \dfrac{5 - 35}{0-15}\\\\m = 2[/tex]
So, the line of best fit is:
y = mx + c
y = 2(x - 0) + 5
y = 2x + 5
The y-intercept will be when x = 0
y = 2x + 5
y = 0 + 5
y = 5
Thus, the slope is 2 and the y-intercept will be 5.
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The given equation has been solved in the table.
Step Statement
1
2
3
4
5
In which step was the subtraction property of equality applied?
A.
step 2
B.
step 3
C.
step 4
D.
The subtraction property of equality was not applied to solve this equation.
From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.
What is the Subtraction Property of Equality?If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:
a + b - b = c - b
a = c - b
Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.
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Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?
Answer:
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Assuming the time changes at a constant rate, the equation for this is linear (so has the equation y=mx +c)
8am = -2
9am = -0.5
10am = 1.0
11am = 2.5
12pm = 4
m = change in each value or the slope , for this it is m=1.5
c = the y intercept, we find this by: when x=8 y must = 1.5 , which it isn't , y has to = -2 . So c = -3.5
The equation then is: y= 1.5*x - 3.5
The gradient/slope/m value is 1.5. The answer is 1.5
Transform this equation to slope-intercept form: 6x + 4y = 8.
O y=3/2x+4
○ y=-3/2x+4
○ y =3/4 x+2
○y=-3/2x+2
Answer:
last option
Step-by-step explanation:
[tex]6x + 4y = 8 [/tex]
[tex]4y = 8 - 6x[/tex]
[tex]y = \frac{8 - 6x}{4} \\ [/tex]
[tex]y = \frac{8}{4} - \frac{6x}{4} \\ [/tex]
[tex]y = 2 - \frac{3x}{2} \\ [/tex]
[tex]y = - \frac{ 3x}{2} + 2 \\ [/tex]
y = -3/2x + 2
The equation of a circle is x^2 + y^2 =16 if the circle is translated 2 units up, what is the equation of the new circle?
The equation of the circle with the new point will be x² + ( y - 2 )² = 16.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.
Given that:-
The circle is translated as 2 units up.The equation of the circle will be formed as:-
We know that the general form of the circle is given as
( x - h )² + ( y - k )² = r²,
where ( h, k ) is the centre and r is the radius. When the circle is shifted 2 units up it means that now its centre will be ( 0, 2). So the equation will be:-
x² + ( y - 2 )² = 16
Therefore the equation of the circle with the new point will be x² + ( y - 2 )² = 16.
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6. Emily rides her bike with a constant speed of
12 miles per hour. How far can she travel in 3
1/2 hours?
Answer:
42 miles
Step-by-step explanation:
If it's a constant 12 miles per hour then it would be
12 mph x 3 hours = 36
then you would add that with the 1/2 hour for
12 mph x 1/2 hours = 6
36 + 6 = 42 miles traveled
Write an expression that represents “divide 0.04 by n''
Answer:.04/n
Step-by-step explanation:solidus represents division
help me plss ty in advance:))
Answer:
See below ~
Step-by-step explanation:
Q1
⇒ S = {1, 2, 3, 4, 5, 6}
===========================================================
Q2
⇒ No. of possible outcomes = 6
===========================================================
Q3
(a)
⇒ P(6) = Number of 6's / Total numbers
⇒ P(6) = 1/6
(b)
⇒ P (negative) = No. of negative numbers / Total numbers
⇒ P (negative) = 0/6
⇒ P (negative) = 0
(c)
⇒ P (odd) = No. of odd numbers / Total numbers
⇒ P (odd) = 3/6
⇒ P (odd) = 1/2
70 is what percent
of 350?
Answer:
20
Step-by-step explanation:
it is easy first think but besides which school are you from
The volume of a pyramid whose base is a
right triangle is 680 units. if the two legs
of the right triangle measure 15 units and
16 units, find the height of the pyramid.
The height of the prism is 5.67 units
How to determine height of the pyramid?
