Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute
Answers
Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]Related Questions
Find the simple interest. Principal Time in Months Rate 1 $11.800 21% 4 The simple interest is $ (Round to the nearest cent.)
Answers
we use the formula
Where Cn is the final amount= co the initial amount, n the number of months and i the rate dividing between 100
transform the mixed number
[tex]2\frac{1}{4}=2.25[/tex]now, replace
[tex]\begin{gathered} Cn=11,800(1+(4)\times(\frac{2.25}{100})) \\ \\ Cn=11,800(1.09) \\ \\ Cn=12862 \end{gathered}[/tex]the solution is 12,862
11. The table lists postage for letters weighing as much as 3 oz. You want to mail a letter that weighs 1.7 oz.Graph the step function. How much will you pay in postage?Weight Less ThanPrice1 oz422 oz66903 Oz
Answers
In the table says that every letter that weighs less that 1 oz. have a price of 42, in the graphic we represented that in this part:
Following the data in the table as above we got the final graphic.
And for the question:
If you have a letter that weighs 1.7 oz. it will be more than 1 oz. but less than 2 oz. so you will pay 66, as we can see in the following graphic:
10. Find the area of ABC. (A) 84 (B) 168 (C) 170 (D) 48 (E) 56A: 10B: 17C: 21Right angle: 8
Answers
we know that
the area of triangle ABC is equal to the area of two right triangles
so
triangle ABD and triangle BDC
D is a point between point A and point C
step 1
Find the length of segment AD
Applying Pythagorean Theorem in the right triangle ABD
10^2=AD^2+8^2
100=AD^2+64
AD^2=100-64
AD^2=36
AD=6
Find teh area of triangle ABD
A=AD*BD/2
A=6*8/2
A=24 units^2
step 2
Find the area of triangle BDC
A=DC*DB/2
DC=21-6=15 units
A=15*8/2
A=60 units^2
step 3
Find teh area of triangle ABC
Adds the areas
A=24+60=84 units^2
therefore
the answer is the option A 84 units^2The function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 1 units vertical shift up, 4 units horizontal shift left.a). Write the transformed equation, h(x).b). Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word.
Answers
To transform a function 1 unit up, we add 1 outside of the function
h(x) = |x| +1
shifting it 4 units to the left, we will add 4 units from x inside
h(x) = |x+4| +1
The transformed function is
h(x) = |x+4| +1
Find ( f+g ) (x) for each of the following functions
Answers
Answer:
(f + g)(x) = 2x³ + 3x² + x + 2
Explanation:
If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)
Then, we can simplify the expression adding the like terms, so
(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5
(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)
(f + g)(x) = 2x³ + 3x² + x + 2
Therefore, the answer is:
(f + g)(x) = 2x³ + 3x² + x + 2
I think is the average of the highest point and the lowest one, what's the midline of the graph?
Answers
The Midline of a Sinusoid
A sinusoid is a periodic function which parent expression is:
f(x) = A. sin (wt)
Where A is the amplitude and w is the angular frequency
The sine function has a maximum value of A and a minimum value of -A.
The midline can be found as the average value of the maximum and the minimum value.
For the parent function explained above, the midline is:
[tex]M=\frac{\text{Mx}+Mn}{2}[/tex]Since Mx and Mn are, respectively A and -A, the midline is zero.
The graph shown in the image has a maximum of Mx=1 and a minimum of Mn=-5.
Thus, the midline is:
[tex]M=\frac{\text{1}-5}{2}=-\frac{4}{2}=-2[/tex]The midline of the graph is y=-2
Triangle RST has the coordinates R(0 , 2), S(2 , 9), and T(4 , 2). Which of the following sets of points represents a dilation from the origin of triangle RST? A. R'(0 , 2), S'(8 , 9), T'(16 , 2) B. R'(0 , 2), S'(2 , 36), T'(16 , 2) C. R'(4 , 6), S'(6 , 13), T'(8 , 6) D. R'(0 , 8), S'(8 , 36), T'(16, 8)
Answers
The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).
What is dilation?In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:
Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).
Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).
Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).
In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.
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As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)
Thus, As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
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A sphere has a radius that is 2.94 centimeters long. Find the volume of the sphere. Round to the nearest tenth.
Answers
The volume of a sphere is given as
[tex]V=\frac{4}{3}\pi r^3^{}[/tex]Where r = 2.94 cm
π = 3.14
Substituting values,
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times2.94^3=1.33\times3.14\times25.41 \\ V=106.12 \end{gathered}[/tex]The volume to the nearest tenth is 106.1 cubic centimeters.
