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Gina is buying 24 oranges. Two stores offer the following deals:
Store A: 12 oranges for $6.48
Store B: 5 oranges for $2.65
Gina can buy oranges individually.
How much will Gina save if she buys 24 oranges at Store B?
Show your work.

If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A is D. The statement is false because the columns of an echelon form B of A are not necessarily in the column space of A.

To understand why this is the case, we need to first define what an echelon form is. An echelon form is a special type of matrix that has certain properties, including having all zero rows at the bottom, and each pivot (non-zero) element located in a higher row than the pivot element in the previous column.

When we perform row operations on a matrix to put it into echelon form, we are essentially transforming it into a simpler form that allows us to solve systems of linear equations more easily.

Now, let's consider the statement in the question: "If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A." The column space of a matrix A, denoted as Col A, is the set of all possible linear combinations of the columns of A. In other words, it is the space spanned by the columns of A.

While it is true that the pivot columns of an echelon form B of A are linearly independent, meaning that they form a basis for the row space of B, they may not necessarily be in the column space of A. This is because the row operations used to put A into echelon form do not affect the column space of A. Therefore, it is possible for the pivot columns of B to be a basis for the row space of B, but not for the column space of A.

In summary, the statement is false because the columns of an echelon form B of A are not necessarily in the column space of A. While the pivot columns of B form a basis for the row space of B, they may not form a basis for the column space of A. Therefore, the correct option is D.

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The area of the shaded region is the area of the rectangle minus the area of the triangle

Find the coordinates of point E: Since point E lies halfway between sides AB and CD, and halfway between sides AD and BC, we can find its coordinates by taking the average of the coordinates of the opposite vertices. That is, if A = (a, b), B = (c, d), C = (e, f), and D = (g, h), then the coordinates of E are ((a+g)/2, (b+h)/2).

Find the equation of the diagonal BD: The diagonal BD passes through points B and D, so we can find its equation by using the point-slope form: y - d = (h - d)/(g - c) * (x - c).

Find the equation of the line perpendicular to BD passing through E: Since the shaded region is formed by the rectangle and the triangle outside it, we can find the equation of the line perpendicular to BD passing through E to find the height of the triangle. The slope of the line perpendicular to BD is the negative reciprocal of the slope of BD, so it is -(g - c)/(h - d). We can use the point-slope form again to find the equation of the line: y - ((b+h)/2) = -(g-c)/(h-d) * (x - (a+g)/2).

Find the intersection of the two lines: The intersection of the two lines is the point where the height of the triangle intersects the diagonal BD. We can solve the system of equations formed by the two lines to find this point.

Find the area of the triangle: Once we have the height of the triangle and the length of the base (which is the length of diagonal BD), we can use the formula for the area of a triangle: A = (1/2)bh, where b is the length of the base and h is the height.

Find the area of the shaded region: The area of the shaded region is the area of the rectangle minus the area of the triangle.

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Answer:

30 degrees

Step-by-step explanation:

Two of the angles will be 75 cause its isoceles so 150 in total. 180 - 150 is 30 so the final angle (x) is 30 degrees.

Your twin is likely to visit the dentist more frequently than you due to the difference in insurance plans.

Based on the given information, your insurance plan has a fixed copay of $40 for each doctor's visit, while your twin's copay is 20% of the total cost. Considering the local dentist charges $150 for a cleaning, you would pay a fixed copay of $40 regardless of the total cost. On the other hand, your twin's copay would be 20% of $150, which amounts to $30. Therefore, your twin would have a lower out-of-pocket expense for each dentist visit compared to you.

Due to the lower copay, your twin is more likely to visit the dentist more frequently. The difference in copayments means that your twin would save $10 on each visit, making it more cost-effective for them to seek dental care. This financial advantage would incentivize your twin to take better advantage of their insurance plan and visit the dentist more often.

Based on this reasoning, it is unlikely that you and your twin would visit the dentist the same number of times. Furthermore, there is no indication in the given information that your twin would switch insurance plans, as their plan offers a more favorable copayment structure for dental visits.

