The linear equations for the two companies are:
Company 1: y = 1.5*x + 5.5
Company 2: y = 0.5*x + 6
So the rate of company 1 is trice the rate of company 2.
What are the constant rates?When we have constant rates, then we have linear relations that can be written as:
y = m*x + b
Where m is the constant rate and b is the y-intercept.
And if we have two points (x₁, y₁) and (x₂, y₂), then the constant rate is:
m = (y₂ - y₁)/(x₂ - x₁)
So for the first table we can use the pairs:
(2.5, 9.25)
(6, 14.5)
So the rate is:
m = (14.5 - 9.25)/(6 - 2.5) = 1.5
Then the line is:
y = 1.5*x + b
To find the value of b, we can replace the values of one of the points, like (2.5, 9.25), we will get:
9.25 = 1.5*2.5 + b
9.25 - 1.5*2.5 = b
5.5 = b
And for company 2 we can try to identify two points on the graph, these can be (0, 6) and (1, 6.50), so the rate is:
m' = (6.50 - 6)/(1 - 0) = 0.50
So the rate of company 1 is 3 times the one of company 2, And the y-intercept is y = 6.
So the equations are:
Company 1: y = 1.5*x + 5.5
Company 2: y = 0.5*x + 6
So the rate of company 1 is trice the rate of company 2.
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help me with this problem pls
Answer:
Heres how to do it
(i know you arent using macbook)
Step-by-step explanation:
four $12$-sided dice are rolled. what is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number? express your answer as a common fraction. (assume that the numbers on the $12$ sides are the numbers from $1$ to $12$ expressed in decimal.)
27/128 is the probability that the number of dice showing a two-digit number is equal to the number of dice showing a one-digit number.
Probability means Possibility. It states how likely an event is about to happen.
The probability of an event can exist only between 0 and 1 where 0 indicates that the event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2
C(4,2) (1/4)^2 (3/4)^2
=27/128.
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Miguel bought 8 equally priced pens for $3.84
How much will 15 pens cost?
For this exponential function,
what is the output value (y),
when the input value (x) is O?
y = 2.3x
(0, [?])
Answer:
When the input value (x) is 0, the output value (y) is also 0. In this exponential function, any value raised to the power of 0 equals 1, and 2.3 raised to the power of 0 equals 1, so 2.3x (0) = 2.3 * 1 = 2.3, and the output value is 0.
How do you determine the equation of a circle in center-radius form whose center is (4,-3) and passes through the point (6,0)?
Using the formula (x - a) 2 + (y - b) 2 = r 2 and knowing the circle's radius and center, you can determine the circle's equation. Here, stands for the circle's center, and is the radius.
How to Find the equation of a circle using the centre and radius?A circle's center and radius can be used to get its equation. The discriminant can identify the type of intersections between two circles or a circle and a line to demonstrate tangency.
Utilize the equation (x - a2 + (y - b)2 = r 2 to determine a circle's equation when you are aware of its radius and center. Here, (a,b) stands for the circle's center and is its radius.
It's merely spelled differently, but this equation is the same as the basic equation of a circle.
Example
A circle with a center at (2,-3) and a radius of √7 has an equation that you must find.
(x - 2 )² + (y - (-3))² = (√7)²
(x - 2 )² + (y + 3 )² = 7
You can add more to this if it's necessary for more labor to provide:
x² - 4x + 4 + y² + 6y + 9 - 7 = 0
x² + y² -4x + 6y + 6 =0.
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Based on these formulas, which scenario would not have been possible?
Following the volumes a cone formula, one can determine a cone's volume given the necessary inputs. When the basis radius or even the see that, height, and slanted height of the cone are determined, the further stages can be carried out.
What is the cone's volume formula?V=1/3hπr²
Cone volume is calculated using the method V=1/3hr2. Learn how to solve a sample problem using this formula.
Step 1: Write down the given parameters, "r" denoting the radius of the cone's base, "d" denoting its diameter, "L" denoting its slant height, and "h" denoting its height.
Step 2: Apply the calculation to determine the cone's volume.
Cone volume using the base radius: V = 1/(r2h) or 1/(r2) (L2 - r2)
Cone volume using the formula V = (1/12)d2h = (1/12)d2 (L2 - r2)
Determine the volume of the a cone with a 3 inch radius and a 7 inch height. (Use π = 22/7).
Solution: We are aware of the volume
As we already know, the cone's volume is (1/3)r2h.
Taking into account that r = 3 inches, h = 7 inches, and = 22/7
So, the volume of the cone is V = (1/3)r2h V = (1/3) × (22/7) × (3)2 × (7) = 22 × 3 = 66 in3
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pls help !!! find area
The required area of the parallelogram and pentagon is 91 unit² and 75 unit².
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram = 13 × 7 = 91 unit²
Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
= 5 [1/2 × 5 × 6]
= 75 suqare units.
Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².
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Find the average rate of change of the function over the given intervals.
f(x) = 10x^3 + 10; a) [1,3] b) [-6,6]
a) The average rate of change of the function f(x) = 10x^3 + 10 over the interval [1,3] is ______ (Simply your answer)
The average rate of change of the function f(x) = 10x³ + 10 over the interval [1,3] is 130, and The average rate of change of the function f(x) = 10x³ + 10 over the interval [-6,6] is 360.
The average rate of change of function f over the interval a≤x≤b is given by the expression:
f(b)−f(a)/b−a
It is a calculation of how much the function changed per unit, on average, over that interval.
It is derived from the straight-line slope connecting the interval's endpoints on the function's graph.
a) [1,3]
Here, a = 1, b = 3
⇒f(3)−f(1)/3−1
⇒[10(3)³ + 10] - [10(1)³ + 10]/2
⇒(270 + 10 - 10 - 10)/2
⇒260/2
⇒130
b) [-6,6]
Here, a = -6, b = 6
⇒f(6)−f(-6)/6+6
⇒[10(6)³ + 10] - [10(-6)³ + 10]/12
⇒(2160 + 10 + 2160 - 10)/12
⇒4320/12
⇒360
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russell is a history teacher who recently held an exam in his class. the mean score result is 65, while the standard deviation was 20. assume that the scores are normally distributed. if a student's z-score was 1.5, how many points did he score on the exam?
If a student's z-score was 1.5, then 95 points he scored on the exam.
The mean score result is 65.
The standard deviation was 20.
A student's z-score was 1.5.
The average of a set of data is known as the set's mean. Each item of data has a z-score that indicates how far it deviates from the mean, whereas the standard deviation of a set of data reveals how dispersed the data is.
We can relate a piece of data using a formula that uses the mean, standard deviation, and z-score to identify various pieces of information in a certain situation.
The formula of z-score is:
Z = (X - Mean)/Standard Deviation
Now putting the value
1.5 = (X - 65)/20
Multiply by 20 on both side, we get
30 = X - 65
Add 65 on both side, we get
X = 95
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for which equation would x = 24 not be a solution
x/6=5
x/4=6
x/3=8
x/12=2
Answer:
x/6=5, False
Step-by-step explanation:
For which equation would x = 24 not be a solution
x/6=5 = 24/6 FALSE
x/4=6 = 24/4 TRUE
x/3=8 = 24/3 TRUE
x/12=2 = 24/12 TRUE
Why is a rhombus not a square?
The primary distinction between a square and a rhombus is that whereas the angles in a square are all 90 degrees, the angles in a rhombus are not.
How do you prove a rhombus is not a square?Since a rectangle need not have equal sides, it is not square. Every square is a rectangle and a rhombus. Due to the fact that every square has an equal number of sides, they are all rhombuses. Due of the 90-degree interior angles, all squares are also rectangles.
The main difference between a square and a rhombus is that whereas a square's angles are all 90 degrees, a rhombus's angles are not. However, both shapes have equal sides on every side.
Both a square and a rhombus have equal-length sides. But while a rhombus only has its opposite angles equal, a square only has angles that are all 90 degrees.
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I need help PLEASE SOMEONE!!!!!
Answer:
Square
4,4,4
Step-by-step explanation:
Where do i put the dots on the graph? Screenshot*
you are told you will have to wait 5 hours in a line with a group of other people determine if you know the number of minutes you have to wait
Answer:
Below
Step-by-step explanation:
There are 60 min / hr
5 hr * 60 min/hr = 300 min
In an isosceles triangle, the two equal sides are
called the
Select one:
O a. altitudes
O b. legs
O c. medians
O d. bases
Answer: B. Legs
Step-by-step explanation: The sides of the triangle are called legs because the actual name of the triangle, isosceles, comes from the greek word Iso meaning same, and the greek word Skelos, meaning leg.
A restaurant sells Thai iced teas and flatbread called roti. The scatter plot shows the relationship between the number of Thai iced teas and the number of roti sold each day for two weeks. Which line best fits the data?
A linear trend line is best fits the data.
Which line best fits the data?The theory used in this question is linear regression, which is used to identify the linear relationship between two variables.
By plotting the points from the scatter plot and fitting a line to the data, we can determine the linear trend of the data.
1. Look at the scatter plot and identify the type of data.
In this case, the data is numeric, showing the relationship between two variables: the number of Thai iced teas and the number of roti sold each day.
2. Determine the type of line that best describes the data.
A linear trend line is best for this type of data, as it shows the relationship between the two variables in a straight line.
3. Draw the line. Using the data points from the scatter plot, draw a straight line that passes through as many of the points as possible.
This line is the linear trend line.
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if she uses 486.7 cm2 of the paper to cover the lateral surface area of the cylinder, what is the diameter of the cylinder?
The diameter of the required cylinder is a function dependent on h given as 155/h
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr2h.
Given here: The lateral surface Area of the cylinder as 486.7 cm²
Let the radius of the cylinder be r then we have
2πrh=486.7
D=486.7/π×h ( where D=2r)
D=155/h
Where h is the height of the cylinder.
Hence, The diameter of the required cylinder is a function dependent on h given as 155/h
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Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities.
y\leqx2 , z\leq0
x\geqz2 , -5\leqy\leq0
The set of points is a pyramid-shaped region in space with a base of the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak. The region is bounded by the planes y = x2, z = 0, and y = -5.
The set of points is bounded by the four planes: y = x2, z = 0, x = z2, and y = -5. The two inequalities, y <= x2 and z <= 0, imply that the region is limited to the space below the plane y = x2 and behind the plane z = 0. The other two inequalities, x >= z2 and -5 <= y <= 0, indicate that the region is limited to the space in front of the plane x = z2 and between the planes y = -5 and y = 0. This forms a pyramid-shaped region with a base at the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak.
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h = 17 + x/6 find the output h when the input is -18
Answer:
x = 6h-102
Step-by-step explanation:
multiply both sides
move the terms
change the signs
reorder the terms
let be a random variable with pdf where is a constant. find the variance of (write it up to first decimal place).
The variance of the random variable X is 0.
To find the variance of the random variable X, we need to compute its mean (μ) and then calculate the expected value of the squared deviations from the mean.
The variance (σ²) is the average of these squared deviations.
First, let's find the mean (μ):
μ = ∫[x × f(x)]dx
Considering the piecewise function, we can split the integral into two parts:
For -3 < x < 0:
∫[-cx × (-cx)]dx = c² × ∫[x²]dx
= c² × [x³ / 3] between -3 and 0
= c² × (0 - (-3)³ / 3)
= c² × (0 - (-27) / 3)
= c² × (-9)
For 0 ≤ x < 3:
∫[cx × (cx)]dx = c² × ∫[x²]dx
= c² × [x³ / 3] between 0 and 3
= c² × (3³ / 3 - 0)
= c² × (27 / 3)
= c² × 9
Therefore, the mean (μ) is given by:
μ = (-9c² + 9c²) / 6
= 0
Now, let's calculate the expected value of the squared deviations from the mean:
E[(X - μ)²] = ∫[(x - μ)² × f(x)]dx
For -3 < x < 0:
∫[(x - 0)² × (-cx)]dx = c × ∫[x²]dx
= c × [x³ / 3] between -3 and 0
= c × (0 - (-3)³ / 3)
= c × (-27 / 3)
= -9c
For 0 ≤ x < 3:
∫[(x - 0)² × cx]dx = c × ∫[x²]dx
= c × [x³ / 3] between 0 and 3
= c × (3³ / 3 - 0)
= c × (27 / 3)
= 9c
Therefore, the expected value of the squared deviations from the mean is:
E[(X - μ)²] = (-9c + 9c) / 6
= 0
Finally, the variance (σ²) is the average of the squared deviations:
σ² = E[(X - μ)²]
= 0
Hence, the variance of the random variable X is 0.
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A construction company completes two projects. The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked. The relationship between the company’s labor expenses and hours worked is linear. Which of the following would correctly calculate the y-intercept of the linear equation? Select all that apply. 3,000 = 50(60) + b 3,000 = 0.02(60) + b 60 = 50(3,000) + b 2,100 = 0.02(42) + b 2,100 = 50(42) + b 42 = 50(2,100) + b
The equation that correctly calculate the y-intercept of the linear equation would be;
3,000 = 50(60) + b
2,100 = 50(42) + b
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked.
Then the relationship between the company’s labor expenses and hours worked is linear.
So, the required equation are;
3,000 = 50(60) + b
2,100 = 50(42) + b
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can someone help please and I will give brainliest :))
Answer: The car is driving 374 meters in 17 seconds, so the car is driving 22 meters in 1 second. The Bus is drving 414 meters in 23 seconds, so the bus is driving 18 meters in 1 second. The car is traveling faster. It is traveling faster by 22 - 18 = 4 meters per second.
Step-by-step explanation:
374/17 = 22.
414/23 = 18.
22-18 = 4.
Twenty-four 4 cm cube are ued to make a olid. If 2 cm cube were ued intead, how many cube would be needed?
Twenty-four 4 cm cube are used to make a solid. If 2 cm cube were used instead, 192 cube would be needed.
A cube is a solid object in three dimensions with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron. Six square faces, eight vertices, and twelve edges make up the form. Since the 3D figure is a square with equal-length sides, the length, breadth, and height of a cube are all the same measurement.
Number of cubes = Volume of the solid / Volume of the cube
= 24 x 4x4x4 / 2x2x2
=24x64/8
=192
Number of cubes will be 192 of 2cm
The area that a cube takes up is known as its volume. Finding the cube of the cube's side length will provide the volume of the cube. There are numerous formulas that use various parameters to calculate a cube's volume.
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Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she
cancels her membership with the first gym and spends the rest of the year with the second gym. The
membership to the first gym costs $80 per month, while the membership for the second gym costs $45 per
month. If she ends up spending a total of $645 over the course of the year, how much time did she spend at
each gym?
Answer:
Jan spent $240 at the first gym and $405 at the second gym.
a disk 2 inches in diameter is thrown at random on a tiled floor, where each tile is a square with sides 4 inches in length. let c be the event that the disk will land entirely on one tile. in order to assign a value to p(c), consider the center of the disk. in what region must the center lie to ensure that the disk lies entirely on one tile?
The probability that the disk will land entirely on one tile is 1/4.
For, this question I have attached an image which shows that the inner red square is the area of a tile in which the centre of the disk could land and the disk would be contained entirely within the tile while the grey area is the area in which the centre of the disk would land and the disk would not be entirely contained within the tile.
Now, The area of a square is the square of side length. The inner square has an area of 2² = 4 and the entire square (red and grey regions combined) has an area of 4² = 16.
Hence, the probability that the disk's centre lands in the red zone is the area of the red zone, divided by the total area, which is
4/16 = 1/4
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Suppose you choose at random a number from the interval
[8,32]
with the following density function:
f(x)= 32256
3
⋅x 2
,8≤x≤32
The probability of the event
E=[10,23]
is
P(E)=
The probability of selecting a number from the interval [10,23] is 3/32256 × (23^2 - 10^2) = 0.7122. Probability of selecting number [10,23] is 0.7122, integrating density function.
The probability of selecting a number from the interval [8,32] is given by the density function f(x)= 3/32256⋅x^2, where 8 ≤ x ≤ 32. We can calculate the probability of the event E=[10,23] by integrating the density function over the interval, i.e. P(E)=∫1023f(x)dx. This can be simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. Therefore, the probability of selecting a number from the interval [10,23] is 0.7122. To calculate this, we first determined the probability density function f(x) by noting that the probability of selecting a number between 8 and 32 is 1. We then divided this probability by the size of the interval, giving us the probability density f(x)= 3/32256⋅x^2. This was used to calculate the probability of the event E=[10,23] by integrating the density function over the interval. The integral was simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. This is the probability of selecting a number from the interval [10,23].
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The normal price of a cooker is £540
Stan has to work out the sale price of the cooker.
Here is his working.
10% of 540 = 54
6 x 54 = 324
Sale price £324
Sale price
60% off normal price
Stan's answer is wrong.
(b) What mistake has Stan made?
Stan forgot to subtract the discount from the total price to correctly calculate the sale price.
What is the price of a cooker if it has 60% off its normal price?Regular price: £540
Now, let's calculate the 60%:
£540 / 100 = £5.4 x 60= £324
In this case, £324 represents 60% of the total price but not the sale price. To find the sale price, let's subtract the discount from the total price as shown below:
£540 - £324 = 216
Based on this, it can be concluded that Stan forgot the last step or subtracting the discount.
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Answer:
stan did not deduct the calculation with the original price hence stan is wrong
Step-by-step explanation:
PLEASE Help I will Mark Brainlist thanks so much :D
Answer:
x = a, p
Step-by-step explanation:
the solution is at the points of intersection of the parabola and the straight line.
the points of intersection of the two graphs are (a, b ) and (p, q )
with x = a and x = p
thus x = a , p are the values of x that make the statement true
All monkeys are good chess players. All wookies are monkeys. All wookies are good chess players. what is the conclusion?
The average conclusion is that since they are monkeys, all wookies are good chess players.
Two premises form the basis for the conclusion. All monkeys are skilled chess players, according to the first postulate. The idea that all Wookies are monkeys is the second premise. The first assumption indicates that all monkeys are brilliant chess players, and since the second premise states that all wookies are monkeys, it follows that all wookies must likewise be good chess players. The conclusion is that since they are monkeys, all wookies are good chess players. This conclusion comes logically from the two supplied premises. The conclusion is also presumptively true because the premises are believed to be true.
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Two types of stereos were on sale at a local car stereo dealer.
The J-Series model sold for $II8. The K-Series model sold for $92. During the sale, 32 stereos were sold. The receipts for these stereos totaled $3,230. How many of each type of stereo did the local dealer sell during this sale?
Answer:
11 J- series and 21 K- series
Step-by-step explanation:
create a pair of equations in 2 variables and solve simultaneously.
let x represent J- series and y the K- series , then
x + y = 32 ( subtract x from both sides )
y = 32 - x → (1)
118x + 92y = 3230 → (2)
substitute y = 32 - x into (2)
118x + 92(32 - x) = 3230
118x + 2944 - 92x = 3230
26x + 2944 = 3230 ( subtract 2944 from both sides )
26x = 286 ( divide both sides by 26 )
x = 11
substitute x = 11 into (1)
y = 32 - 11 = 21
11 of J- series and 21 of K- series models were sold