A 4-pound box of blackberries costs $16.64. What is the price per ounce?

The numbers of new CDs is 30 and the old CDs is 21.

To solve this problem, we have to write a system of equations in which we would know the numbers of each types of CD she bought.

This is used to solve a series or complex of word problems in which we can represent in a mathematical statements;

The equations can be represented as

\(n + u = 51 ...equation(i)\\15n + 6u = 576 ... equation(ii)\)

Let's take equation (i)

Making n the subject of formula

\(n + u = 51\\n = 51 - u...equation(iii)\)

we can put equation (iii) into equation (ii)

\(15n + 6u =576\\n = 51 - u\\15(51 - u) + 6u = 576\\765-15u + 6u = 576\\collect like terms\\765-576=15u - 6u\\189=9u\\9u/9 = 189/9\\u = 21\)

Let's put the value of u into equation (i)

\(n + u = 51\\u = 21\\n + 21 = 51\\n = 51 - 21\\n = 30\)

From the calculations above, the numbers of new CDs is 30 and the old CDs is 21.

Learn more on system of equations here;

https://brainly.com/question/13729904

The given order of integration is in the form of triple integrals, where the integration is performed first over the z-coordinate, then over the y-coordinate, and finally over the x-coordinate.

To obtain an equivalent integral in the given order of integration, we can use the substitution method and change the order of integration.

First, we integrate with respect to z from 0 to √(4-x^2), then we integrate with respect to y from -√(4-x^2) to √(4-x^2), and finally, we integrate with respect to x from 2 to 0. This can be expressed as:

∫2 0 ∫-√(4-x^2) √(4-x^2) ∫0 f(x,y,z) dz dy dx

We can then change the order of integration to obtain an equivalent integral in the form ∫ba∫g(z)f(z)∫k(x,z)h(x,z)f(x,y,z)dydxdz by integrating w.r.t. x first, then w.r.t. y, and finallyw.r.t. z.

This gives us:

∫0 √4-y^2 ∫-√(4-x^2) √(4-x^2) ∫0 f(x,y,z) dz dx dy

Using the limits of integration for each variable, we can rewrite this as:

∫0 2 ∫-√(4-y^2) √(4-y^2) ∫0 f(x,y,z) dz dy dx

Therefore, the equivalent integral in the given order of integration is ∫0 2 ∫-√(4-y^2) √(4-y^2) ∫0 f(x,y,z) dz dy dx.

To know more about equivalent integral, visit:

https://brainly.com/question/31744185

#SPJ11

Answer:

78

Step-by-step explanation:

because I know everything

Answer:

The area of a rectangle is 5/4

Step-by-step explanation:

a) The graph of the position function is a parabolic curve opening upward.

b) The velocity function is v(t) = 8t - 5. The object is stationary at t = 0.625, moving to the right for t > 0.625, and moving to the left for t < 0.625.

c) At t = 1, the velocity of the object is 3 ft/s and the acceleration is 8 ft/s².

d) The acceleration of the object when its velocity is zero is 8 ft/s².

e) The speed is increasing for t > 0.625.

a) To graph the position function, we plot the values of s as a function of t within the given range.

The position function is given by: \(s = f(t) = 4t^2 - 5t\)

Let's calculate the position values for t = 0 to t = 6:

\(For\ t = 0: s = 4(0)^2 - 5(0) = 0\\For\ t = 1: s = 4(1)^2 - 5(1) = -1\\For\ t = 2: s = 4(2)^2 - 5(2) = 8\\For\ t = 3: s = 4(3)^2 - 5(3) = 21\\For\ t = 4: s = 4(4)^2 - 5(4) = 36\\For\ t = 5: s = 4(5)^2 - 5(5) = 45\\For\ t = 6: s = 4(6)^2 - 5(6) = 48\)

Now we can plot these points on a graph with t on the x-axis and s on the y-axis.

b) The velocity function v(t) can be obtained by taking the derivative of the position function f(t) with respect to t:

\(v(t) = f'(t) = d/dt (4t^2 - 5t)\)

      = 8t - 5

To find when the object is stationary, moving to the right, or moving to the left, we need to determine the signs of the velocity function.

If v(t) > 0, the object is moving to the right.

If v(t) < 0, the object is moving to the left.

If v(t) = 0, the object is stationary.

Let's find the critical point by setting v(t) = 0:

8t - 5 = 0

8t = 5

t = 5/8 = 0.625

Now we can determine the behavior of the object for different values of t:

For t < 0.625, the object is moving to the left.

For t > 0.625, the object is moving to the right.

At t = 0.625, the object is stationary.

We can now graph the velocity function by plotting the values of v(t) for t = 0 to t = 6.

c) To find the velocity and acceleration of the object at t = 1, we substitute t = 1 into the velocity function and differentiate the velocity function with respect to t to obtain the acceleration function.

At t = 1:

v(t) = 8t - 5

v(1) = 8(1) - 5 = 3 (velocity at t = 1)

To find the acceleration, we differentiate the velocity function with respect to t:

a(t) = v'(t) = d/dt (8t - 5)

      = 8 (acceleration at t = 1)

d) To determine the acceleration of the object when its velocity is zero, we need to find the values of t where v(t) = 0. We can do this by setting the velocity function v(t) = 0 and solving for t:

8t - 5 = 0

8t = 5

t = 5/8 = 0.625

At t = 0.625, the object has zero velocity. To find the acceleration at this point, we substitute t = 0.625 into the acceleration function:

a(t) = 8 (acceleration at t = 0.625)

e) The speed of the object can be determined using the absolute value of the velocity function:

speed = |v(t)| = |8t - 5|

To determine the intervals where the speed is increasing, we need to find where the derivative of the speed function is positive:

d/dt |8t - 5| > 0

The speed will be increasing when 8t - 5 > 0. Solving this inequality, we find:

8t - 5 > 0

8t > 5

t > 5/8 = 0.625

Therefore, the speed is increasing for t > 0.625.

To know more about parabolic curve, refer here:

https://brainly.com/question/33156499

#SPJ4

Answer:

b=(3a/(2h)), x=(y-b)/m

Step-by-step explanation:

Simply isolate b ;

a=2/3bh, Divid both sides by 2/3 and h

a/(2/3h)=b, simplify

b=(3a/(2h))

Simply isolate x;

y=mx+b; subtract b from both sides and divide by m

y-b=mx

(y-b)/m=x

The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

We have a polynomial function:

\(\rm f(x) = x^{3}+2x^{2}-5x-6\)

The function is a cubic function and the graph of the cubic function will be a curve.

As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.

Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

Answer:

1/6

Step-by-step explanation:

questions which include 'of 'usually means "×" (multiplication sign) so when u multiply them it gives 1/6

The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

To know more about quantitative discrete refer here:

https://brainly.com/question/32236127#

#SPJ11

The final solution of the given problem is X = 2.82, Y = 1.04 for an Optimal solution Value of -16.93.

Given the optimization problem in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 8, we have to find the minimum solution to the given problem.

Solution To find the solution to the given optimization problem, we need to use the Lagrange multiplier method. Using this method, we have the following system of equations: 2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 8Solving the above equations, we get the following solutions:x = 3, y = 1, λ = 6

The optimal solution is X = 3, Y = 1, for an optimal solution value of -17. If the right-hand side of the constraint is increased from 8 to 9, the objective function would change by -2.29. (Decrease by 2.29)Now, we have to resolve the problem with a new right-hand side of 9.

The new optimization problem will be in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 9

Using the same method as above, we have the following system of equations:2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 9Solving the above equations, we get the following solutions:x = 2.82, y = 1.04, λ = 6.07

The objective function value is -16.93 so the actual increase/decrease is only -0.07 rather than -2.29. Hence, the actual change is very different from the estimated change.

Therefore, the final solution of the given problem is X = 2.82, Y = 1.04 for an optimal solution value of -16.93.

For more questions on Value  .

https://brainly.com/question/843074

#SPJ8

The probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10.

To find the probability that both digits in a New York State daily lottery game are different, we need to first calculate the total number of possible outcomes. Since there are 10 digits (0-9) that can be selected for each of the two digits in the sequence, there are a total of 10 x 10 = 100 possible outcomes.

Now, we need to determine the number of outcomes where both digits are different. There are 10 possible choices for the first digit and only 9 possible choices for the second digit, since we cannot choose the same digit as the first. Therefore, there are a total of 10 x 9 = 90 outcomes where both digits are different.

The probability of both digits being different is equal to the number of outcomes where both digits are different divided by the total number of possible outcomes. Thus, the probability is 90/100, which simplifies to 9/10, or 0.9.

In summary, the probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10. This means that there is a high likelihood that both digits selected will be different.

To know more about probability, refer to the link below:

https://brainly.com/question/13941450#

#SPJ11

Answer:

hello brother or sister can you please send a picture of the graph in provided but if not there are no specific calculations on reflection so you have to be smart on it and try imagining it or have your own scratch

Answer:

x=4

Step-by-step explanation:

3x+5=17 is the equation you need to setup as all square sides are equalivent. Simplify the equation getting 3x=12, Divide all terms by 3 and you get x=4.

Answer: x = 4

Step-by-step explanation:

Answer:

144.5 cm²

Step-by-step explanation:

length x breathe + 1/2 base x height

9*13 + 1/2 11(5)

117 + 55/2

144.5

Answer:

144.5cm²

Step-by-step explanation:

Think of this as 2 different shapes, the triangle and the rectangle. Adding these 2 areas together gives you the total area.

A rectangle's area is given by a=lw.

By substituting in the values, you get a=13*9. This can be solved to a=117cm² for the rectangle.

A triangle's area is given by a=\(\frac{bh}{2}\).

By substituting in the values, you get a=\(\frac{5*11}{2}\) or \(\frac{55}{2}\), which can be solved to a=27.5cm² for the triangle.

Adding the 2 together gives the total area.

a=117+27.5, which gives 144.5cm².

**This content involves area, which you may want to look at. If you are required to do this without a calculator, consider revising long multiplication and division. I'm always happy to help!

Answer:

STEP

1

:

Equation at the end of step 1

4x • (2x - 5) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

The solutions of the equation f(x) = g(x) include the following: B. -3, 0, 2, -4.

In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in both Quadrant II and IV and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-3, 0) and (2, -4).

Read more on a graph here: brainly.com/question/4546414

#SPJ1

The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

Learn more about unsubsidized loan here:

https://brainly.com/question/30280583

#SPJ12

The hypothesis test to be used to test the relationship between x and y at 5% significance level. Slope indicates price-demand relationship.

To test the connection between the quantity of blaze drives sold each day (x) and their costs (y), we can direct a speculation test. The invalid speculation is that there is no critical connection between the two factors, while the elective theory is that there is a huge connection between them.

Expecting a direct relationship, we can play out a basic straight relapse examination to gauge the slant of the line, which addresses the adjustment of the quantity of blaze drives sold each day for each unit change in cost. A positive slant shows that the higher the value, the more blaze drives sold each day, while a negative slant demonstrates the inverse.

To decide if the slant is fundamentally unique in relation to nothing, we can compute the t-measurement and contrast it with the basic t-esteem at the 5% degree of importance. Assuming that the t-measurement is more noteworthy than the basic t-esteem, we can dismiss the invalid speculation and infer that there is a huge connection between the two factors.

As far as deciphering the slant of the line, a positive slant proposes that the interest for streak drives increments as their cost increments, which suggests that clients will pay something else for streak drives when they see a higher worth or quality. In any case, it is essential to take note of that the connection among cost and request may not be straight or might be impacted by different elements, for example, rivalry, market patterns, and shopper inclinations.

To learn more about slope, refer:

https://brainly.com/question/30550290

#SPJ4

Answer:

4/9 of the students chose summer.

Step-by-step explanation:

Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.

Answer:

43.2

Step-by-step explanation:

40/100 * 108

4/100*108

43.2

We can sum up the results of all three cases to get the total number of strings with exactly 4 occurrences of a or 4 occurrences of b or 4 occurrences of c. Total number of strings = C(12, 4) * 2^8 + C(12, 4) * 2^8 + C(12, 4) * 2^8.

To find the number of strings of length 12 over the alphabet {a, b, c} that have exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c, we can use combinatorics.

First, let's consider the case of a string length of 12.

We have three possibilities: exactly 4 occurrences of a, exactly 4 occurrences of b, or exactly 4 occurrences of c. We will calculate each case separately and then sum up the results.

Case 1: Exactly 4 occurrences of a.

We have 12 positions in the string and we need to choose 4 of them to place the a's. The remaining 8 positions can be filled with b's or c's, giving us 2 options for each position. Therefore, the number of strings with exactly 4 occurrences of a is C(12, 4) * 2^8.

Case 2: Exactly 4 occurrences of b.

Similar to Case 1, we have 12 positions and we need to choose 4 of them to place the b's. The remaining 8 positions can be filled with a's or c's, giving us 2 options for each position. So, the number of strings with exactly 4 occurrences of b is C(12, 4) * 2^8.

Case 3: Exactly 4 occurrences of c.

Again, we have 12 positions and we need to choose 4 of them to place the c's. The remaining 8 positions can be filled with a's or b's, giving us 2 options for each position. Hence, the number of strings with exactly 4 occurrences of c is C(12, 4) * 2^8.

If the length of the string is 17, the approach will remain the same. We will calculate the number of strings with exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c using the formula mentioned above. The only difference will be in the length of the string and the number of positions to be chosen for each case. We will have C(17, 4) instead of C(12, 4), and the remaining positions will be filled with the remaining characters from the alphabet.

Learn more about combinatorics at: brainly.com/question/32015929

#SPJ11

Answer: 4.4 per minute?

Step-by-step explanation:

dividing 53.5 by 12?

Answer:

P=(a+b)*2

P=(2x+8+5x-2)*2=(7x+6)*2=14x+12

Step-by-step explanation:

perimeter is the distance round. Add all the algebras

2x+8+5x-2+2x+8+5x-2

{combine the like terms}

P= 14x+12

Given that:

- Your sister will give you $15 for heads and $25 for tails.

- Your mother will give you $6 times the number that the spinner lands on.

you must calculate the Expected Value of each game:

- Game 1:

When you through the coin, the probability of getting a head is 50% and the probability of getting a tail is 50%.

You need to use the following formula for calculating the Expected Value:

Where "x" is the random variable, and p(x) is the probability obtained.

Therefore, for Game is:

- Game 2:

When you spin the spinner with six different outcomes. Therefore:

Then:

Hence, the answer is:

- Expected Value of your sister's game:

- Expected Value of your mother's game:

- You should take your mother's offer, because it has the greatest Expected Value.

My friend consumed 8 donuts in one sitting. 8 donuts is a lower bound on how many donuts he is physically capable of eating in one sitting option A.

An element of K that is bigger than or equal to each member of S is referred to as an upper limit or majorant of a subset S of some preordered set (K, ) in mathematics, notably in order theory. In addition, each element of K that is smaller than or equal to each element of S is characterised as a lower limit or minorant of S.

A set that has an upper (or lower) bound is referred to as being majorized (or minorized), bounded from above, or minorized by that bound. In the mathematical literature, sets that have upper (or lower, respectively) limits are referred to as being bounded above (or below).

Friend consumed 8 doughnuts. So it is

lower bound on how can eat in a sitting.

Many donuts he lower bound is the lowest quantity in a set, as in our.

example, we definitely know he can eat 8 of them. We don't know how many more can be eat (upper bound) or is it exact amount be can eat.

Hence option (a) is correct.

Learn more about Lower bound:

https://brainly.com/question/28845797

#SPJ4

The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is approximately 82.38%.

Assuming the sample of 30 Americans is representative of the population, we can calculate the sample proportion as the number of individuals in the sample who agree divided by the total sample size. Let's assume that the sample proportion is p'.

To calculate the probability of the proportion exceeding 35%, we need to find the z-score of the value 0.35 using the formula:

z = (p' - p) / √[p * (1 - p) / n]

where p is the population proportion (which we don't know), and n is the sample size (30 in this case). We can use p' as an estimate of p.

Once we find the z-score, we can use a standard normal distribution table or a calculator to find the probability that the z-score is greater than the value we calculated. This probability is the probability that the proportion of Americans who agree that climate change is an immediate threat to humanity exceeds 35%.

For example, if p' = 0.4, then the z-score is:

z = (0.4 - 0.35) /√ [0.35 * (1 - 0.35) / 30] = 1.03

Using a standard normal distribution table, we can find that the probability of a z-score being greater than 1.03 is approximately 0.8238, or about 82.38%.

To learn more about probability click on,

brainly.com/question/29035617

#SPJ4

Answer:

(-5,-4)

Step-by-step explanation:

i think this is correct because i tried to solve in paper.