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Given data:

Total packs 3x3 sticky notes: 24 packs

Cost of 24 packs: 28.99

Number of sticky notes in a pack: 100

With the information above, we can proceed to find the answers to the questions

Part A: What is the price for each pack?

Since 24 packs cost 28.99

Then 1 pack will cost =

Hence, a pack will cost $1.21

Part B: How much is every single sticky note?

Since each pack cost 1.21, and each pack has 100 sticky notes, then

each sticky note will cost

=> every single sticky note will cost $0.012

Answer:

go to photo math thank me later

Step-by-step explanation:

Answer: After “4 hours” of work will the store earn $68.

Step-by-step explanation: To find the answer you plug in 4 into all values of x in the equation it looks like this y = -8(4)^2 + 64(4) - 60. Once you multiply, the numbers it turns into is y = -128 + 256 - 60. Then. Once you do all the addition and subtraction you get y = $68.

Have a nice day!

Answer:

Step-by-step explanation:

4x+(-2x)=2x

Answer:

(x+2)^2 - 6

Step-by-step explanation:

The coordinate plane is missing, so i have attached it.

Answer:

Perimeter of room = 140 ft

Area of room = 1200 sq.ft

Step-by-step explanation:

From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.

Thus;

The length of the sides of the room are;

ST = RQ = 30

QT = RS = 40

Perimeter of a rectangle is the sum of all sides of the rectangle.

Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft

Now, area of a rectangle is the product of two perpendicular sides.

Thus area of room = 40 x 30 = 1200 sq.ft

Answer:

vchj k,.µnkmgjcuvyikuonjlk .m

Step-by-step explanation:

cguvhijnl hkvcgufgvihjonl hkgviuctfviyjkhn

Answer:

-28

Step-by-step explanation:

Answer:

She can make 12 balls of dough

Answer: 12

Step-by-step explanation:

Im pretty sure its 12

The total cost of diesel is R459.0.

A liter (L) is a metric unit of volume that is commonly used for measuring liquids. It is equal to 1 cubic decimeter (dm³) or 1000 cubic centimeters (cm³). One liter of water has a mass of approximately one kilogram (kg) at standard temperature and pressure conditions. The liter is widely used around the world as a unit of volume for measuring liquids such as milk, gasoline, and cooking oil.

In the given questions,

To find the total cost of diesel, we need to multiply the price per litre by the number of litres taken:

Total cost = Price per litre x Number of litres

Using the given values, we have:

Total cost = R11.43/litre x 40.25 litres

Total cost = R459.0175

Rounding this to one decimal place, we get:

Total cost = R459.0

Therefore, the total cost of diesel is R459.0.

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The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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Answer:

$48.96

Step-by-step explanation:

Given data

Length= 10inches

Width=14 inches

Let us find the perimeter of the  certificate

P=2L+2W

P= 2*10+2*14

P=20+28

P= 48 inches

Hence if 1 inche cost $1.02

Then 48 inches will cost x

cross multiply we

x= 48*1.02

x= $48.96

Hence it will cost $48.96 to frame the certificate

The mean of the age data of the players is 20 and on average the age of each player is 1 far from mean.

The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.

The data of the age of the player is,

18,19,20,21,21,21

The number of player are 6. Thus, the mean of the data is,

Mean=(18+19+20+21+21+21)/6

Mean=20

The distance form mean 20 of each player age is, 2,1,0,1,1,1. The mean deviation is,

Mean Deviation= (2+1+0+1+1+1)/6

Mean Deviation=1

Thus, the mean of the age data of the players is 20 and on average the age of each player is 1 far from mean.

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The general solution of the differential equation e3t y" – 6y' + 9y for t > 0 is y = Ae3t + Bte3t, where A and B are arbitrary constants.

The method of variation of parameters is a method for finding the general solution of a nonhomogeneous linear differential equation. In this case, the differential equation is e3t y" – 6y' + 9y. The complementary solution is y_c = Ae3t + Bte3t, where A and B are arbitrary constants.

To find the particular solution, we need to find two functions, u(t) and v(t), such that u'(t) = –6u(t) + 9v(t) and v'(t) = –6v(t) + 9y_c(t). Once we have found these functions, the particular solution is y_p = u(t)y_c(t) + v(t)y_c'(t).