5. Which of the following expressions isequivalent to the expression below?2 394Х4AC29;woltON Alw94B+D1M
Answers
A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
f(n) = -11 + 22(n - 1)Complete the recursive formula of f(n).f(1) = f(n) = f(n - 1) +
Answers
F(n) = -11 + 22(n-1)
[tex]\begin{gathered} f(1)\text{ implies that n=1} \\ F(1)\text{ = -11+22(1-1)} \\ f(1)=-11 \end{gathered}[/tex]Hence F(1) = -11
[tex]\begin{gathered} f(n-1)\text{ implies n=n-1} \\ f(n-1)=-11\text{ +22(n-1-1)} \\ f(n-1)=-11+22(n-2)_{} \\ =\text{ -11+22n-44} \\ f(n-1)=22n-55 \end{gathered}[/tex][tex]\begin{gathered} f(n)=\text{ -11+22(n-1)} \\ =-11+22n-22 \\ 22n-33 \\ \end{gathered}[/tex]
let An = F(n) -F(n-1)
[tex]\begin{gathered} 22n-33\text{ - (22n-55)} \\ 22n\text{ - 33-22n+55} \\ =-33+55 \\ =22 \end{gathered}[/tex]Hence F(n)= f(n-1) +22
In 2011, the average daily temperature in Darrtown was 65°F. In 2012, the average daily temperature increased by 3% but then decreased by 4.5% in 2013.What was the daily average temperature in Darrtown in 2013?A.62°FB.64°FC.68°FD.74°F (thank you in advanced for who helps i was having trouble with this question)
Answers
Solution
In 2011 The temperature in Darrtown is
[tex]65^{\circ}F[/tex]The temperature increased by 3% in 2012
The temperature will be
[tex](1+\frac{3}{100})\times65=(1.03)(65)=66.95^{\circ}F[/tex]The temperature decreased by 4.5% in 2013
The temperature will be
[tex]\begin{gathered} (1-\frac{4.5}{100})\times66.95=0.955\times66.95=63.93725 \\ \\ (1-\frac{4.5}{100})\times66.95=64^{\circ}F\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the temperature in 2013 is 64 degrees Fareheint
Option B
Which one of the following angle measurements is the largest?
Answers
We have
[tex]\pi\approx3.14\text{ radians}[/tex]and
[tex]\pi=180^0[/tex]From these,
[tex]2\text{ radians<3 radians<}\pi<200^o[/tex]The largest measurement is 200 degrees. Thus, option B is correct.
solve for x and y (2x+7)(x+1)(y+5)(x-4)
Answers
Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
Imagine you are four years old. A rich aunt wants to provide for your future. She hasoffered to do one of two things.Option 1: She would give you $1000.50 a year until you are twenty-one.Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amounteach year until you were 21.If you only received money for ten years, which option would give you the most money?
Answers
Given the situation to model the arithmetic and the geometric sequences.
Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.
Option 1: She would give you $1000.50 a year until you are twenty-one.
This option represents the arithmetic sequence
The first term = a = 1000.50
The common difference = d = 1000.50
The general formula will be as follows:
[tex]\begin{gathered} a_n=a+d(n-1) \\ a_n=1000.50+1000.50(n-1) \\ \end{gathered}[/tex]Simplify the expression:
[tex]a_n=1000.50n[/tex]Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.
This option represents the geometric sequence
The first term = a = 1
The common ratio = r = 2/1 = 2
The general formula will be as follows:
[tex]\begin{gathered} a_n=a\cdot r^{n-1} \\ a_n=1\cdot2^{n-1} \end{gathered}[/tex]Now, we will compare the options:
The first term of both options is when you are four years old that n = 1
you only received money for ten years so, n = 10
So, substitute with n = 10 into both formulas:
[tex]\begin{gathered} Option1\rightarrow a_{10}=1000.50(10)=10005 \\ Option2\rightarrow a_{10}=1\cdot2^{10-1}=2^9=512 \end{gathered}[/tex]So, the answer will be:
For ten years, the option that gives the most money = Option 1
What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
Answers
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
Tommy paid $8.25 for three pounds of gummy candy.Tommy created a graph from the data on his chart. Is his graph correct? Why or Why not?
Answers
Notice that the relationship between the number of pounds of gummy candy and the number of dollars that that number of pounds costs is a function because there cannot be two prices for the same number of pounds.
Now, notice that the graph that Tommy creates does not represent a function because it fails the vertical line test at x=3.
Also, from the given table we get that (4,11) is a point of the graph.
Then the graph that Tommy creates is not correct.
Answer: No, because the graph does not represent a function and the point (4,11) is not part of the graph.
plot the graph f on the graphf(x)=|1/2x-2|
Answers
• We will determine the domain, range and x ;y intercept then plot the graph
1. The domain is given by :
[tex]\begin{gathered} \text{Domain = }x<0\text{ = (-}\infty\text{ },\text{ 0) } \\ \text{ x >0 = ( 0 },\infty)\text{ } \\ \text{ =(-}\infty;0)\text{ U ( 0 ;}\infty) \end{gathered}[/tex]2. Range is given by :
[tex]\begin{gathered} \text{Range = f(x) }\ge0\text{ } \\ \text{ =}\lbrack0;\infty) \end{gathered}[/tex]3. x - and y -intercept :
[tex]x\text{ - intercept = ( }\frac{1}{4};\text{ 0) }[/tex]4. asymptote :
[tex]\begin{gathered} \text{vertical : }x\text{ = 0 } \\ \text{horizontal : y = 2 } \end{gathered}[/tex]Now that we have the necessary points to plot the f(x) = | 1/2x -2 | , the graph will look as follows :URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer:
translated 8 units down and then reflected across the y-axis
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answers
The linear equation that gives the values of P in terms of x which is Madeline's total pay on a given day is; P + 20·x + 80
What is an equation in mathematics?An equation consists of two expressions that are joined by an equal to sign to complete a mathematical statement.
