All the statements about Arithmetic sequence and linear function are correct.
What is Arithmetic sequence and linear function?
When used in mathematics, the term "linear function" describes two different but related ideas: A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.
In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time.
Since the Linear Function has a y-intercept.
Also all the points on a Linear Function connect.
When a line slopes down from left to right, it has a negative slope. This means that a negative change in y is associated with a positive change in x.
That means the Domain of the Linear Function includes negative numbers when the function is decreasing.
Therefore, all the statements are correct.
To know more about the Arithmetic sequence and linear function, click on the link
https://brainly.com/question/28084813
#SPJ13
evaluate the expression 8.2x- 6.1 when x=7
Answer:
51.3
Step-by-step explanation:
Since it's telling us that (x=7) then that means 8.2x is going to be multiplied
8.2(7) or 8.2 x 7.
Then you end up getting an answer of 57.4
But you are not finished yet and need to subtract 6.1
so 57.4 - 6.1 = 51.3
And your result will be (51.3)
I hope this helps you understand this problem!
Given p=q=0
, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
y = –x
y = q
y = 2x + (2p – q)
Equation of the line which passes through the given points (-p ,-q) and
(p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
As given in the question,
Given condition is :
p ≠ q ≠ 0
Equation of the line which passes through the given points (-p ,-q) and
(p, q) is given by:
(x₁ , y₁) = (-p ,-q)
(x₂ , y₂) = (p, q)
(y -y₁)/ (x -x₁) = (y₂ -y₁)/ (x₂ -x₁)
⇒(y +q)/(x+ p) = (q +q)/(p +p)
⇒(y +q)/ (x +p) = 2q /2p
⇒p(y+ q) =q( x +p)
⇒yp + pq = qx +pq
⇒yp = xq
⇒y = (q /p)x
Therefore, equation of the line which passes through the given points (-p ,-q) and (p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
The complete question is :
Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
A. y = –x
B. y = q/px
C. y = q
D. y = 2x + (2p – q)
Learn more about equation here
brainly.com/question/14686792
#SPJ1
Answer:
b
Step-by-step explanation:
just did it
HELP PLS GIVING BRAINLIEST TO PERSON WHO ANSWERS FIRST
A rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven. Malik wants to rent a car, knowing that:
He plans to drive 250 miles.
He has at most $350 to spend.
Which inequality can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget?
The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven
Let the number of days be d.
Let the number of miles be m.
The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.
Learn more about inequalities on:
brainly.com/question/25275758
#SPJ1
help meeeeeeeeeeeeeee pleaseee
The table of solutions for the given equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.
How to determine the solution?In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;
At x = -2, the value of point y is as follows:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At x = -1, the value of point y is as follows:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At x = 0, the value of point y is as follows:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At x = 1, the value of point y is as follows:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At x = 2, the value of point y is as follows:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
Read more on graphs here: brainly.com/question/4546414
#SPJ1
If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 4 volts
New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
What is a current simple definition?
The speed at which electrons go past a particular location in an electrical circuit is known as current. Current = flow, at its most fundamental level. The international unit for measuring current is an amp (AM-pir), sometimes known as an amp.amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.
=> I ∝ V
=> I = V/R
R is a constant
and R is resistance
When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.
=> 75 x 10⁻³ = 3 /R
=> R = 3 x 10³/75
=> R = 10³/25
=> R = 40
I = V/R
V = 4
R = 40
=> I = 4/40
=> I = 1/10
=> I = 0.1 A
or 100 mA
new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
Learn more about Current
brainly.com/question/13076734
#SPJ4
Britney can do a job in 12 hours. if she works with jimmy, together they can get the job done in eight hours. how long would it take jimmy to do the job alone?
Jimmy will take 24 hours to do the given job alone.
What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)
Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.
To learn more about teamwork equation, tap on the link below:
https://brainly.com/question/27824138
#SPJ4
−8×{108÷12−(−3×11−15)÷12}
Answer:
[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]
[tex] - 8(9 - ( - 48) \div 12[/tex]
[tex] - 8(9 + 4)[/tex]
[tex] - 8(13)[/tex]
[tex] - 104[/tex]
Answer:
-104
Step-by-step explanation:
Divide 108 by 12
Calculate -3 × 11 - 15 which is 48
Remove the parentheses
Divide 48 by 12 which is 4
9 + 4 is 13
-8 × 13 = -104
On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). A point is at (negative 3, 1).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?
y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)
The equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)
The line is passing through (-2, -4) and (2, 2)
The slope of the line is change in y coordinate with respect to the change in x coordinate of the line
Slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
Slope of the line = (2--4) / (2--2)
= 6/2
= 3/2
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point is given that (-3, 1)
The slope of the line = 3/2
because both are parallel lines
Substitute the both values in the equation
y - 1 = 3/2( x - (-3))
y - 1 = 3/2(x + 3)
Hence, the equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)
Learn more about point slope form here
brainly.com/question/14331653
#SPJ1
Answer:
y – 1 = 3/2(x + 3)
Step-by-step explanation:
given that AC is 38. Find bc
Answer:
x = 12
Step-by-step explanation: You start off with this
3x + 2
Then since AC is 38 you make it
3x+2=38
Then you do -2 getting rid of the 2 and doing 38 - 2 which is 36
you now have:
3x = 36
then you do 3x divided by 3 on both sides
you do 36 divided by 3 then you get
x = 12
PLEASE HELPPP ILL BRAINLIST/5 STAR.
The total surface area of a cube with a side length of 8cm is:
A) 513 cm square
B) 384 cm square
C) 96 cm square
D) 64 cm Square
The letter representing the gradient in the formula y = mx + c is:
A) y
B) m
C) x
D) c
The gradient and y - intercept of the line y = -3x + 4 is:
A) -3x and 4
B) 3 and 4
C) -3 and 4
D) 4 and -3
The gradient of the line passing through the points (3, -2) and (2,-3) is:
A) 1
B) -1
C) 3b (b+4) - 4 (b-5)
Answer:
1. 384 cm square
2. m
3. -3 and 4
4. 1
Answer:
1) B
2) B
3) C
4) A
Step-by-step explanation:
Area of cube:[tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]
Here, a is the side of the cube.
Area of cube = 6 * 8 * 8
= 384 square cm
Option B
2) y = mx + c.
Here, m is the slope or gradient and c is the y-intercept.
Option B
3) y = -3x + 4
Compare with y =mx + c,
where m is the gradient and c is the y-intercept.
m = -3 and = 4
Option C
4)
[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]
[tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]
Option A
8.
y=
Which word describes the connection between the shape and its reflection?
[] congruent
[] similar
[ ] translation
[] corresponding
The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
what is congruency?Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If the matching sides and angles of two triangles are the same, they are said to be congruent. In this post, we will learn more about congruence and congruent figures.The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
learn more about congruency here:
https://brainly.com/question/1675117
#SPJ13
Which statement is logically equivalent to the following conditional statement?
"If it has exactly four sides, then it is not a hexagon."
O If it does not have exactly four sides, then it is not a hexagon.
O If it does not have exactly four sides, then it is a hexagon.
O If it is a hexagon, then it does not have exactly four sides.
O If it is not a hexagon, then it has exactly four sides.
The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
What is a regular hexagon?
It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.
Here, we let
P = it has exactly four sides.
Q = it is not an hexagon.
The negation is like this;
If it is a hexagon, then it does not have exactly four sides.
Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).
Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
To learn more about the hexagon from the given link
https://brainly.com/question/15424654
#SPJ1
Suppose you have 50 blueberry scones and 75 cranberry scones you wanted to make as many identical birds of scones as possible each bread should have an equal number of blueberry scones and an equal number of cranberries called what is the greatest number of bags you can fill explain
He can fill a total of 25 bags.
The values are,
50 blueberry scones total.
75 cranberry scones total.
