Answer:
We make the table of these values at different values of x.
x A B C D
2 66.66 49.3 52.5 50
4 94.57 71.44 106.3 104
6 134.14 103.57 160.1 158
8 190.27 150.14 213.9 212
10 269.91 217.64 267.7 266
12 382.85 315.5 321.5 320.
Hence, the function that best represents the data is:
Option C.
y=26.9x-1.3
Step-by-step explanation:
Considering the situation described, it is found that a linear model best represents the data, because there is a relatively consistent additive rate of change.
When to use a linear model and when to use an exponential model?If the rate of change is additive, that is, the difference between consecutive terms is the same, a linear model is used.If the rate of change is multiplicative, that is, the quotient between consecutive terms is the same, an exponential model is used.In this problem, when the input changes by 2, the output always increases between approximately 50 and 60, that is, the same values, hence a linear model best represents the data, because there is a relatively consistent additive rate of change.
More can be learned about linear models at https://brainly.com/question/24808124
(3x2y2)3
What is the answer
Answer:
27x^6y^6
Step-by-step explanation:
We assume you want to simplify ...
[tex](3x^2y^2)^3=3^3x^{2\cdot3}y^{2\cdot3}=\boxed{27x^6y^6}[/tex]
__
The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
ACTIVIDAD 1: En el Parque Nacional Selva de Florencia Un explorador
se pierde dentro de un inmenso terreno circular de diámetro 27 km.
La información que se tiene es que si camina 10 km hacia el Occidente
o 5 km hacia el Oriente, llegará al borde de la circunferencia.
Responde:
a) El punto del borde más cercano a la posición del explorador a
cuantos Km se encuentra?
b) ¿Cuánto mide el perímetro y área de este terreno sabiendo
que tiene un diámetro de 27 Km?
Answer:
a) La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro del área = 84,823 km
El área de la tierra = 572.555 km²
Step-by-step explanation:
a) La distancia desde el punto del borde más cercano a la posición del escáner viene dada por la fórmula de Pitágoras;
r = √a² + b²
Por lo tanto, la distancia = √ (10² + 5²) = √125 = 5 · √5 km
La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro está dado por la fórmula para el perímetro de un círculo que es, perímetro, s = π × D
Dónde;
D = El diámetro de la tierra = 27 km.
El perímetro = π × 27 = 84.823 km
El perímetro del área = 84.823 km
El área está dada por la fórmula del área de un círculo = π × D² / 4
El área = π × 27² / 4 = 572.555 km²
El área de la tierra = 572,555 km².
The surface area S of the sphere varies directly as square of radius r and = 16 when = 2. Find when = 36 ........ with proper steps and explanation.
Answer:
r = 3
Step-by-step explanation:
Here in this question, we are told that the surface area of the sphere varies directly as square of radius;
The first thing to do here is to assign variables;
let s be the surface area and r be the radius;
Now;
Since it is a direct proportional relationship;
s = k•r^2
where k represents the constant of proportionality.
now, let’s get k at first.
From the first part of the question, s = 16 and r = 2; Substituting this, we have
16 = k•2^2
4k = 16
k = 16/4
k = 4
Now from the second part of the question, we want to find r when s = 36
Let’s rewrite our equation;
s = k•r^2
where in this case, r = ? and s = 36
36 = 4 * r^2
4r^2 = 36
r^2 = 36/4
r^2 = 9
r = √9
r = 3
Kindly note we do not pick the negative square root value as radius cannot be negative
The surface area of the sphere when the radius is 5 inches is [tex]100\pi[/tex] and this can be determined by using the given data.
Given :
The surface area of a sphere varies directly as the square of the radius. The surface area is 36 when the radius is 3 inches.The following steps can be used in order to determine the surface area S of the sphere:
Step 1 - According to the given data, the surface area S of the sphere varies directly as the square of the radius.
Step 2 - The mathematical expression of the above statement is:
[tex]\rm S= k\times r^2[/tex] --- (1)
where k is the proportionality constant.
Step 3 - Now, substitute the value of r and S in the above expression.
[tex]\rm 36\pi=k \times 3^2[/tex]
[tex]\rm k = 4\pi[/tex]
Step 4 - Now, substitute the value of [tex]\rm k = 4\pi[/tex] and r = 5 in the expression (1).
[tex]\rm S = 4\pi \times 5^2[/tex]
[tex]\rm S = 100\pi[/tex]
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Find the measure of Angle R if a = 9 square root 2 and b = 18 square root 2.
Please help!!
Answer: ∠TRa = 30°, ∠aRA = 90°, ∠TRA = 120°
Step-by-step explanation:
I'm not sure if you need the angle of the left triangle only (= 30°)
or if you need the the triangle plus the rectangle (= 120°)
Left Triangle (∠TRa)
The hypotenuse is twice the base so it is a 30° - 60° - 90° triangle
where the base corresponds to the 30° angle.
Rectangle (∠aRA)
A rectangle has four right angles --> four 90° angles.
Angle Sum Theorem
∠TRA = ∠TRa + ∠aRA
= 30° + 90°
= 120°
When constructing the bisector of a line segment, you are also constructing the perpendicular bisector of a line segment. true or false Explain your reasoning.
Answer:
True
Step-by-step explanation:
A perpendicular bisector may be defined as the line segment that intersects some other given line perpendicularly and it also divides it into two congruent or equal parts. Now, two lines are said to be cut at right angles or perpendicular to each other if they intersect in a way that they form ninety degrees to each other.
Constructing a line bisector.
1. Take any line segment of any length.
2. Take your compass and adjust its length to more than the half of the length of the line segment.
3. Placing the compass pointer on one edge at a time cut arcs above and below the line segment.
4. Now mark the points where both opposite arcs meet and join the point to cut the given line segment in two equal parts.
Thus the bisector will divide the line into two equal line segments and it will be at right angles to the given line segment.
Thus it is true that constructing a line bisector is also constructing a perpendicular bisector of the line segment.
1 point
Two benefits of having a checking account are safety and convenience.
Which of the following statements is FALSE?
a. If you have a checking account, you won't need to carry as much cash with you
b. With a checking account, you have several options for how to pay bills
c. You can cash checks for free when you cash your paycheck at your bank
d. In order to shop online, you must use a debit card
the answer is A right
Using the frequency table given, find the mean, median, and mode.
You must show all of your work to receive credit.
Answer:
[tex]Mean = 69[/tex]
[tex]Mode = 66[/tex]
[tex]Median = 69[/tex]
Step-by-step explanation:
Given
The frequency table
Required
Determine the mean, median and mode
Calculating Mean
[tex]Mean = \frac{\sum fx}{\sum f}[/tex]
Where
fx = product of frequency and inches
f = frequency
So;
[tex]Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}[/tex]
[tex]Mean = \frac{1587}{23}[/tex]
[tex]Mean = 69[/tex]
Calculating Mode
[tex]Mode = 66[/tex]
Because it highest frequency of 4
Calculating Median
[tex]Median = \frac{\sum f}{2}th\ position[/tex]
[tex]Median = \frac{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}{2}th\ position[/tex]
[tex]Median = \frac{23}{2}th\ position[/tex]
[tex]Median = 11.5th\ position[/tex]
Approximate
[tex]Median = 12th\ position[/tex]
At this point we, need to get the cumulative frequency (CF)
Inches ---- Frequency ---- CF
63 -------------2------------------2
65 -------------1------------------3
66 -------------4------------------7
67 -------------3------------------10
68 -------------1------------------11
69 -------------2------------------13
70 -------------2------------------15
71 -------------1------------------16
72 -------------3------------------19
74 -------------2------------------21
75 -------------2------------------23
From the above table
Since the median fall in the 12th position, then we consider the following data
69 -------------2------------------13
because it has a CF greater than 12
Hence;
[tex]Median = 69[/tex]
a theater has 675 seats. there are three times as many seats in a row as their are rows
Answer: 15 rows with 45 seats each
Step-by-step explanation:
Let x = the number of rows, then 3x= the number of seats in a row.