The given parameters are:
Madeline's daily base pay = $80
Madeline's commission for each computer sold = $20
The given table of values is presented as follows:
Daily pay, in Dollars, P; [tex]{}[/tex] 80, 100, 120, 140
Number of computers sold, x; [tex]{}[/tex] 0, 1, 2, 3
From the above table of values, given that the independent variable, x, is increasing at a constant rate, and that the first difference is constant, we have that the relationship is a linear relationship, that has an equation of the form; P = m·x + c
Where:
m = The slope
c = The y-intercept
The slope which gives the ratio of the rise to the run of the graph is given by the equation; [tex]m = \dfrac{100-80}{1-0} =20[/tex]
The equation in point and slope form is therefore: P - 80 = 20·(x - 0) = 20·x
P - 80 = 20·x
P = 20·x + 80
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5. (20 x 5 + 10) - (8 × 8 - 4)=
a. 58
b. 50
c. 40
Answers
Answer:
b. 50
Step-by-step explanation:
20 x 5 + 10 = 110
8 × 8 - 4 = 60
110 - 60 = 50
Answer:
b. 50
Step-by-step explanation:
(20x5+10)- (8x8-4)
(100+10) - (64-4)
110 - 60
equals 50
A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
Answers
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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can someone please help me find the mesauser of the following?
Answers
Answer:
The measure of the given arcs are;
[tex]undefined[/tex]Given the figure in the attached image.
we want to find the measure of the given arcs.
For arc ED.
The measure of arc ED is equal to the measure of arc AB;
[tex]\begin{gathered} ED=AB=\measuredangle AOB=50^{\circ} \\ ED=50^{\circ} \end{gathered}[/tex]To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.
[tex]\begin{gathered} AB+BC+CD=180^{\circ} \\ 50^{\circ}+BC+40^{\circ}=180^{\circ} \\ BC=180^0-(50^{\circ}+40^{\circ}) \\ BC=90^{\circ} \end{gathered}[/tex]To get arc BED;
[tex]\begin{gathered} \text{BED}=BE+ED \\ \text{BED}=180+50 \\ \text{BED}=230^{\circ} \end{gathered}[/tex]find distance between 2 points A(-1,-7), B(-8,7)
Answers
To calculate the length between A and B you have to draw them in the cartesian system and link them with a line, then using that line as hypothenuse, draw a right triangle, whose base will be paralel to the x-axis and its height will be paralel to the y-axis.
Using the coordinates calculate the length of the base and height of the triangle:
Base= XA-XB= (-1)-(-8)=7
Height= YB-YA=7-(-7)=14
Now you have to apply pythagoras theorem you can calculate the length of the hypotenuse:
[tex]\begin{gathered} a^2+b^2=c^2 \\ c^2=7^2+14^2 \\ c^2=245 \\ c=\sqrt{245}=15.65 \end{gathered}[/tex]The distance between poins A and B is 15.65
A shop, had a sale.
(a) In the sale, normal prices were reduced by 15%.
The normal price of a chair was reduced in the sale by $24.
Work out the normal price of the chair.
Answers
Answer:
$160
Step-by-step explanation:
A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.
if 15% of normal price equals $24 then:
24/15% or 24/0.15 = $160 normal price
CHECK:
$160 * 0.15 = $24
Answer:
$160
Step-by-step explanation:
We want to know the price of the chair
So:
24 / 0.15 = 160$
or
24 / 15% = 160
A box contains 4 red balls and 6 green balls. If a ball is drawn at random, then find the probability that the ball is red.1/102/104/106/10
Answers
To calculate the probability of event A, divide the number of outcomes favorable to A by the total number of possible outcomes.
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
a)let
[tex]\begin{gathered} favourable\text{ outcomes=red balls = 4 \lparen there are 4 red balls\rparen=4} \\ total\text{ outcomes= total balls= 4 red+6 green=10 balls=10} \end{gathered}[/tex]b) now, replace in the formula and simplify
.
[tex]P(A)=\frac{4}{10}=\frac{2}{5}[/tex]therefore, the answer is
[tex]\frac{4}{10}[/tex]I hope this helps you
can you help with this question please
Answers
We need to give the steps for proving the corresponding angles theorem for parallel lines crossed by a transverse line.
Westart with the
p || q as Given info
Next we use that
< 1 = <7 due to internal alternate angles among parallel lines
< 7 = <5 due to angles opposed by vertex
<1 = <5 due to transitive property <1 = <7 = <5
Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
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The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answers
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
....................
Answers
Answer:
oop
Step-by-step explanation:
oh
Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Answers
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]Find the length of AC
Answers
The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft