Answer:
(a)Exponential
(b)[tex]P(t)=4.70(1.0136)^t[/tex]
(c)The price of milk next year will be: $4.76
(d)5 years
Step-by-step explanation:
The price of a gallon of milk has been rising about 1.36% per year since 2000.
(a)Since the price grows by a percentage (or constant factor) each year, an exponential function would be best to model the scenario.
(b)The exponential growth model is given as:
[tex]P(t)=P_0(1+r)^t$ where:\\P_0$=Initial Price\\r=Growth factor\\t=time (in years, for this case)[/tex]
The independent variable in the function is t. This represents the number of years since 2000.
(c)
[tex]I$nitial Price, P_0=\$4.70\\r=1.36\%=0.0136\\P(t)=4.70(1+0.0136)^t\\\\P(t)=4.70(1.0136)^t[/tex]
Therefore, the price of milk next year will be:
[tex]P(1)=4.70(1.0136)^1=\$4.76[/tex]
(d)We want to determine how long it will take for the price to top $5.
P(t)=$5
[tex]5=4.70(1.0136)^t\\$Divide both sides by 4.7$\\(1.0136)^t=\frac{5}{4.7} \\$Change to logarithm form\\t=Log_{1.0136}\frac{5}{4.7}\\t=4.58[/tex]
Therefore, in exactly 4.58 years, the milk price would be $5. Therefore, by the 5th year, the milk price would top $5.
A straight line passes through the origin and has a gradient of 4. Find the equation
Answer:
y = 4x
Step-by-step explanation:
The slope is 4.
The line passes through (0, 0).
Equation of a line y = mx + b, m is the slope, and b is the y-intercept.
y = 4x + b
Put x and y as 0.
0 = 4(0) + b
0 = b
The y-intercept is 0.
The equation of the line is y = 4x.
A bug splatters on the windshield of a moving car. Describe the 1. Forces 2. Impulses 3. Momentum changes 4. And accelerations of both the bug and the car
Answer:
acceleration=force/mass
Due to variation in the mass[ as same force as per magnitude acts on both of them] the acceleration developed in the bug will be more and the acceleration developed in the car is negligible.
impulse=change in momentum
The impulse of bug is more and that of car is small.
momentum changes=change in momentum
force=change in momentum/time of contact
the force exerted by car on the bug will be more than the converse
Total. momentum is conserved , so magnitude of change in momemtum or impulse is same. By Newtons third law, since the bug have smaller mass, its change in magnitude of velocity is larger.
Step-by-step explanation:
Which of the following is not a function?
A. {(4,5), (4,2), (5,4), (2,4)}
B. {(1,2), (2,3), (3,4), (4,5)}
C. {(1,2), (2,3), (3,3), (4,5)}
D. {(4,1), (5,1), (6,1), (7,1)}
Answer:
A
Step-by-step explanation:
it is A for for two outgoing (y)there is one in going(x)
Answer:
The answer is (A)
Step-by-step explanation:
An infinite series is represented by:
A regular hexagon has a radius of 4 inches. What is the approximate area of the hexagon? a. 24 b. 42 c. 48 d. 84
Answer:
The approximate area of the hexagon is 42 in²
Now, the length of one side is 4 inches.
Answer:
B. 42 in.^2
Step-by-step explanation:
Just took the Unit Test on Edg (2020-2021)!!
find the length of this
Answer:
Hey there!
We have tan 9= 21/BW
tan 9 (BW)=21
BW= 21/tan 9
BW= 132. 59
Hope this helps :)
Answer:
A- 132.59
Step-by-step explanation:
since we have to find the adjacent and already have the opposite we'll use tanθ = opp/adj
tan(9)= 21/WB
WB = 21/tan(9) (make WB the subject)
WB = 132.5887818 or 132.59
Write an equation for the vertical translation y=-2/9 |x| -7; 1 units down
Answer:
y = -2/9 |X| - 8
Step-by-step explanation:
I'm not certain whether the -7 is part of the |X| or it's just out of the equation. But shifting an equation up or down is very intuitive.