In this case, the functions u(t) and v(t) are u(t) = t and v(t) = 1. Therefore, the particular solution is y_p = ty_c(t) + y_c'(t) = Ae3t + Bte3t.

The general solution is the sum of the complementary solution and the particular solution. Therefore, the general solution is y = Ae3t + Bte3t, where A and B are arbitrary constants.

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The function that represents the balance after t years can be written as:

A(t) = 200(1 + 0.03)^t

To represent the balance after t years for an investment of $200 that earns 3% annual interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the balance after t years

P = the principal amount (initial investment)

r = the annual interest rate (in decimal form)

n = the number of times the interest is compounded per year

t = the number of years

In this case, the principal amount P is $200, the annual interest rate r is 3% (or 0.03 as a decimal), and we'll assume the interest is compounded once per year (n = 1).

Therefore, the function that represents the balance after t years can be written as:

A(t) = 200(1 + 0.03)^t

Simplifying further:

A(t) = 200(1.03)^t

This function can be used to calculate the balance after any number of years t.

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Answer:

y=-12x-42

Step-by-step explanation:

y-6=-12(x+4)

y= -12(x+4)+6

y=-12x-48+6

y=-2x-42

if he had $13.50 and now he has $9 all you have to do is minus $13.50 by 9 like this 13.50-9=4.50 the ice coffee costs $4.50 simple.

If you still have a question and don't understand this please ask again thank you.

Answer:

x = 12 , y = 10

Step-by-step explanation:

Let x , y are two numbers.

x > y

1 ) Three times the greater is 18 times their

difference

3x = 18( x - y )

x = 6( x - y )

x = 6x - 6y

6y = 5x

y = 5x/6 ——-( 1 )

2 ) 4 times the smaller is 4 less than twice

the sum of the two

4y + 4 = 2 ( x + y )

2y + 2 = x + y

y = x -2 ——( 2 )

From ( 1 ) and ( 2 ) ,

5x/6 = x -2

( 5x /6 ) - x = -2

( 5x - 6x ) /6 = -2

-x = -12

x = 12

Put x = 12 in equation ( 2 ) , we get

y = 12 - 2

y = 10

Therefore ,

x = 12 , y = 10

1. f(g(2))

Find g(2); evaluate g for x=2

Find f(g(2)) or f(3)

2. g(f(0))

Find f(0)

Find g(f(0)) or g(3)

3. f(g(h(1)))

Find h(1): (All the values of h are euqual to 2

Find g(h(1)) or g(2):

Find f(g(h(1))) or f(3):

4. f(y); substitute the x in f by y:

5. g(w); substitute the x in g by w:

6. h(z); substitute the x in h by z:

(a.1) The transfer function corresponding to the given differential equation y+2y = 4x is G(s) = 4/(s+2).

(b.1) The system is a third-order system.

(c) The output response of the first-order system with a unit step input is y(t) = 5 * (1 - e^(-2t)).

(a.1) To find the transfer function corresponding to the given differential equation, we can use the Laplace transform. The Laplace transform of a derivative is given by:

L{dy/dt} = sY(s) - y(0)

where Y(s) is the Laplace transform of y(t) and y(0) is the initial condition of y(t). Applying the Laplace transform to the given differential equation, we get:

sY(s) + 2Y(s) = 4X(s)

Now, we can rearrange the equation to solve for Y(s):

Y(s)(s + 2) = 4X(s)

Dividing both sides by (s + 2), we obtain:

Y(s) = (4X(s))/(s + 2)

Therefore, the transfer function corresponding to the given differential equation is:

G(s) = Y(s)/X(s) = 4/(s + 2)

(b) Let's analyze the given transfer function step by step:

G(s) = (3s + 10)/(s^3 + 4.8s^2 + 64)

(b.1) Order of the system:

The order of a system is determined by the highest power of 's' in the denominator of the transfer function. In this case, the highest power is 3. Therefore, the system is a third-order system.

(b.2) First-order system:

A first-order system has a transfer function of the form:

G(s) = K / (Ts + 1)

Comparing the given transfer function, we can see that it is not a first-order system.

(b.3) Second-order system:

A second-order system has a transfer function of the form:

G(s) = K / (s^2 + 2ζω_ns + ω_n^2)

Comparing the given transfer function, we can see that it is not a second-order system either.

(c) The transfer function of a first-order system is given as:

G(s) = K / (Ts + 1)

In this case, the transfer function is given as:

G(s) = 5 / (s + 2)

To find the output response when the input is a unit step function, we can use the Final Value Theorem. The Final Value Theorem states that the limit of the time-domain response as time approaches infinity is equal to the limit of the s-domain transfer function as s approaches zero.

Applying the Final Value Theorem to our transfer function, we can find the steady-state value of the output:

lim (t→∞) y(t) = lim (s→0) sY(s)

We need to find the inverse Laplace transform of Y(s), which is equal to y(t). Taking the Laplace transform of a unit step function, we have:

L{u(t)} = U(s) = 1/s

Multiplying both sides by the transfer function G(s), we get:

Y(s) = G(s) * U(s) = (5 / (s + 2)) * (1 / s)

To find the inverse Laplace transform of Y(s), we can use the property of the Laplace transform:

L^-1{F(s) / s} = ∫ f(t) dt

Applying this property, we find:

y(t) = L^-1{(5 / (s + 2)) * (1 / s)} = 5 * (1 - e^(-2t))

Therefore, the output response of the first-order system with a unit step input is given by y(t) = 5 * (1 - e^(-2t)).

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The correct option is none of the given choices (E. $3,600). No money will go uncollected based on the provided information.

To calculate the amount of money per year that will go uncollected, we need to determine the annual amount based on the monthly average sales.

Annual uncollected amount = Monthly average sales * 12 - Annual sales

Given that the firm's sales average $100,000 per month, the annual sales would be:

Annual sales = Monthly average sales * 12 = $100,000 * 12 = $1,200,000

Substituting this value into the equation:

Annual uncollected amount = $100,000 * 12 - $1,200,000 = $1,200,000 - $1,200,000 = $0

Therefore, the correct option is none of the given choices (E. $3,600). No money will go uncollected based on the provided information.

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The missing number from the diagram is 26. Option D

First, we need to know that square of a number is the number times itself

From the diagram shown, we have that;

a. 2² = 4

4² = 16

Add the values

4 + 16 = 20

Also, we have that;

3² = 9

9² = 81

Add the values

= 81 + 9 = 90

Then,

1² = 1

5² =25

Add the values

25 + 1 = 26

Thus, to determine the value, we need to find the square of the other two and add them.

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The temperature of a certain liquid increases by 350 C in 7 minutes when it is heated. Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/min.

Given, The temperature of a certain liquid increases by 150 C in 3 minutes when it is heated.The rate of temperature increase in the liquid can be calculated as follows:Rise in temperature / time taken = 150/3= 50C/minTo find the increase in temperature in 7 minutes, the following formula can be used:Increase in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.

To find the increase in temperature in 7 minutes when the temperature of a certain liquid increases by 150 C in 3 minutes when it is heated, follow these steps:Step 1: Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/minTherefore, the rate of temperature increase in the liquid is 50C/min.Step 2: Calculate the increase in temperature in 7 minutesIncrease in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.

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Multiply the upper system by -4:

\( - 7x - 5y = - 11\)

\(7x + 5y = 7\)

\(0 = - 3\)

\(this \: system \: admits \: no \: solutions\)

Chad used the scale of 1 scale inch which is equal to 9 feet.

In the conventional system of measuring, an inch is a unit of length. Either in or " can be used to denote length in inches. For instance, 16 in or 16" can be used to write 5 inches.

Given that,

The length of the gym in real life = 81 feet

The length of the gym in scale drawing = 9 inches

1 scale inch = length of the gym in real life/length of the gym in the scale drawing

1 scale inch = 81/9 = 9

Thus, Chad used the scale of 1 scale inch which is equal to 9 feet.

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\(\huge \tt༆ Answer ༄\)

The respective terms used for the lines are ~

Step-by-step explanation:

a is tangent

b radius

c diameter

d chord