seats × row= total
3x × x=675
3x²=675
x²=225
x=15
Answer:
Step-by-step explanation:
let the number of rows=x
seats in each row=3x
so number of seats=x(3x)=3x²
3x²=675
x²=225
x=15
number of rows=15
and seats in each row=15×3=45
A candy store makes a 12-lb mixture of gummy bears, jelly beans, and Runts. The cost of gummy bears is $1.50 per pound, jelly beans cost $1.00 per pound, and Runts cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
g= 6
j = 2
r= 4
Step-by-step explanation:
Gummy bears = $1.50 per pound
Jelly beans = $1.00 per pound
Runt = $1.00 per pound
Total cost of the mixture = $15.00
Let
g = quantity of gummy bears
j = quantity of jelly beans
r = quantity of runts
g + j + r=12 (1)
1.5g + 1.0j + 1.0r = 15 (2)
three times as many gummy bears as jelly beans.
g=3j
Substitute g=3j into 1
g + j + r = 12
3j + j + r =12
4j + r =12 (3)
Substitute g=3j into 2
1.5g + 1.0j + 1.0r = 15
1.5(3j) + 1.0j + 1.0r =15
4.5j + 1.0j + 1.0r = 15
5.5j + 1.0r =15 (4)
4j + r =12 (3)
5.5j + 1.0r =15 (4)
Subtract (3) from (4)
5.5j - 4j = 15-12
1.5j = 3
Divide both sides by 1.5
j = 3/1.5
= 2
j = 2
Substitute j = 2 into (3)
4j + r =12
4(2) + r =12
8 + r = 12
r= 12-8
r= 4
Substitute j=2 and r= 4 into (1)
g + j + r=12
g + 2 + 4 = 12
g + 6 = 12
g = 12-6
=6
g=6
g= 6
j = 2
r= 4
2. What is an expression for the distance between the origin and a point P(x, y)?
Step-by-step explanation:
Using distance formula: { origin is (0,0)}
√(x - 0)² + (y - 0)²
√x² + y²
The distance between the origin and the point P(x,y) is √(x² + y²).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The distance between the origin (0,0) and the point P(x,y) is calculated as below:-
Distance = √(x - 0)² + (y - 0)²
Distance = √(x² + y²)
Therefore, the distance between the origin and the point P(x,y) is √(x² + y²).
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f(x)=1-3x and g(x)=x+4 calculate f(-2)
Answer:
7Step-by-step explanation:
[tex]f(x)=1-3x\\f(-2) = 1-3(-2)\\= 1+6\\=7[/tex]
Un tanque de almacenamiento de agua instalado en una comunidad tiene forma de prisma rectangular y una capacidad de 8 000 litros, su base mide 2.5 m por 2 m. ¿Qué altura tiene este tanque? ¿Qué cantidad de agua contendría si sólo llegara el agua a una altura de 75 cm?
Answer:
a) la altura es de 1.6 metros
b) contendría 3750 litros
Step-by-step explanation:
1000 litros = 1m³
8000 litros = 8000/1000 = 8m³
La formula del volumen de un prisma rectangular es:
v = área de la base * altura
el área de la base es:
ab = 2.5m * 2m = 5m²
entonces:
v = 5 * altura
v = 8m³
así que:
8m³ = 5m²* altura
altura = 8m³/5m²
altura = 1.6 metros
Si la altura fuese de 75cm1 metro = 100 centímetros
75 cms = 75/100 = 0.75 metros
entonces:
volumen = 5m² * 0.75m
volumen = 3.75m³
3.75m³ = 3.75*1000 = 3750 litros
El agua que contendría sería de:
3750 litros
Dan is a software salesman Y represent his total pay in dollars let X represent the number of copies English is fun he sells suppose that X and y are related by the equation 80x+2400=y
Answer:
1. 80
2. 2400
Step-by-step explanation:
1. what is the change in Dan's total pay for each copy of math is fun he sells?
2. what is Dan's total pay if he doesn't sell any copies of math is fun?
Given
y=80x + 2400
When x=0
y=80(0)+2400
=0+2400
=2400
When x=1
y=80x + 2400
=80(1) + 2400
=80+2400
=2480
change in Dan's total pay for each copy of math is fun he sells is
= 2480 - 2400
=80
2. Dan's total pay if he doesn't sell any copies of math is fun?
y=80x+2400
When x=0
y=80(0)+2400
=0+2400
=2400
10. A bird flies at a speed of 4 m/s. It flies for 2160 seconds from its nest to the field. How much
distance did the bird cover?
Answer:
8640 m, or 8.64 km, assuming it flew in a straight line
Step-by-step explanation:
Distance = rate (or speed) * time (d = rt)
The rate is 4 m/s and the time is 2160 s.
d = rt
d = 4 * 2160
d = 8640 m, or 8.64 km, assuming it flew in a straight line
Fraiser drew a model of his hometown on the coordinate plane below. Each unit of the coordinate plane represents 1 mile. A grocery store is located at (6, 4) and a school is located at (6, 8). What is the distance between the grocery store and the school?
Answer:
The distance between the grocery store and the school is 4 miles.
Step-by-step explanation:
Given that each point is represented in rectangular form. The staight-line distance ([tex]d[/tex]) between two points on a plane is given by the Pythagorean Theorem:
[tex]d =SF\cdot \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex]
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Horizontal locations of points A and B, dimensionless.
[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Vertical locations of points A and B, dimensionless.
[tex]SF[/tex] - Scale factor, measured in miles.
If [tex]SF = 1\,mi[/tex], [tex]A = (6, 4)[/tex] and [tex]B = (6,8)[/tex], the straight line distance is:
[tex]d = (1\,mi)\cdot \sqrt{(6-6)^{2}+(8-4)^{2}}[/tex]
[tex]d = 4\,mi[/tex]
The distance between the grocery store and the school is 4 miles.
Given the formula: d=m/V , which answer choice correctly rearranges the variables to solve for V?
Answer:
V = m/dStep-by-step explanation:
[tex]d = \frac{m}{V} \\Cross\:Multiply\\\\dV = m\\\\Divide\:both \:sides \:of\:the\:equation\:by\:d\\\\\frac{dV}{d} = \frac{m}{d} \\\\\\V = \frac{m}{d}[/tex]
convert y=2x-5 to slope intercept form
Answer:
y = 2x - 5
Step-by-step explanation:
y = 2x - 5 is in the form
y = mx + b
which is the slope-intercept form.
Answer: Answer below :)
Write a function g whose graph represents a reflection in the x-axis of the graph of f(x)=1/2x-3
Answer: g(x) = -(1/2)*x + 3.
Step-by-step explanation:
First, let's define a reflection over the x-axis.
If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).
Now, when we have a function
f(x) = y, the points can be written as:
(x, y = f(x) ) = (x, f(x))
Then, after the reflection over the x-axis, we have:
(x, y = g(x)) = (x, -f(x))
So now we have g(x) = -f(x)
and we know that f(x) = (1/2)*x - 3
then our new function is g(x) = y = -f(x) = -( (1/2)*x - 3) = -(1/2)*x + 3.
g(x) = -(1/2)*x + 3.
Solve the equation
(If possible please show work)
Answer:
N= -3
Step-by-step explanation:
Answer:
-3=n or n=-3
Step-by-step explanation:
7+2+4n+3=n+3
9+4n+3=n+3
12+4n=n+3
-3 -3
9+4n=n
-4n -4n
9=-3n
______
-3 -3
-3=n or n=-3
Does anybody know what -3/4 = -1/8x is? And can you please show work. Thank uuu.
Answer:
x = 6
Step-by-step explanation:
3 1
- ---- = - ---- x
4 8
3 1
- ---- = - ---- x
4 2³
3 x
- ---- = - ----
4 2³
x = 6
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
Answer:
Perimeter is irrational
Step-by-step explanation:
The attachment is missing but the question is still answerable
Given
[tex]Area = 24200 yd^2[/tex]
Required
Determine if the Perimeter is rational or not
First, we need to determine the sides of the square;
[tex]Area = Length * Length[/tex]
Substitute [tex]Area = 24200 yd^2[/tex]
[tex]24200 = Length * Length[/tex]
[tex]24200 = Length^2[/tex]
Take Square root of both sides
[tex]\sqrt{24200} = Length[/tex]
[tex]Length = 155.563492[/tex]
The perimeter of a square is calculated as:
[tex]Perimeter = 4 * Length[/tex]
[tex]Perimeter = 4 * 155.563492[/tex]
[tex]Perimeter = 622.253968[/tex]
Because the value of perimeter can't be gotten by dividing two integers, then perimeter is irrational
Sally begins hiking at an elevation of 224 ft then she descends 131 ft and climbs 67 feet higher than her current position she then descends 163 ft write an addition sentence to describe the situation then determine and interpret the sum
Answer:
Sally ends at 3 feet below zero point.
Step-by-step explanation:
Let be [tex]h[/tex] the height with respect to zero point, which is represented by the following sum:
[tex]h = \Sigma_{i=1}^{n} h_{i}[/tex]
Where:
[tex]h_{i}[/tex] - i-th travelled height, measured in feet.
In addition, positive sign means ascension, whereas negative sign means descent.
The statement can be translated into the following mathematical identity:
[tex]h = h_{1}+h_{2}+h_{3}+h_{4}[/tex]
[tex]h = 224\,ft+(-131\,ft)+67\,ft -163\,ft[/tex]
[tex]h = -3\,ft[/tex]
Sally ends at 3 feet below zero point.
The diameter of a car wheel is 60 cm, if the car travels at an average speed of 13.2m/s, find the number of revolutions made by the car per hour , hiving the awnser correct to nearest whole number. (take pie to be 3.142 )
The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.
In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of
(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s
There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives
(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h
what expression has a negative value?
7+3(-4)(2)
-2[12/(-3)]
(15-7)-(9/3)
-5[7+(-14)]-30
Answer:
7+3(-4)(2)= -17
Step-by-step explanation:
7+3(-4)(2)
(-4)*2=-8
∴ 7+3(-8)= 7-24
= -17
Use trig ratios to find the measure of the angle in this Triangle (Image)
Answer:
θ = 36.9°
Step-by-step explanation:
Trigonometric ratios in a right triangle will be,
Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{AC}}{\text{AB}}[/tex]
Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{BC}}{\text{AB}}[/tex]
Tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex] = [tex]\frac{\text{AC}}{\text{BC}}[/tex]
In the picture attached,
Given sides are,
AB = 5 and BC = 4
Therefore, to find the given angle θ only Cosine will be applicable.
Cos θ = [tex]\frac{\text{BC}}{\text{AB}}[/tex]
= [tex]\frac{4}{5}[/tex]
θ = [tex]Cos^{-1}(0.8)[/tex]
θ = 36.87°
θ ≈ 36.9°
Please help ASAP!!!!
Answer:
8
Step-by-step explanation:
1/4πr² + (2x4) - 1/4πr²
r = 4
8
i will give brainliest for anyone that can correctly answer my question, its in a photo
Answer:
x = 122
Step-by-step explanation:
Step 1: State what is known
In the picture we can see they marked ∠ABC with a box meaning it is a 90° angle, given that information we can now solve
Step 2: Solve
∠ABC = x - 32
90 = x - 32
90 + 32 = x
122 = x
Therefore 'x' is equal to 122
William's car used 2 gallons to travel 68 miles. How far can he travel on 9 gallons?
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 is 34
34 times 9 equals
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 = 34
a.k.a. 34 miles a gallon
34 times 9 miles = 306 miles
William's car can travel 306 miles with 9 gallons in its tank.
Solve for b.
-b - 19 = -3b – 9
Answer:
b=5
Step-by-step explanation:
-b - 19 = -3b – 9
Add 3b to each side
-b+3b - 19 = -3b+3b – 9
2b -19 = -9
Add 19 to each side
2b-19+19 = -9+19
2b = 10
Divide by 2
2b/2 =10/2
b=5
could I have some help with this?
Answer:
1.1783
Step-by-step explanation:
The attached picture shows a cross section of the cylindrical shell that it is convenient to use as a differential of the volume. The radius from the center of revolution is (1-x), so the circumference of the shell is 2π(1-x). Of course, its height is tan(x), so the differential of volume is ...
dV = 2π(1-x)tan(x)
The indefinite integral does not have a nice closed-form solution, but it can be easily integrated numerically from x = 0 to 1 by most scientific and graphing calculators. The attached shows the volume to be about 1.1783 cubic units.