If you want to move an equation up a certain unit, you just add that many units (positive) onto the end of an equation. The same goes for moving a unit down, where you subtract that many units you want to go down.
Answer:
y=-2/9 |x| -8
Step-by-step explanation:
y = f(x) + C C < 0 moves it down
y=-2/9 |x| -7 Shift down 1 by subtracting 1
y=-2/9 |x| -7-1
y=-2/9 |x| -8
A kite is flying at an angle of elevation of about 55°. Ignoring the sag in the string, find the height of the kite if 85 m of string has been let out.
Answer: 69.6 m
Step-by-step explanation:
Sin 55 deg = opposite side/hypotenuse
0.819 = height/string length
0.819 * 85= height
height = 69.6 m
In a plane, line e is perpendicular to line f, line f is perpendicular to line g, and line h is parallel to line f. which of the following must be true?
Answer:
a). line h is perpendicular to line g
Step-by-step explanation:
In these cases, always make a litle scetch, and just plot what is given.
You can immediately see the answer, which is answer a).
lf h is parallel to f and line f is perpendicular to line g,
then line h is perpendicular to line g.
If EB = 5, find the value of CD.
3
CD = [?]
Enter
Answer: 10
Step-by-step explanation:
AB = 2EB
AB=CD
Due to that
Cd = 2EB therefore
CD = 10
The value of CD is 10.
What is perpendicular?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
EB= 5
As, OE is perpendicular to AB
AB = 2EB
Also, AB=CD
so, CD= 2 EB
CD = 2*5
CD= 10
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What is the length of the side opposite the 45degree angle
Answer:
In a 45 - 45 - 90 triangle, the legs are equal and the ratio of sides from shortest to longest is 1 : 1 : √2 where 1 are the legs and √2 is the hypotenuse. In this case the leg is 10 / √2 = 5√2.
I need the answer to C.
Answer:
The answer to c is an arc
Answer:
it's an arc of the circle.
Step-by-step explanation:
An arc of a circle is a "portion" of the circumference of the circle.
this is the question is Estimate. 9.8 * 5.2 Choose 1 answer: a 5 b 50 c 500 d 5000
Answer: 50
Step-by-step explanation:
I am rounding it to 1 significant figure.
9.8 = 10 (round up when the last digit is 5, 6, 7, 8 or 9)
5.2 = 5 (round down when the last digit end with 0, 2, 3 or 4)
So it now is 10 x 5 = 50
Rounding to 1 significant figure, we get the product of 9.8 * 5.2 is 50. Thus, option B is correct.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
Given product is 9.8 * 5.2
Now we are rounding it to 1 significant figure.
Round up when the last digit is 5, 6, 7, 8 or 9
9.8 = 10
Round down when the last digit end with 0, 2, 3 or 4
5.2 = 5
So, 10 x 5 = 50
Thus, option B is correct.
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factor out the greatest common factor. 6x^5-15x^2+12x=?
Answer:
Factor GCF: 3x(2x⁴ - 5x + 4)
Step-by-step explanation:
Simply take out the greatest variable first and then take out the GCF of the numbers to find out factored GCF.
What is the product of 6x – y and 2x – y + 2? 8x2 – 4xy + 12x + y2 – 2y 12x2 – 8xy + 12x + y2 – 2y 8x2 + 4xy + 4x + y2 – 2y 12x2 + 8xy + 4x + y2 + 2y
Answer:
(6x – y) * (2x – y + 2) =12x2 – 8xy + 12x + y2 – 2y
Step-by-step explanation:
(6x – y) * (2x – y + 2)
= 6x*(2x – y + 2) - y*(2x – y + 2)
= 12x^2 - 6xy + 12x - 2xy + y^2 -2y
= 12x^2 + 12x - 8xy - 2y + y^2
Out of the answer choices:
8x2 – 4xy + 12x + y2 – 2y
12x2 – 8xy + 12x + y2 – 2y
8x2 + 4xy + 4x + y2 – 2y
12x2 + 8xy + 4x + y2 + 2y
the second choice is a correct answer.
Answer:
Step-by-step explanation:
B. 12x2 – 8xy + 12x + y2 – 2y
Find the greatest common factor of 24, 36, and 48. help
Answer:
24, 36, and 48
Step-by-step explanation:
those numbers are the most high common factor of 24, 36, and 48.
Answer:
12
Step-by-step explanation:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
hopefully this helped :3
Plz help I’ll mark Brainlynest
Answer:
36.00 units
Step-by-step explanation:
Lengths of horizontal and vertical segments are easily determined by subtracting coordinates or counting grid squares:
ST = 6 -1 = 5
TR = 5 -(-1) = 6
IP = 1 -(-6) = 7
PE = 2 -(-3) = 5
The lengths of the diagonal segments are found using the Pythagorean theorem. Those lengths are the root of the sum of the squares of the rise and run. As before, you can determine those from counting squares or subtracting coordinates.
RI = √(2^2 +5^2) = √29 ≈ 5.385
ES = √(3^2 +7^2) = √58 ≈ 7.616
Then the perimeter is the sum of segment lengths:
Perimeter = ST +TR +RI +IP +PE +ES
= 5 + 6 + 5.385 +7 +5 +7.616 = 36.001
Rounded to hundredths, the perimeter is 36.00 units.
5) El peso en kilos de 9 niños es 15, 25, 17, 19, 16, 26, 18, 19 ,24 a) ¿Cuál es la media y mediana? El promedio es 20 b) ¿Cuál es la mediana si incluimos el peso de otro niño que pesa 43 kg? c) En el segundo caso ¿sería la media aritmética un buen representante de los 10 datos? Argumenta tu respuesta.
Respuesta: 19; 19,89
B) 19 C) No
Explicación paso a paso:
Dados los datos:
15, 25, 17, 19, 16, 26, 18, 19, 24
Reorganizando los datos:
15, 16, 17, 18, 19, 19, 24, 25, 26
Mediana de los datos:
(N + 1) / 2
Donde N = número de observaciones
Mediana = (9 +1) / 2 = 10/2 = 5 a observación = 19.
Media = suma de valores observados / número de observaciones
Media = (15 + 16 + 17 + 18 + 19 + 19 + 24 + 25 + 26) / 9
Media = 179/9 = 19.89
B) mediana si se agrega otro niño que pese 43 kg
Los nuevos datos se convierten en:
15, 16, 17, 18, 19, 19, 24, 25, 26, 43
Mediana = (N + 1) / 2
Mediana = (10 + 1) / 2 = 11/2 = 5.5 Como tenemos un decimal:
La mediana será el promedio de la quinta y sexta observación: (19 +19) / 2 = 38/2 = 19
C) No, la media aritmética no parece ser un buen representante de la observación de 10 datos con el valor de peso recién agregado de 43 kg, ya que el valor parece considerablemente más alto que el conjunto de los 9 valores anteriores. Con el peso recién agregado, la media aritmética se convierte en: Media = (15 + 16 + 17 + 18 + 19 + 19 + 24 + 25 + 26 + 43) / 10 Media = 222/10 = 22.2
Instructions: Write the explicit rule. Remember to simplify and do not put spaces in your answer. Sequence: 30,0,−30,−60,… 30 , 0 , − 30 , − 60 , … = a n = Answer
Answer:
a(n)=60-30n
Step-by-step explanation:
Equation to use:
a(n) = a(1) + d(n-1)
where a(1) is the first term, d is the common difference between terms, and n is the nth term you are trying to find.
In this case, a(1) is 30, d is -30, and n is just n.
If you plug that into the equation and use the distributive property, you would get: a(n) = 30 -30n + 30.
Adding the two 30's gets you: a(n) = 60 - 30n, which is the solution.
one and two third minus two and two third
Answer:
[tex]1 \frac{2}{3} - 2\frac{2}{3} = -1[/tex]
Step-by-step explanation:
[tex]1\frac{2}{3} - 2 \frac{2}{3\\} \\\\\frac{5}{3} - \frac{8}{3} = \frac{-3}{3} \\ \\\frac{-3}{3} = -1[/tex]
Hope this helps! :)
Suriland cannot both export wheat and keep bread plentiful and affordable in Suriland. Accordingly, Suriland's wheat farmers are required to sell their crop to the government, which pays them a dollar per bushel less than the price on the world market. Therefore, if the farmers could sell their wheat on the world market, they would make a dollar per bushel more, less any additional transportation and brokerage costs they would have to pay.
Which of the following, if true, most seriously weakens the argument?
(A) Suriland's wheat farmers have higher production costs than do farmers in many other wheat-producing countries.
(B) Sale of a substantial proportion of Suriland's wheat crop on the world market would probably depress the price of wheat.
(C) The transportation and brokerage costs that Suriland's farmers would face if they sold their wheat outside Suriland could amount to almost a dollar per bushel.
(D) Suriland is surrounded by countries that do not import any wheat.
(E) The price of a bushel of wheat on the world market occasionally drops below the average cost of producing a bushel of wheat in Suriland.
Answer:
the most accurate argument is (C) The transportation and brokerage costs that Suriland's farmers would face if they sold their wheat outside Suriland could amount to almost a dollar per bushel.
Step-by-step explanation:
The cost of transportation and other logistics is being covered by the government that is why the government pay less than dollar per bushel.
so the price of the wheat would have to decrease at home so that the cost of the transportation can be covered by the government who are buying directly from the farmers.
Please explain how you would prove that all circles are similar?
Answer:
Shapes are similar when one can be scaled to be like another one. Circles are always the same shape and they only vary in size. A very small circle can be expanded to be the same size as any other without changing it's shape, only size. However this is not true for ovals since they come in different shapes.
Step-by-step explanation:
A ladder is 8m long. It leans against a wall with one end on the ground 6m from the wall. How far up the wall does the ladder reach?
Step-by-step explanation:
Use pythagoras theorem
a^2=b^2+c^2
a^2=64+36
a=10m
The length up to the wall of the ladder will be around 5.2915.
What is Pythagoras theorem?The Pythagoras theorem is a theorem used to find out any length of a right-angle triangle.
Pythogoroous theorem is
Hypotenuse² = base² + perpendicular²
Given that a ladder leans against a wall so the ladder will act like a hypotenuse.
Let 6m be the base then we have to find the perpendicular.
Hypotenuse² = base² + perpendicular²
perpendicular² = Hypotaneous² - base²
perpendicular = [tex]\sqrt{ (Hypotenuse)^2 - (base)^2}[/tex]
Given hypotenuse is 8m and the base is 6m.
perpendicular² = 8² - 6²
perpendicular² = 28
perpendicular = √(28) = 5.2915 hence this much be far up the wall does the ladder reach.
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A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism? 3 4 4 5
Answer: 3.5
Step-by-step explanation:
Given: Dimensions of larger prism = length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm.
Dimensions of smaller prism = length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm.
Scale factor = [tex]\dfrac{\text{Size of image}}{\text{Size of original figure}}[/tex]
Since, smaller figure is the original figure and the bigger one is the image.
So, scale factor = [tex]\dfrac{14.7}{4.2}=3.5[/tex] [Taking lengths
Hence, the factor to produce the corresponding dimensions of the larger prism = 3.5
Answer:
A
Step-by-step explanation:
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
Answer:
We operate the principle of sets to solve the problem. We are given the number of women to be 28 and men to be 23. The intersection will be while the union of both sets will be 24. To calculate the number of women teachers attending the lecture we first sum up the number of women and men and subtract from the intersection of both sets which gives us 3. Therefore, the number of teachers that are men are 3 while the number of women teachers are 1.
Step by step explaination:
Given the following, Let the set for men be represented by MM, that of women be represented by WW and that of teachers represented by TT.
Therefore, number of men i.e n(MM)= 23,
number of women i.e n(WW)= 29
number of teachers i.e n(TT)=4
number of men or teachers i.e n(MM U TT)= 24
Therefore, we have:
n(MM U TT)=n(MM) + n(TT) - n(MM n TT)
Therefore:
n(MM n TT)=n(MM) + n(TT) -n(MM U TT)
n(MM n TT)= 23+ 4 - 24 = 3
There fore number of men that are teachers are n(MM n TT)= 3 .
Therefore, from the number of teachers n(TT)=4
the number of teachers that are men are 3 while the number of women teachers are 1.
can someone help me with this question
Answer: a (see explanation below) .b.) rhombus .c) trapezoid in USA or trapezium elsewhere in the world
Step-by-step explanation:
For a.) Draw a horizontal from the bottom vertex, extending 2 units to the right. Then form a triangle by connecting a line from the right end of that line up to the right angle at the top of the original triangle
As per the given diagram
(a) represents a parallelogram not rectangle as shown in construction.
(b) Shape made by three congruent triangles on the grid below represents trapezium.
(c) Four congruent triangle in the grid below represents rhombus.
What are congruent triangles?"Two triangles are said to be congruent if the measure of all the three corresponding sides and angles of one triangle are equal to that of other triangle."
According to the question,
(a) First diagram we have to construct a triangle with given triangle in such a way it forms a parallelogram but not rectangle.
As shown in the constructed diagram.
(b) In the fourth diagram given quadrilateral having one pair of parallel line , therefore trapezium.
(c) In the second diagram all the four sides are congruent and parallel to each other and diagonals bisects each other at 90°, therefore it is rhombus.
Hence, (a) as shown in construction ,(b) trapezium and (c) rhombus is the correct answer.
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Which inequality is represented by the accompanying graph?
Thank you!!!
Answer:
y<3
Step-by-step explanation:
It is y<3 because all areas below y=3 are shaded.
In addition, the line y=3 is dotted, which means it is not part of the inequality (i.e. strict inequality).
If it had been a full line, then it would be y<=3.
Which of the following pairs of angles are supplementary? Select all that apply.
The supplementary angles are:
<1 and <3
<1 and <4
<2 and <3
<2 and <4
what are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees.
Given:
As, the supplement angles forms 180 angles.
So, from the angles that are supplementary are
<1 and <3
<1 and <4
<2 and <3
<2 and <4
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Here is the histogram of the data distribution all websites are One what is the median of this distribution? 7, 9, 5, 4
Answer:
5
Step-by-step explanation:
To find the median of the distribution, since the columns are divided into boxes(segments), we simply count the number of individual boxes
Here, the total number of boxes would be 15 boxes , so we count 7 boxes starting form each of the ends, then the middle box is the median
Counting from each end, the middle box falls on 5 which makes it our median
Answer:
5
Step-by-step explanation:
The awnsers 5
the number 5 is in the middle of all the numbers.
Samad's age and his father's age
are 12 years old and 40 years old
respectively. How many years later
will Samad's father be twice as old as
Samad?
Answer:
Step-by-step explanation:
let x= time period in years between age now and when father's age=2* the samad's age
in x years father's age will be 40 + x years old
in x years samad's age will be 12+x years old
at a certain point in time, the father's age = 2*the samad's age
40+x=2*(12+x)
or, 40 +x=24 + 2x
or, 40-24 = x
x=16
test:
father=40+16=56
son=12+16=28
hence , after 16 years samad's father will be twice as old as samad