Match each item to its equivalent unit price. Round prices to the nearest cent.

es

12-oz tube of toothpaste for $3.10

$0.22

oz

re

16-oz tube of toothpaste for $3.52

$0.26/oz

8-oz tube of toothpaste for $1.85

$0 23/Oz

10-oz tube of toothpaste for $2.92

$0.29/oz

Answer:

A

Step-by-step explanation:

ΔABD ≅ ΔCBD based on the SAS Congruence Postulate.

The SAS Congruence Postulate is a principle in geometry that states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Since B is the midpoint of AC, therefore AB ≅ CB (one pair of congruent sides).

Based on the reflexive property of congruence, BD ≅ BD (another pair of congruent sides).

Since AC is perpendicular to BD, therefore angles ABD and CBD are right angles, which means <ABD ≅ <CBD (one pair of included congruent angles).

Therefore, based on the SAS congruence postulate, ΔABD ≅ ΔCBD.

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There is a point that doesnt go in the curve.

So the procedure is to replace x by 2 ,and y by 7 in every option to see which doesnt belongs

So we see

\(tom \: will \: get \:£166 \\ ben \: will \: get \: £581\\ solution \\ let \: the \: ratios \: be \: 2x \: and \: 7x \\ 2x + 7x = 747 \\ or \: 9x = 747 \\ or \: x = \frac{747}{9} \\ x = £83 \\ replacing \: value \\ 2x \\ = 2 \times 83 \\ = 166 \\ 7x \\ = 7 \times 83 \\ = 581 \\ hope \: it \: helps\)

Answer:

Tom=£166

Ben=£581

Step-by-step explanation:

Answer:

y - 12 = 3(x - 5)

Step-by-step explanation:

Going from (-2, -9) to (5, 12), x (the run) increases by 7 and y (the rise) increases by 21.  Thus, the slope of this line is m = rise / run = 21/7 = 3.

Using the point-slope formula y - k = m(x - h), we get:

y - 12 = 3(x - 5)

The probability that one team wins in exactly five games assuming each team has an equal likelihood of winning each game is 0.29.

Algorithm World Series(n, p)

//Computes the odds of winning a series of n games

//Input: A number of wins n needed to win the series and probability p of one particular team winning a game

//Output: The probability of this team winning the series

q ← 1 − p

for j ← 1 to n do

P[0, j] ← 1.0

for i ← 1 to n do

P[i, 0] ← 0.0

for j ← 1 to n do

P[i, j] ← p ∗ P[i − 1, j] + q ∗ P[i, j − 1]

return P[n, n]

Both the time efficiency and the space efficiency are in Θ(n2) because each entry of the n + 1-by-n + 1 table (except P[0, 0], which is not computed) is computed in Θ(1) time

a. Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series. If team A wins the game, which happens with probability p, A will need i − 1 more wins to win the series while B will still need j wins. If team A looses the game, which happens with probability q = 1 − p, A will still need i wins while B will need j − 1 wins to win the series.

This leads to the recurrence

P(i, j) = pP(i − 1, j) + qP(i, j − 1) for i, j > 0

The initial conditions follow immediately from the definition of P(i, j):

P(0, j)=1 for j > 0, P(i, 0) = 0 for i > 0

b. Here is the dynamic programming table in question, with its entries rounded-off to two decimal places. (It can be filled either row-by-row, or column-by-column, or diagonal-by-diagonal.)

i/jj 0  1      2     3     4

0       1      1     1     1

1    0  0.40  0.64  0.78  0.87

2    0  0.16  0.35  0.52  0.66

3    0  0.06  0.18  0.32  0.46

4    0  0.03  0.09  0.18  0.29

Thus, P[4, 4] ≈ 0.29.

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Complete question:

World Series Odds. [20 marks total] Consider two teams, A and B, playing a series of games until one of the teams wins n games. Assume that the probability of A winning a game is the same for each game and equal to p and the probability of A losing a game is q = 1 − p. (Hence, there are no ties.) Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series.

(a) Set up a recurrence relation for P(i, j) that can be used by a dynamic programming algorithm. Hint: In the situation where teams A and B need i and j games, respectively, to win the series, consider the result of team A winning the game and the result of team A losing the game.

(b) Find the probability of team A winning a seven-game series if the probability of it winning a game is 0.4. Hint: Set up a table with five rows (0 ≤ i ≤ 4) and five columns (0 ≤ j ≤ 4) and fill it by using the recurrence derived in part (a).

(c) Write C/C++ pseudocode for a dynamic programming algorithm to solve this problem and determine its time and space efficiencies. Hint: Your pseudocode should be guided by the recurrence you set up in part (a).

The amount paid for 0.4 pounds of much after deducting $0.50 coupon is $1.58. option B

Cost of mulch : pounds of mulch

5.20 : 1 = x : 0.4

5.20/1 = x/0.4

5.20 × 0.4 = 1 × x

2.08 = x

Cost of 0.4 pounds of mulch = x = $2.08

Amount paid for 0.4 pounds of much after deducting $0.50 coupon

= $2.08 - $0.50

= $1.58

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Answer:

b) $1.58

Step-by-step explanation:

Now we have to,

→ find the amount the customer must pay.

One pound of mulch costs,

→ $5.20

Then 0.4 pounds of mulch costs,

→ $5.20 × 0.4

→ 5.20 × 0.4

→ $2.08

Total cost after reducing $0.50,

→ 2.08 - 0.50

→ $1.58

Hence, customer must pay $1.58.

On solving the provided question, we cans ay that thee equation is x+y=62.50 and she buys 5 hand towels and 3 bath towels

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let x=bath towels

y=hand towels

x+y=62.50

she spends 17.25 more on bath towels

\(x =y+17.25\\y+(y+17.25)=62.25\\ 2y+17.25=62.25\\ y=22.50\)

she spends 22.50 on hand towel

22.50+17.25 on bath towels

she buys 5 hand towels and 3 bath towels

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Answer:

y intercept is (0, -4)

equation is y = x - 4

Step-by-step explanation:

The slope is rise/run which you can find by choosing "any" two points on the line. For instance (0,-4) and (4,0)

The rise is the difference in y direction: 0 - - 4 = 4, the graph "rises" by 4.

The run is the difference in x direction: 4 - 0 = 4, the graph "runs" by 4.

So the slope is 4/4 = 1.

The y intercept is the point on the y axis where the line passes through. This is (0,-4). The intercept value is y= - 4.

The equation is slope times x plus y intercept value.

So putting this all together gives you an equation of

y = 1·x + -4

a.k.a.

y = x-4

The curve of best fit is an illustration of a quadratic regression

The equation of the curve of best fit is \(y = -\frac{17}{18}x^2 + \frac{17}3x + 2\), and the height of the frog after 6 seconds is 2 feet

To determine the equation of the curve of best fit, we make use of a graphing calculator

Using the graphing calculator, we have the following calculation summary

The equation of the curve of best fit is represented as:

\(y = ax^2 + bx + c\)

Substitute the values for a, b and c.

So, we have:

\(y = -\frac{17}{18}x^2 + \frac{17}3x + 2\)

After 6 seconds, the value of x is 6.

So, we have:

\(y = -\frac{17}{18} * 6^2 + \frac{17}3 * 6 + 2\)

Evaluate

\(y = 2\)

Hence, the height of the frog after 6 seconds is 2 feet

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The perimeter of the parallelogram is 30 units, and m∠BCD is  127°.

Polygon ABCD is a parallelogram with angle ABC measuring 127°, we can determine various properties of the parallelogram.

The length of AB is 10 units.

The length of BC is 5 units.

Since opposite sides of a parallelogram are congruent, we can conclude that the length of CD is also 10 units (same as AB) and the length of AD is 5 units (same as BC).

To find the perimeter of the parallelogram, we add the lengths of all four sides:

Perimeter = AB + BC + CD + AD = 10 + 5 + 10 + 5 = 30 units.

Therefore, the perimeter of the parallelogram is 30 units.

Now, let's determine the measure of angle BCD (m∠BCD). In a parallelogram, opposite angles are congruent. Since angle ABC measures 127°, angle BCD, which is opposite to angle ABC, will also measure 127°.

Therefore, m∠BCD = 127°.

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To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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area of OAB = 72 = (1/2) sin (AOB) * OA * OB solve the above for sin(AOB) to find sin(AOB) = 1/2 area of ODC = 288 = (1/2) sin (DOC) * OD * OD Note that sin(DOC) = sin(AOB) = 1/2, OD = 18 + y and OC = 16 + x and substitute in the above to obtain the first equation in x and y 1152 = (18 + y)(16 + x)...

HOPE SO IT HELPS YOU

Answer:

15120in3

Step-by-step explanation:

2 1/2=30in

3 1/2=42 in

30x42x12=15120

Answer:

5/6

Step-by-step explanation:

15/18

Divide the top and bottom by 3

15/3 = 5

18/3 = 6

5/6

I have simplified:)

To simplify, you have to divide the numerator & denominator by 3

BTW,I am also an Acellus student!:)

Answer:

\(-\frac{2}{15}\)

Step-by-step explanation:

   \(\frac{2-\left|-\frac{2}{3}-2\left(-\frac{1}{5}\right)\right|}{-13}\)

\(\mathrm{Apply\:rule}:\quad \:-a\left(-b\right)=ab\)

\(-2\left(-\frac{1}{5}\right)=2\cdot \frac{1}{5}\)

\(=\frac{2-\left|-\frac{2}{3}+2\cdot \frac{1}{5}\right|}{-13}\)

\(-\frac{2}{3}+2*\frac{1}{5}=-\frac{4}{15}\)

\(=\frac{2-\left|-\frac{4}{15}\right|}{-13}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\)

\(=-\frac{2-\left|-\frac{4}{15}\right|}{13}\)

\(Simplify\;2-|-\frac{4}{15}|:\frac{26}{15}\)

\(=-\frac{\frac{26}{15}}{13}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{c}=\frac{a}{b\cdot \:c}\)

\(\frac{\frac{26}{15}}{13}=\frac{26}{15\cdot \:13}\)

\(=-\frac{26}{15\cdot \:13}\)

\(\mathrm{Multiply\:the\:numbers:}\:15\cdot \:13=195\)

\(=-\frac{26}{195}\)

\(Cancel-\frac{26}{195}:-\frac{2}{15}\)

Answer = -2/15

[RevyBreeze]

The probability of falling while skiing is 0.025, or 2.5%.

Multiplying the probability of a ski accident if the resort sells out by the probability of a ski accident if the resort sells out (0.25% or 10%) yields the probability of a ski accident.

We must use conditional probability to determine the likelihood of a ski accident. We start with the way that there's a 25% likelihood of the ski resort selling out, and a 10% likelihood of a ski mishap assuming it sells out. We can involve the equation for contingent likelihood:

P(A|B) = P(A and B) / P(B), where A represents the occurrence of the "ski accident" and B represents the "ski resort sells out"

P(ski mishap) = P(sells out) * P(accident | sells out) = 0.25 * 0.10 = 0.025 or 2.5%.

As a result, there is a 2.5% chance of an accident while skiing.

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The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.

In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.

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Answer:

rational

irrational

rational

Step-by-step explanation:

2 × 2 = 4 rational

2 × √2 = 2√2  irrational

√2 × √2 = √4 = 2 rational

Answer:

Can you please upload the diagram?

Answer: 2 cups of water to 8 cups of flour

Step-by-step explanation:

Answer:

2 cups of water to 8 cups of flour

Step-by-step explanation:

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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Answer:

\(5.72\)g of fiber is contained in the black beans.

Step-by-step explanation:

Given:

No.of. ounces\(=4.4\)

Each ounce contains \(1.3\)g of fiber

To calculate the fiber contained in the black beans

Total Fiber = No.of. ounces × Fiber contained in each ounce

\(=4.4\) × \(1.3\)

\(=5.72\)g

Therefore, fiber contained in the black beans is \(5.72\)g.

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Answer:

radius =3cm

volume of the sphere =4/3 πr^3

=4/3*22/7*3*3*3=88/7*3*3=88/7*9=792/7

=113.1cm^3

Answer:

D

Step-by-step explanation:

Answer:

288 in.

Step-by-step explanation:

when it comes to finding the volume of a box you just multiply the width, length and height and you will get the volume

6 in. x 12 in. x 4 in. = 288 in.

Answer:

1/12 as a fraction

Step-by-step explanation:

1/2 x 1/6 =1/12

Answer:

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

Step-by-step explanation:

Hamish and Harry work as plumbers. Harry earns a dollar more than 5/4 the amount Hamish earns per hour. The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour. How much does each of them earn per hour?

Hamish earnings per hour = x

Harry earnings = 1 + 5/4x

The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

Harry also earns = 7/5x - 2

Equate both Harry's earnings

1 + 5/4x = 7/5x - 2

Collect like terms

1 + 2 = 7/5x - 5/4x

3 = 28x-25x/20

3 = 3/20x

Divide both sides by 3/20

x = 3 ÷ 3/20

= 3 × 20/3

x = 20

Hamish earnings per hour = x

= $20

Substitute Harry's earnings into 7/5x - 2

= 7/5 × 20 - 2

= 28 - 2

= 26

Harry's earnings = $26

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

Answer:

A. The system could have no solution or infinitely many solutions.

Step-by-step explanation:

Parallel lines have the same slope, meaning that they cannot intersect. So, the system can either have no solution (no intersection), or infinite possible solutions (the same line).