For each bag to have an equal quantity of blueberry scones & cranberry scones, he must determine the maximum amount of bags he can fill.
H.C.F. of 50 & 75 is thus 25.
As a result, he can fill 25 bags.
There would be scones with blueberries in each bag of
50 ÷ 25 = 2
There would be cranberry scones for each bag, for a total of
75 ÷ 25 = 3
As a result, he may fill a total of 25 bags.
Learn more about the greatest common factor at
https://brainly.com/question/2190808?referrer=searchResults
#SPJ4
A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
The graph of the coordinate points of the vertices of ABCD indicates;
Part A The perimeter of ABCD ia approximately 61.2 units
Part B. The area of ABCD is 199.5 square units
What is the perimeter of a figure in geometry?The perimeter of a figure is length of the line that goes round the figure.
A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;
AB = √((21-11)²+(11-(-1))²) ≈ 15.6
BC = √((21-26)²+(11-(-1))²) = 13
CD = √((26-2)²+(-1-(-8))²) = 25
AD = √((2-5)²+(-8-(-1))²) ≈ 7.6
The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2
The polygon has a perimeter of approximately 61.2 unitsB. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD
The base length of triangle ΔABC = 26 - 5 = 21
The height of triangle ΔABC = 11 - (-1) = 12
The area of triangle ΔABC = 0.5 × 21 × 12 = 126
Base length of triangle ΔADC = 21
Height of triangle ΔADC = -1 - (-8) = 7
Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5
Area of the composite figure is therefore;
A = 126 + 73.5 = 199.5
The area of the figure is therefore; 199.5 square units
Learn more about finding the distance between points on the coordinate plane here;
https://brainly.com/question/21608477
#SPJ1
Diego's solar car traveled 3.16 meters farther than Justine's solar car. The equation d=j+3.16 represents this situation. What is the value of j if d=158?
The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.
How to find the missing parameters of an equation?Distance Diego's car traveled farther than Justine's solar car = 3.16 metersd = 158d = j + 3.16
substitute the value of d into the equation
d = j + 3.16
158 = j + 3.16
substract 3.16 from both sides
158 - 3.16 = j
j = 154.84
So therefore, based on the given equation d = j + 3.16, j = 154.84
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
The value of j in the equation = 154.84
Distance
Distance is the length of space covered by the car when it moves from one location to another
Given;
Equation d=j+3.16 represent the situation
distance travelled by the car= 3.16meters
d=158
Step 1: Substituting the value of d into the equation d=j+3.16
158= j +3.16
Step 2: Subtract 3.16 from both sides
158-3.16 = j + 3.16 -3.16
Step 3: Add the equation
j= 154.84
Therefore, the value of j in the equation = 154.84
Learn more about Distance here: https://brainly.com/question/4931057
#SPJ1
al would take six hours to paint a wall working alone, while bob would take four hours to paint it, and chuck would take three hours to paint it. al starts painting at noon. at 1:00 pm, bob joins him. chuck joins them at 1:30 pm. at what time do they finish painting the wall?
At 2:20 pm they finish the paint of wall.
Given, Al took 6 hours to paint a wall.
Bob took 4 hours and Chuck took 3 hours for same.
Let the work of painting wall is = LCM(6,4,3) = 12 Units
So in 1 hour Al works = 12/6 = 2 units
In 1 hour Bob works = 12/4 = 3 units
In 1 hour Chuck works = 12/3 = 4 units
In 1 hour, Al and Bob together do = 2+3 = 5 units
In 1 hour, all three together do = 2+3+4 = 9 units
Now from noon i.e. 12 to 1.00 pm Al works alone.
So 2 units of work is done.
From 1 pm to 1.30 pm, Al and Bob work together.
In 30 minutes i.e. ½ hour Al and Bob did = (1/2)*5 = 5/2 units
From 1.30 pm they all three work together.
Now the remaining work is = 12-(2+5/2) = 12-9/2 = 15/2 units
So they complete rest in = (15/2)/9 = 5/6 hours = 50 minutes
Hence the time of finishing the work = 1.30 + 50 minutes = 2.20 pm.
To know more about Time refer to:
https://brainly.com/question/26046491
#SPJ4
6x+5y=2
4x+2y=8
solve by elimination
Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.
How to Solve a System of Linear Equations by Elimination?Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.
Given the equations:
6x + 5y = 2 --> eqn. 1
4x + 2y = 8 --> eqn. 2
Multiply eqn. 1 by 2 and eqn. 2 by 5:
12x + 10y = 4 --> eqn. 3
20x + 10y = 40 --> eqn. 4
Subtract
-8x = -36
x = 4.5
Substitute x = 4.5 into eqn. 2
4(4.5) + 2y = 8
18 + 2y = 8
2y = 8 - 18
2y = -10
y = -5
The solution is: x = 4.5 and y = -5.
Learn more about system of linear equations on:
https://brainly.com/question/14323743
#SPJ1
what sample size is necessary for a 90% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.
The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
Learn more about margin of error here: brainly.com/question/10218601
#SPJ4
A health food store makes trail mix using dried fruit and nuts.the cost of the dried fruit is $2.50 per pound,and the cost of the nuts is $2.00 per pound .the total cost to make the trail mix is $225.if the total cost can be represented by the equation 2.5x +2y=225,what does the term 2.5x represent?
I need help:’)
The equation 2.5x + 2y = 225 represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.
Let the quantity of the dried fruit is x,
And the quantity of nuts is y,
As per the given question, the equation would be as:
2.5x + 2y = 225
The above equation represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
Thus, 2.5x represents the cost of dried fruit when its quantity is x.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ1
What are the x and y intercepts? What do they mean in terms of the graph?
Step-by-step explanation:
these intercepts are the points where the graph intersects with the coordinate axes (x and y).
the x-intercept is a point on the x-axis, meaning when y = 0.
the y-intercept is a point on the y-axis, meaning when x = 0.
so, the x-intercept here is 14 at the point (14, 0).
the y- intercept is 7 at the point (0, 7).
that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.
the falling speed was then
7 meters / 14 seconds = 0.5 meters / second
what are we talking about ? an asteroid with very little gravity ?
-5/8 + 1/4. Add.
Simplest form.
Answer: -3/8 or -0.375
Step-by-step explanation:
you have to get similar denominators to simplify
so times 1/4 by 2 to get 2/8
and then just do 2/8 - 5/8 and you get the answer
Solve for
x
xx.
x
=
x=x, equals
Two triangles A B C and A D E. Triangle A B C is on top of Triangle A D E at point A. Side A C is smaller than A E and side A B is smaller than side A D. Side C B has a length of three. Side E D has a length of x. Side A B has a length of nine. Segment B D has a length of six. Angle A B C and A D E are both ninety degrees.
A
A
E
E
D
D
B
B
C
C
9
9
3
3
6
6
x
x
The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5
What are similar triangles?Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.
Please find attached a possible drawing that is based on the parameters of the question
From the question and the drawing created with MS Word, we have;
Length of AB = 9
Side CB = 3
Segment BD = 6
∠ABC = ∠ADE = 90°
∠ABC ≅ ∠ADE by definition of congruency
From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality
Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate
Segment AD = Segment AB + Segment BD by segment addition postulate
AD = 9 + 6 = 15
The pair of corresponding sides of similar triangles are proportional, therefore;
[tex]\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}[/tex]
Which gives;
[tex]\dfrac{9}{15} = \dfrac{3}{x}[/tex]
9 × x = 15 × 3 = 45
x = 45 ÷ 9 = 5
The length of side ED, x = 5
Learn more about similar triangles in geometry here:
https://brainly.com/question/2644832
#SPJ1
Answer: 12
Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.
9 x 2 = 18
7 x 2 = 14
6 x 2 = 12
change 4-1/2 to a improper fraction
Answer: 9/2
Step-by-step explanation: Hope this helps.