The given parameters are:
Volume = 680 cubic unitsBase dimensions = 15 and 16 unitsThe volume of a right triangle pyramid is:
Volume = 0.5 * Height * Base dimensions
So, we have;
680 = 0.5 * Height * 15 * 16
Evaluate
Height = 5.67
Hence, the height of the prism is 5.67 units
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The equation y - 5 = 6(x+1) is written in point-stope form. What is the equation written in slope-intercept form?
A. y = 6x + 11
B. y = 6x - 1
C. y = 6x - 4
D. y = 6x + 6
Answer:
A
Step-by-step explanation:y-5=6(x+1)
y-5=6x+6 Combine like terms so you add -5 to +6 which would be y=6x+11
How can you represent writing a check of$10 as an integer
Answer:
Step-by-step explanation:
La cantidad numérica es donde escribes la cantidad del cheque con números/dígitos. Escribe los dólares en forma numérica y luego indica los centavos después del punto decimal. En el ejemplo a continuación, los dólares son ciento veinticinco (125) y los centavos son setenta y cinco (. 75).
Estimate a 20% tip on a dinner bill of $161.86 by first rounding the bill amount to the nearest ten dollars.
Answer:
See below
Step-by-step explanation:
If you just want the tip
[tex]0.20*161.86\approx\frac{1}{5}*160=32[/tex]
If you want the total bill
[tex]1.20*161.86\approx160+32=192[/tex]
Chris needs a clever pattern for Math class tomorrow. He comes up with this pattern: 8, 4, 12, 6, 16, 8, 20, 10, ___, __.
What is his rule for this pattern
A. each set of 4 numbers adds to 36.
B. each set of four numbers adds up to 30.
C. each set of 2 numbers makes up a prime number.
D. the first number in each set of 2 numbers is 4 more than the last first number, and the second number is ½ of the first.
Answer:
D
Step-by-step explanation:
can't really explain it just is the answer
hope this helps!
given lim x→0 f(x)=4. what is lim x→0 1/4 [f(x)]^4?
Given that
[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]
we can use the properties of limits to show
[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]
[tex]\\ \rm\Rrightarrow 64[/tex]
Garrett throws a dart at a circular dart board. the dart board has a radius of 16 inches and the bull's eye in the center of the dart board has a radius of 6 inches. what is the probability that a dart thrown at random within the dartboard will hit the bull's eye? round your answer to the nearest tenth, if necessary
Answer:14.1%
Step-by-step explanation:
A table of data is given.x(-2,-1,0,1,2)f(x)(71,13,3,0.6,0.1) which exponential model best represents the data
The equation of the exponential model is f(x) = 3 * 0.2^x
How to determine the exponential model?The table of data is given as:
x(-2,-1,0,1,2)
f(x)(71,13,3,0.6,0.1)
An exponential model is represented as:
f(x) = ab^x
When x= 0 and f(x) = 3;
We have:
ab^0 = 3
This gives
a = 3
When x= 1 and f(x) = 0.6
We have:
ab^1 = 0.6
This gives
ab = 0.6
Substitute 3 for a
3b = 0.6
Divide both sides by 3
b = 0.2
Substitute b = 0.2 and a =3 in f(x) = ab^x
f(x) = 3 * 0.2^x
Hence, the equation of the exponential model is f(x) = 3 * 0.2^x
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Please help! 20 points if u answer
Answer:
find the measure of J
180-45=135
find the measure of K
360-135=225
At Dairy Freeze, 2 of the last 10 sundaes sold had nuts. Considering this data, how many of the next 20 sundaes sold would you expect to have nuts?
sundaes
A penny, nickel, and dime are simultaneously flipped. What is the probability that heads are showing on at least 6 cents worth of coins
Answer:
5/8
Step-by-step explanation:
The number of possible outcomes after flipping 3 coins is $2 \times 2 \times 2 = 8$. If the dime isn't heads, we need both the penny and nickel to be heads. If the dime is heads, the other two could be anything. So there are a total of $1+(2 \times 2)=5$ ways for us to get at least 6 cents. The answer is $\boxed{\dfrac58}.$
what adds to -288 and adds to -41?
Answer: -329 sorry if i'm not right
Kerri has a germen shepherd that has a mass of 30,000 grams. how many kilograms is 30,000 grams
MATH!!! find the volume of the pyramid. pleaseee answer correctly and tell me how you got your answer.
