a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)
b. The increase in cost between 12 noon and 3 pm is $2.
c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
How do you express a data set in interval notations?Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.
The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.
We can represent it as (8am, 9am) U (11am, 12pm).
It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).
And stays constant at : (9am, 10am) U (10am, 11am)
Cost increase from 12 to 3pm,We simply deduct the 12pm's cost from 3pm's cost.
So, we have
Cost increase = $3.5 - $1.5
Evaluate the difference
Cost increase = $2
Hence, the cost increase is $2
The time interval where the cost is lowerWhen you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
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Calculate the slope of the line
Answer:
8/3
Step-by-step explanation:
Slope of line =
[tex] \frac{y2 - y1}{x2 - x1} = \frac{4 - - 4}{0 - - 3} = \frac{4 + 4}{0 + 3} = \frac{8}{3} [/tex]
OR
Slope of line = vertical distance ÷ horizontal distance (vd/hd) = 8 ÷ 3 = 8/3
8/3 is an improper fraction so if you need it as a mixed number, it becomes 2⅔
Question
The average of 3 numbers is 15, and the average of 6 other numbers is 12. What is the
average of all 9 numbers?
+
O 11
O 12
O 13
O 15
Answer:
13
Step-by-step explanation:
The average of a group of numbers is calculated by adding all of the numbers up and then dividing by the number of numbers. Because of this, we can easily find the sum of the numbers by multiplying the average by the numbers.
1.) The average of the first 3 numbers is 15, meaning that the total of the numbers is 15*3 = 45.
2.) The average of the 6 other numbers is 12, meaning that the total of the numbers is 6*12 = 72.
3.) Since we know the totals of both groups of numbers, to find the total of all the numbers, we add these totals together. 45 + 72 = 117.
4.) Finally, we are finding the average, and since we know the total is 117 and there are 9 numbers, we just divide 117 by 9 to get 13. Therefore, the average of the numbers is 13.
Create a list of steps, in order, that will solve the following equation.
1/2(x+5) ^2 +2=42.5
Answer:
1/2(x+5) ^2 +2=42.5
Subtract 2 from both sides of the equation.
1/2(x+5) ^2 +2 -2=42.5-2
Subtracting 2 from itself leaves 0.
1/2(x+5) ^2 =42.5-2
Subtract 2 from 42.5.
1/2(x+5) ^2 =40.5
Multiply both sides by 2.
1/2(1/2(x+5) ^2 =(40.5)1/2
(x+5) ^2 =81
Take the square root of both sides of the equation.
x+5=9
x+5=−9
Subtract 5 from both sides of the equation.
x+5−5=9−5
x+5−5=−9−5
Subtracting 5 from itself leaves 0.
x=9−5
x=−9−5
Subtract 5 from 9.
x=4
Subtract 5 from −9.
x=−14
The equation is now solved.
x=4
x=−14
I’m am really confused on this question
Answer:
2x^7
Step-by-step explanation:
add the exponents because they both are x
2x^4*x^3=2x^7
Question 22 Solve. Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 9 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope. 3.9 ft. 10.8 ft. 6.7 ft 117 6 A
Answer:
10.8 ft
Step-by-step explanation:
So the rope and the pole are going to create a right triangle with the ground. It's going to be a simple Pythagorean theorem question
a = height of the pole
b = distance from bottom of the pole to the stake
c = length of rope
a^2 + b^2 = c^2
Solve for c
c = sqrt(a^2 + b^2)
a = 6
b = 9
c = sqrt(6^2 + 9^2)
c = 10.8
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
O A. About 60% of the books have fewer than 150 pages.
OB. About 16% of the books have fewer than 150 pages.
About 16% of the books have fewer than 150 pages
Given data ,
The numbers of pages in the books in a library follow a normal distribution
The mean number of pages is 180 and the standard deviation is 30 pages
Now , about 68% of the books will have a number of pages within one standard deviation of the mean, or between 150 and 210 pages
And , using a standard normal distribution table or a calculator that has a normal distribution function.
Using a standard normal distribution table, we find that the area to the left of -1 (which corresponds to a z-score of -1) is about 0.16
Hence , 16% of the books have fewer than 150 pages
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Find x for the image attached
Answer:
x = 72 degrees
Step-by-step explanation:
By the Vertical Angles Theorem, the angle opposite the angle (let's call it angle z, the red text in the image I sent) with 108 degrees is also equal to 108 degrees.
By the Linear Pair Theorem, angle z degrees + angle x degrees = 180 degrees.
108 + x = 180, x = 72 degrees
determine if there is enough information to prove that the pair of triangles are congruent by sss, sas, asa, or aas. write the congruent statements to justify your reasoning.
Which transformations could have occurred to map ДВС to AA'B"C"? O a rotation and a dilation O a rotation and a reflection O a reflection and a dilation O a translation and a dilation
A reflection and a dilation occurred to map △ABC to △A"B"C" (option C)
What is reflection and dilation transformation?Geometry is all about understanding shapes and their various attributes, whether its symmetry, area, volume, or something else entirely. Two common operations that can significantly alter our perception of shapes are reflections and dilations.
A reflection involves transforming a shape by flipping it over an imaginary "mirror" - called the line of reflection - while preserving certain key features such as distance between points on either side of this mirror axis.
Alternatively dilation allows us to increase or decrease the size of shapes based on some scaling factor; this can also affect other key attributes like perimeter or surface area.
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Please read the picture of the problem
Teddy can make 26 ornaments with 37/53 of clay left over
How to correct the correction?You should recall that Proportion is a mathematical comparison between two numbers, denoted using the symbol "::" or "=". It is an equation in which two ratios are set equal to each other
(20/1 ÷ 3/8)
Simplifying the fraction
20/1 * 8/3
Multiplying through to have
= 80/3
The correct solution is 26.66666
Covert the decimal to a mixed fraction to get 26 37/53
Therefore Teddy can make 26 ornaments with 37/53 of clay left over
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PLEASE HELP
If f(x) = 3x² - 5√2x - 1, find the value of f(√2).
a.-5
b.-2
d. -8
c. 0
Answer:
A
Step-by-step explanation:
Let's find the value of the function f(x) for x = √2. We'll substitute x by √2 in the equation:
f(√2) = 3(√2)² - 5√2√2 - 1
First, let's simplify the terms:
(√2)² = 2 ⇒ 3(2) = 6
5√2√2 = 5*2 = 10
Now, substitute these in the equation:
f(√2) = 6 - 10 - 1
f(√2) = -4 - 1
f(√2) = -5
Thus, the value of f(√2) is -5. The correct answer is (a).
Which number represents the front and back side of the rectangle? Please answer as fast as possible.
4 1/4 inches
That number is the bottom side of the front, so it will also be the same side as the back.
If the demand equation is
Q + 4 P = 60
fi nd a general expression for the price elasticity of demand in terms of P . For what value
of P is demand unit elastic?
The general expression for the price elasticity of demand in terms of P is E = - (P / (15 - P)).
The value of P that makes the demand to be unit elastic would be 7.5.
Price elasticity of demandThe price elasticity of demand is given by the formula:
E = (%ΔQ / %ΔP) * (P/Q)
We can solve the demand equation for Q in terms of P as:
Q = 60 - 4P
Taking the derivative of Q with respect to P, we get:
dQ/dP = -4
We can now express the percentage change in Q as a function of the percentage change in P:
%ΔQ / %ΔP = (ΔQ / Q) / (ΔP / P) = (-4P/Q) / (P/Q) = -4
Substituting this expression into the formula for price elasticity of demand, we get:
E = (%ΔQ / %ΔP) * (P/Q) = -4 * (P / (60 - 4P))E = - (P / (15 - P))To find the value of P for which demand is unit elastic, we need to set the absolute value of the price elasticity of demand equal to 1. So we have:
|E| = 1(P / (15 - P)) = 1P = 7.5In other words, the value of P for which demand is unit elastic is 7.5.
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Janie walks 1 mile to get to a running track. She then runs at a speed of 3.5 miles per hour. Which linear model represents the total distance she ran and walked, d, as a function of t, the time she runs, in hours?
Answer:
Linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:
d(t) = 1 + 3.5t
Step-by-step explanation:
To represent the total distance Janie ran and walked as a function of time, we need to consider two components: the distance she walks to the running track and the distance she runs on the track.
Distance walked to the running track: Janie walks 1 mile to reach the track. This distance remains constant regardless of the time she spends running.
Distance run on the track: Janie runs at a speed of 3.5 miles per hour. The distance she runs can be calculated by multiplying her running speed (3.5 miles/hour) by the time she spends running (t hours).
Therefore, the linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:
d(t) = 1 + 3.5t
Here, the constant term '1' represents the distance she walks to the track, and '3.5t' represents the distance she runs on the track, where t is the time she spends running in hours.
given triangle ABC below. Side lengths of the triangle and a = 12, b = 7₁ c = 8. What
is the area of triangle (round to nearest tenth)
Answer: 28
Step-by-step explanation:
Triangle area formula is (bh)/2. Base is 7, height is 8. So those multiplied will be 56, and then divide by 2 to get 28. hope this helps!
PLS HELP ME ASAP
FOR THE THIRD PICTURE, I JUST NEED THAT ANSWER FOR THE SECOND ONE
the graph of a certain quadratic function has no x-intercepts. Which of the following are possible values or the disriminant?
The possible values for the discriminant include the following:
A. -1
D. -18
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.
Discriminant, D = b² - 4ac
In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.
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Complete Question:
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A. -1
B. 3
C. 0
D. -18
The weights of bags of chips are normally distributed with a mean of 180 grams and a standard deviation of 4 grams.
What percent of the bags of chips weigh less than 176 grams?
2.5%
16%
32%
34%
The percent of the bags of chips weigh less than 176 grams is b 16%
What percent of the bags of chips weigh less than 176 grams?From the question, we have the following parameters that can be used in our computation:
Mean = 180
Standard deviation = 4
Bags of chips weigh less than 176 grams
This means that
x = 176
So, the z-score is
z = (176 - 180)/4
Evaluate
z = -1
The percent of the bags of chips weigh less than 176 grams is represented as
P = P(z < -1)
Using a graphing calculator, we have
Percentage = 0.15866
So, we have
Percentage = 16%
Hence , the percentage is 16%
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Find the area of the figure. Type your answer as just a number, without units.
The total area of the composite figure is 704 sq cm
Calculating the area of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the areas of the individual shapes
So, we have
Area = Area of Square + Area of Triangle
Using the above as a guide, we have the following equation
Area = 22 * 22 + 1/2 * 22 * (42 - 22)
Evaluate the products
Area = 484 + 220
Evaluate the sum
Area = 704
Hence. the total area of the figure is 704 sq cm
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A stock lost 7 1/8 points on Monday and then another 1 7/8
points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stock for these three days?
•a gain of 4 points
•a gain of 7 3/4 points
•a gain of 18 1/4 points
•a loss of 22 points
The net gain of 4 points for these three days.
To find the net gain or loss of the stock for these three days, we need to add up the changes in value for each day.
On Monday,
the stock lost 7 1/8 points. This is the same as -7 1/8.
On Tuesday,
the stock lost another 1 7/8 points. This is the same as -1 7/8.
So the total change in value for Monday and Tuesday is:
= -7 1/8 - 1 7/8
= -9
On Wednesday,
the stock gained 13 points. This is the same as +13.
So the net change in value for the three days is:
= -9 + 13 = +4
Therefore, the net gain of 4 points for these three days.
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Average Rate of Change Function Comparison
The option that represents the ordering of the functions according to their average rates of change on the interval -1<=x<=1 goes least to greatest is f(x), h(x), g(x). Therefore, option A is the correct answer.
From the given graph, zeros are x=-3 and x=7.
(x+3)=0 and (x-7)=0
So, the equation is (x+3)(x-7)=0
x(x-7)+3(x-7)=0
x²-7x+3x-21=0
x²-4x-21=0
So, f(x)=x²-4x-21
From the table, the coordinates (-2, 27) and (-1, 18), we get
Slope(m) = (27-18)/(-1+2)
m=9
Substitute m=9 and (x, y)=(-2, 27) in y=mx+c, we get
27=9(-2)+c
c=27+18
c=45
So, the equation is g(x)=9x+45
Given that, h(x)=-x²+x+49
Therefore, option A is the correct answer.
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20 POINTS TO WHOEVER ANSWERS
This shape can be made by putting together different shapes. Which combination would NOT make this shape?
A) 2 quadrilaterals
B) 4 triangles
C) 2 hexagons
D) 1 square and 2 trapeziums
E) 2 pentagons
The composite shape is made up of different simpler shapes, the option that would make the complex shape is
D) 1 square and 2 trapeziums
How to make the shapeAssuming the shape at the middle is of equal length and width, this describes a square and in this case the square is sitting on another shape and capped with another shape
Examining the image shows that the image at the base and on top are alike and this shape is called trapezoid hence we can say that
The complex shape is made up of a square and 2 trapeziums
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The following data relate to the operations of Shilow Company, a wholesale distributor of consumer goods:
Current assets as of March 31:
Cash $ 7,200
Accounts receivable $ 18,800
Inventory $ 37,800
Building and equipment, net $ 123,600
Accounts payable $ 22,425
Common stock $ 150,000
Retained earnings $ 14,975
A. The gross margin is 25% of sales.
B. Actual and budgeted sales data:
March (actual) $ 47,000
April $ 63,000
May $ 68,000
June $ 93,000
July $ 44,000
C. Sales are 60% for cash and 40% on credit. Credit sales are collected in the month following sale. The accounts receivable at March 31 are a result of March credit sales.
D. Each month’s ending inventory should equal 80% of the following month’s budgeted cost of goods sold.
E. One-half of a month’s inventory purchases is paid for in the month of purchase; the other half is paid for in the following month. The accounts payable at March 31 are the result of March purchases of inventory.
F. Monthly expenses are as follows: commissions, 12% of sales; rent, $2,000 per month; other expenses (excluding depreciation), 6% of sales. Assume that these expenses are paid monthly. Depreciation is $927 per month (includes depreciation on new assets).
G. Equipment costing $1,200 will be purchased for cash in April.
H. Management would like to maintain a minimum cash balance of at least $4,000 at the end of each month. The company has an agreement with a local bank that allows the company to borrow in increments of $1,000 at the beginning of each month, up to a total loan balance of $20,000. The interest rate on these loans is 1% per month and for simplicity we will assume that interest is not compounded. The company would, as far as it is able, repay the loan plus accumulated interest at the end of the quarter.
Required:
Using the preceding data:
1. Complete the schedule of expected cash collections.
2. Complete the merchandise purchases budget and the schedule of expected cash disbursements for merchandise purchases.
3. Complete the cash budget.
4. Prepare an absorption costing income statement for the quarter ended June 30.
5. Prepare a balance sheet as of June 30.
The Balance sheet is shown below.
1. Schedule of expected cash collections:
| Month | Cash Sales | Credit Sales | Total Sales | Collections in the Month of Sale | Collections in the Following Month |
| March | $28,200 | $18,800 | $47,000 | $28,200 | $18,800 |
| April | $37,800 | $25,200 | $63,000 | $25,200 | $37,800 |
| May | $40,800 | $27,200 | $68,000 | $27,200 | $40,800 |
| June | $55,800 | $37,200 | $93,000 | $37,200 | $55,800 |
| July | $26,400 | $17,600 | $44,000 | $26,400 | $17,600 |
2. Merchandise purchases budget and schedule of expected cash disbursements for merchandise purchases:
| Month | Cost of Goods Sold | Desired Ending Inventory | Total Needs | Less: Beginning Inventory | Required Purchases | Total Cost of Purchases | Payments in the Month of Purchase | Payments in the Following Month |
| April | $35,100 | $30,240 | $65,340 | $37,800 | $27,540 | $27,540 | $13,770 | $13,770 |
| May | $37,440 | $31,920 | $69,360 | $30,240 | $39,120 | $39,120 | $19,560 | $19,560 |
| June | $51,390 | $43,200 | $94,590 | $31,920 | $62,670 | $62,670 | $31,335 | $31,335 |
3. Cash budget:
| Month | Beginning Cash Balance | Cash Receipts | Cash Disbursements | Equipment Purchase | Interest Expense | Net Increase/(Decrease) in Cash | Ending Cash Balance | Borrowing (Repayment) | Loan Balance |
|-------|--------------------------|------------------|----------------------|-----------------------|---------------------|----------------------------------|-------------------------|---------------------------------------|----------------|
| April | $7,200 | $53,000 | $58,110 | ($1,200) | $0 | ($6,110) | $1,090 | $0 | $19,910 |
| May | $1,090 | $68,000 | $59,670 | $0 | $200 | $9,620 | $10,710 | $0 | $19,910 |
| June | $10,710 | $93,000 | $98,640 | $0 | $200 | ($5,940) | $4,770 | $0 | $19,910 |
| Total | $7,200 | $214,000 | $216,420 | ($1,200) | $400 | ($6,020) | $4,770 | $0 | $0 |
4. Absorption costing income statement for the quarter ended June 30:
Shilow Company
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I need help with this question please with details
The dimensions of the rectangular box are given as follows:
All the dimensions.
A. 6 inches long, 3 inches wide, 3 inches tallB. 9 inches long, 2 inches wide, 3 inches tallC. 18 inches long, 3 inches wide, 1 inch tallD. 27 inches long, 2 inches wide, 1 inches tallHow to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The box's volume is obtained as follows:
54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)
Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.
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Find the real zeros of the polynomial function
f
(
x
)
=
(
x
+
7
)
(
9
x
2
+
5
x
+
4
)
.
The real zero of the polynomial function f(x) = (x+7)(9x²+5x+4) is -7.
The complete question is:
Find the real zeros of the polynomial function f(x) = (x+7)(9x²+5x+4).
What are the real zeros of the given function?Given the function in the question:
f(x) = (x+7)(9x²+5x+4)
To find the real zeros of the polynomial function f(x) = (x+7)(9x²+5x+4), we need to find the values of x that make f(x) equal to zero.
Using the zero product property, we know that the product of two factors is equal to zero if and only if at least one of the factors is equal to zero.
Hence:
x + 7 = 0 or 9x² + 5x + 4 = 0
For the first equation:
x + 7 = 0
x = -7
To solve the second equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
Where a = 9, b = 5, and c = 4. Substituting these values, we get:
x = (-5 ± √(5² - 4(9)(4)))/(2(9))
x = (-5 ± √(25 - 144))/18
x = (-5 ± √(-119))/18
Since the discriminant (b² - 4ac) is negative, the quadratic equation has no real roots.
Therefore, the only real zero is -7.
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What is the volume of the triangular pyramid
The volume of the given triangular pyramid is 16740.768 cubic feet.
In the given triangular pyramid, dimensions of rectangular base are length=33.2 feet and width=19.1 feet.
Height of the triangular pyramid is 26.4 feet.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, volume = 33.2×19.1×26.4
= 16740.768 cubic feet
Therefore, the volume of the given triangular pyramid is 16740.768 cubic feet.
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Consider the following system of equations. − 2 x + 5 y = 19 y = − 5 6 x − 1 6 Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. ( − 13 4 , 5 2 ) B. ( 5 2 , − 13 4 ) C. ( 13 4 , − 5 2 ) D. ( − 5 2 , 13 4 )
Answer:
Approximate solution of the system is:
B. (5/2, -13/4)
Step-by-step explanation:
To approximate the solution of the given system of equations using the graph, we need to find the point where the two lines intersect. Let's analyze the equations and the graph to determine the approximate solution.
The given system of equations is:
-2x + 5y = 19 ...(1)
y = (-5/6)x - (1/6) ...(2)
Looking at equation (2), we can see that it represents a diagonal line with a negative slope, passing through the points (-5, 1) and (6, 6).
Now let's plot this line on the graph:
|
6 | x
|
| x
5 | x
|
| x
4 |
|
3 |
|
2 |
|
1 | x
|
0 |____________________
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
The line rises from (-5, 1) to (6, 6).
Next, let's analyze equation (1), which can be rearranged as:
5y = 2x + 19
y = (2/5)x + (19/5)
Comparing equation (1) with equation (2), we can see that the slope of the line in equation (1) is positive, and it intersects the other line at a point. Therefore, we are looking for the point where the rising diagonal line intersects the line with a positive slope.
By visually examining the graph, we can approximate the intersection point to be around (5/2, -13/4).
Hence, the approximate solution of the system is:
B. (5/2, -13/4)
30. Which of these sentences uses active voice?
The winning homerun was hit by the worst player on the baseball
team.
My friend invited his whole class to Saturday's soccer championship.
The children were taken to the circus by their doting grandfather.
At noon, some cookies were going to be baked by the baker.
The option that represents the active voice is:
B: My friend invited his whole class to Saturday's soccer championship.
What is the difference between active and passive voice?The active voice is one that asserts that the person or thing represented by the grammatical subject performs the action represented by the verb. The passive voice is one that makes the subject the person or thing acted on or affected by the action represented by the verb.
Looking at the given options and applying the definitions above, we can see that options A, C and D are passive voice because the subject is the recipient of the action.
Thus, the statement "My friend invited his whole class to Saturday's soccer championship." represents the active voice.
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Deandre needs to buy plastic spoons. Brand A has a box of 25 spoons for $1.99. Brand B has a box of 42 spoons for $3.89.
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Unit price for the Brand A spoons:
Unit price for the Brand B spoons:
The better buy:
Brand A
Brand B
Neither (They have the same unit price)
Answer:
Step-by-step explanation:
To find the unit price for each brand, we will divide the price of the box by the number of spoons in the box.
Unit price for the Brand A spoons:
$1.99 ÷ 25 = $0.0796 ≈ $0.08
Unit price for the Brand B spoons:
$3.89 ÷ 42 = $0.0926 ≈ $0.09
The better buy:
Brand A is the better buy, as its unit price is lower at $0.08 per spoon compared to Brand B's unit price of $0.09 per spoon.