Toby the Turkey needs you to buy place cards so that everyone will know where to sit during his Thanksgiving dinner. He would like to buy them in bulk. The card shop offers 3 different packs. Use the chart below to determine which pack offers Toby the best deal, then find the price per card.
Pack #1
Quantity 12 place cards
Cost $29 per pack
Pack #2
Quantity 24 place cards
Cost $89 per pack
Pack #3
Quantity 24 place cards
Cost $213 per pack
( This is confusing to me I don't even understand why my math teacher decided to give us it when she didn't explain it. currently gonna cry on this I need to show work what.)
The solution is Pack #1
The pack which offers Toby the best deal is Pack #1
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the price per card of each pack be = A
Now , the equation is
a)
Pack #1
The number of cards = 12 cards
The cost per pack = $ 29
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 2.416
Therefore , the cost of one card in pack 1 is $ 2.416
b)
Pack #2
The number of cards = 24 cards
The cost per pack = $ 89
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 3.708
Therefore , the cost of one card in pack 2 is $ 3.708
c)
Pack #3
The number of cards = 24 cards
The cost per pack = $ 213
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 8.875
Therefore , the cost of one card in pack 3 is $ 8.875
And ,
cost of one card in pack 3 is $ 8.875 > cost of one card in pack 2 is $ 3.708 > cost of one card in pack 1 is $ 2.416
Therefore , the cost of one card in pack 1 is $ 2.416 and this is the best deal
Hence , The pack which offers Toby the best deal is Pack #1
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer:
(f+g)(x) = x - 7
Step-by-step explanation:
(f+g)(x) tells you to add the functions together. It means
f(x) + g(x)
= -3x - 5 + 4x - 2
combine like terms.
= 4x-3x - 5 - 2
= x - 5 - 2
simplify.
= x - 7
(f+g)(x) means
f(x) + g(x)
= x - 7
Identify three segments parallel to AE using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively
From the figure, the lines parallel to AE are DH, CG, and EF.
What are parallel and perpendicular lines?Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.
If two straight lines are in the same plane and never intersect, they are said to be parallel lines.
So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.
As equidistant lines, they are always the same distance apart.
To know more about parallel and perpendicular lines, visit:
brainly.com/question/18271653
#SPJ1
The manager of a large ocean front hotel would like to survey their guests to determine their satisfaction with the view from their room. The hotel has 10 floors. Half of the rooms overlook the ocean and the other half overlook the street. There are 50 rooms on each floor, for a total of 500 rooms. The hotel manager would like to select a sample of 50 rooms.
A stratified sample in this case can be selected as follows:
The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.
How are samples classified?The five most common classifications for sampling are listed as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, the groups are given as follows:
Floors overlooking the ocean.Floors overlooking the street.50 rooms will be sampled, hence the number that is sampled from each group is given as follows:
50/2 = 25 rooms from each group.
Missing InformationThe problem asks to describe a stratified sample for this situation.
More can be learned about stratified sampling at https://brainly.com/question/28413252
#SPJ1
(a) A box is a cuboid with length 45 cm, width 30 cm and height 42 cm.
The box is completely filled with 90.72 kg of sand.
Calculate the density of this sand in kg/m³.
[Density = mass + volume]
The density of this sand is 1600 kg/m³.
What is the meaning of density?
The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.
Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.
The volume of the cuboid is (45 × 30 × 42) cm³
= 56,700 cm³
= (56,700/100³) m³
= 0.0567 m³
The mass of the sand is 90.72 kg.
The density of the sand is
= mass /volume
=90.72 kg / 0.0567 m³
= 1600 kg/m³
To learn more about density, click on below link:
https://brainly.com/question/6329108
#SPJ1
Plot a point for some of the ordered pairs from the example problem shown at the right. Model the relationships by drawing a line from the y-axis through each point. Explain how the graphs show which relationship is proportional and which is not proportional.
Both the pairs of the points are linear.
Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.
To know more about linear. https://brainly.com/question/2541253
#SPJ1