The area of polygons formulas to V=2.56m^2
We have to determine,
The volume of the pyramid.
What is the volume of the pyramid?The volume of a pyramid is found using the formula,
V = (1/3) Bh
where 'B' is the base area and 'h' is the height of the pyramid.
hight =2.4m
base=1.4+1.8
base=3.2m
V = (1/3) (3.2)(2.4)
V=2.56m^2
As we know the base of a pyramid is any polygon,
we can apply the area of polygons formulas to find 'B.
V=2.56m^2.
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i will ask alot of questions again sorry
Answer:
7.5 m = 0.0075 km (Correct)
0.31 = 310 mm (Correct)
46 m = 4,600 cm (Correct)
457 mm =4.57 cm (Incorrect)
0.6 km = 6,000 m (Incorrect)
Step-by-step explanation:
Tell me if something is wrong.
Which is the completely factored form of 12x3 – 60x2 + 4x – 20?
Answer:
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is [tex]4.[/tex]
2 - What is the highest degree of [tex]x[/tex] that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is 1, since [tex]x[/tex] is not in every term.
3 - Multiplying the results above,
The GCF is 4.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})[/tex]
3) Simplify each term in parentheses.
[tex]4(3{x}^{3}-15{x}^{2}+x-5)[/tex]
4) Factor out common terms in the first two terms, then in the last two terms.
[tex]4(3{x}^{2}(x-5)+(x-5))[/tex]
5) Factor out the common term [tex]x-5[/tex].
[tex]4(x-5)(3{x}^{2}+1)[/tex]
How many 1/12 pieces are in 3/3? 3/3 = __/12
Answer:
Is your teacher trying to confuse us or what?
Step-by-step explanation:
well 3/3 is full so it's just like 12/12, so 12 pieces of 1/12 piece are in 3/3
Help me to answer this math please
The water consumption based on the information for three months will be 22267m³.
How to calculate the values?The total water consumption for the three months will be:
= 7219 + 7390 + 7658
= 22267m³
In conclusion, the information simply wants you to add the values of the water given.
Therefore, the water consumption based on the information for three months will be 22267m³.
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The lengths of 10 ribbons are 100 cm, 110 cm, 95 cm, 60 cm, 20 cm, 60 cm, 110 cm,
88 cm, 102 cm and 120 cm.
(i) State the modal lengths of the ribbons.
(ii) If a ribbon of length 110 cm is removed, what will be the new modal length of
the ribbons?
The modal lengths of the ribbons are 60 cm and 110cm.
If the length 110 is removed, the new model length would be 60 cm.
What is the mode?
Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency. 110 and 60cm occur twice in the dataset. Thus, they are the mode lengths.
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A hyperbola centered at the origin has a vertex at (0,−40) and a focus at (0, 41). which are the equations of the asymptotes? y = ±x y = ±x y = ±x y = ±x
The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x
How to Interpret the equation of a hyperbola?We are given;
Vertex at (0,−40)
Focus at (0, 41).
Thus, the equation of the asymptote of the given hyperbola is;
y = ±(40/(√41 - (-40))
y = ±(40/(√81)
y = ±40/9
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Which operations is the following set closed under? Explain your answer. \(\left\{2,4,6,...\right\}\)
The operation that is being used to complete the sequence is an addition, in which each number is added + 2.
What is a sequence?A sequence is a mathematical term that refers to the succession of numbers or other mathematical objects related to each other, which is characterized by taking into account the relative position of each number with respect to the previous one.
According to the above, it can be inferred that from the following sequence:
2, 4, 6, ...The operation that is defining the sequence is:
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Answer:The operation that is being used to complete the sequence is an addition, in which each number is added + 2.
What is a sequence?
A sequence is a mathematical term that refers to the succession of numbers or other mathematical objects related to each other, which is characterized by taking into account the relative position of each number with respect to the previous one.
According to the above, it can be inferred that from the following sequence:
2, 4, 6, ...
The operation that is defining the sequence is:
x + 2
0 + 2 = 2
2 + 2 = 4
4 + 2 = 6
Step-by-step explanation: