Marlene decided to buy 2 bags of apples weighing 3 1/4 pounds each, instead of 3 bags weighing 2 2/5 pounds each. Did she end up with more apples or fewer apples by buying the bigger bags?

To find the total weight of 2 bags of apples weighing 3 and 1/4 pounds, multiply.

Answer Choices: 5 1/4, 5 1/2, 6 1/4, 6 1/2.

To find the total weight of 3 bags weighing 2 and 2/5 pounds, multiply.

Answer Choices: 5 2/5, 6 2/5, 7 1/5, 7 2/5.

She ended up purchasing [fewer, more, the same amount of,] apples by buying the bigger bags.

SHORT QUESTION (answer if you are too lazy to rad all of this lol like me): Multiply 3 and 1/4 times 2, Multiply 2 and 2/5 times 3. Thanks <3

I will mark brainliest if the answer is correct :) But you have to ask for brainliest too! Thanks so much, I really need a quick answer :)

The simplified form of the expression is 1.55x - 2.16.

To simplify the expression 0.2[5x + (-0.3)] + (-0.5)(-1.1x + 4.2), we can distribute the coefficients and simplify the terms.

First, distribute 0.2 to the terms inside the brackets: 0.2 * 5x + 0.2 * (-0.3) = x - 0.06.

Next, distribute -0.5 to the terms inside the second brackets: -0.5 * (-1.1x) + (-0.5) * 4.2 = 0.55x - 2.1.

Now, we can combine the simplified terms: (x - 0.06) + (0.55x - 2.1) = 1.55x - 2.16.

Thus, the simplified expression is 1.55x - 2.16.

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Answer:

The answer is $49.95

Step-by-step explanation:

I Took the quiz :D i hope this helps <3

Answer:

Commutative Property of Addition

Answer:

d) f(n) = 4 . 3^(n-1)

______________

Answer:

40 units^2

Step-by-step explanation:

The area of the triangle is

A = 1/2 bh

A = 1/2 ( 8 * 10)

   = 1/2 (80)

  = 40 units^2

Step-by-step explanation:

a=1/2*b*h

a=1/2*8*10

a=40

Answer:

The total distance is 129

Step-by-step explanation:

In order to answer this question you will need to find 2 distances and then add them to each other.

Begin at -29.  How far will you have to move to the right 29 in order to get to 0?

Now how far will you have to more to get from 0 to 100?

Draw an open number line to help you.

_____________________________________________________

-29                                           0                                                   100

Your first distance is 29.  Your second distance is 100.

The total distance is 129.

Answer:

Slope = 2

Y - intercept = (0, -12)

Step-by-step explanation:

I did the quiz!

The average rate of change of the function F(x) shown in the graph over the interval -4 ≤ x ≤ -2 is 4

An equation is an expression showing the relationship between two or more numbers and variables.

The average rate of change of a function F(x) over the interval a < x < b is given by:

Average rate of change = [F(b) - F(a)] / [b - a]

From the graph, over the interval -4 ≤ x ≤ -2.

F(-4) = 0; F(-2) = 8

Hence:

Average rate of change = [F(-2) - F(-4)] / [-2 - (-4)]

Average rate of change = [8 - 0] / [-2 + 4] = 8/2 = 4

The average rate of change is 4

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Answer:

B. 3/4

Step-by-step explanation:

64 x 3/4=48

48 x 3/4=36

and so on...

Answer:

B 3/4

Step-by-step explanation:

The nth term of a geometric progression is given by

an = a1 . rn - 1

Where;

an = the nth term

a1 = the first term

r = common ratio

n = the number of terms in the series

Common ratio, r = the ratio of the second term to the first term

= a2 : a1

Given from the series,

a2 = 48

a1 = 64

Common ratio, r = 48 : 64

= 48/64 = 3/4

The utilization rate is 83.33

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times,

Then, the utilization rate is 83.33.

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Answer:

Step-by-step explanation:

x + 4 + 2x - 6 + 10 > 50

4 - 6 + 10 = 8

x + 2x = 3x

3x + 8 > 50

Subtract 8 from both sides

3x > 50 - 8

3x > 42

Divide 3 from both sides

42/3 = 14

x > 14

Step-by-step explanation:

x^2 -y^2 = 25

x/y = 3/2    or   x = 3/2 y   <=====sub into first equation

(3/2 y)^2 - y^2 = 25

9/4 y^2 - y^2 = 25

5/4 y^2 = 25

y^2 = 25 (4/5) = 20

y = sqrt (20) = 2 sqrt 5

                then x = 3/2 y =  3 sqrt5

To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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Answer:

Step-by-step explanation

5(4m+1)-2m=-13

20m+5-2m=-13

20m-2m=-13-5

18m=-18

m=-1

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{5(4m+1)-2m=-13 } \end{gathered}$}\)

Apply the multiplicative law of distribution.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{20m+5-2m=-13 } \end{gathered}$}\)

Combine as terms.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{18m+5=-13 } \end{gathered}$}\)

Rearrange the unknown terms to the left side of the equation.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-13-5 } \end{gathered}$}\)

Calculate the sum or difference.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-18 } \end{gathered}$}\)

Divide both sides of the equation by the coefficient of the variable.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-\frac{18}{18} } \end{gathered}$}\)

Solve for the common factor.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-1 \iff } \end{gathered}$}\boxed{\boxed{\bf{Answer}}}\)

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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The maximization problem described is not a concave program because the objective function is not concave.

To determine whether the maximization problem is a concave program, we need to analyze the objective function and the constraint set.

The objective function is given as xy^4. Let's examine its second-order partial derivatives:

∂^2/∂x^2 (xy^4) = 0

∂^2/∂y^2 (xy^4) = 12x^2y^2

∂^2/∂x∂y (xy^4) = 4y^3

In order for the objective function to be concave, it must satisfy the condition that the Hessian matrix (the matrix composed of the second-order partial derivatives) is negative semidefinite. That is, the following inequality must hold for any values of x and y:

| 0    4y^3 |

| 4y^3 12x^2y^2 | ≤ 0

However, this inequality does not hold because there exist values of x and y for which the Hessian matrix is positive definite. For example, consider x = 1 and y = 1. In this case, the Hessian matrix becomes:

| 0   4 |

| 4   12 |

The determinant of this matrix is 48, which is greater than zero. Therefore, the Hessian matrix is positive definite, indicating that the objective function is not concave.

Regarding the constraint set, xe^y ≤ 3e^2, c ≥ y, x ≥ 0, and y ≥ 0, it is important to note that the constraint set is a combination of linear and exponential functions, as well as inequalities. Since concavity refers to the shape of the objective function, the constraint set does not affect the concavity of the program.

In conclusion, the maximization problem described is not a concave program because the objective function is not concave.

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The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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The length of the segment BE is 2 units.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Given:

Quadrilateral ABCD is a rectangle.

BE=3x−7 and AC=8x−20.

E is the intersection point of the diagonals.

So,

AC/2 = BE

(8x−20)/2 = 3x−7

4x - 10 = 3x - 7

x = 3

So, BE = 2

Therefore, BE = 2 units.

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To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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whilst plotting the calibration curve, various concentrations and respective absorbance is at the x-axis and the y-axis, respectively

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

calibrating curve:

A calibration curve, additionally called a well-known curve, is a fashionable technique for figuring out the awareness of a substance in an unknown pattern via way of means of evaluating the unknown to a fixed of well-known samples of recognized awareness.

A calibration curve is a linear graphical representation of standard solutions of varying concertation on the X-axis and their respective absorbance on the Y-axis.

Therefore, when plotting the calibration curve, varying concentrations and   respective absorbance is on the x-axis and the y-axis, respectively

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Answer:

not a complete question..

Step-by-step explanation:

Answer:

I think (c) is the correct answer.

Step-by-step explanation:

The diagonals bisect each other.

Answer: The diagonals are congruent

Step-by-step explanation: (if this is wrong I am sorry) There are Different Types of Quadrilaterals

Trapezium.

Parallelogram.

Rectangle.

Rhombus.

Square.

Kite.

If this is wrong I am very sorry

Answer:

E would be 6 spaces or the middle of points C and D.

Step-by-step explanation:

Please see picture.

The required simple interest of 10% of four year on principle amount is $857.

Simple interest depends on the chief measure of a credit or the first store in quite a while account. Straightforward interest doesn't build, and that implies a loan boss will just compensation interest on the chief sum and a borrower couldn't have ever to pay more interest on the recently gathered interest.

We have,

Amount of four year = $1200

simple interest = 10%

Let loaned amount is x

Then,

interest of four year =×4 x×10/100 = 4x/10

According,

x + 4x/10 = $1200

14x/10 = $1200

x = $12000/14

X = $857 (appox)

Thus, the required loaned amount is $857.

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Answer:

b

Step-by-step explanation:

you have to add the 3 numbers together to get 170

The best way to examine an association claim between a categorical variable and a quantitative variable is a scatterplot.

A scatterplot is a graph format that displays individual data points as dots on a Cartesian plane. It is the most suitable choice for examining the association claim between a categorical variable and a quantitative variable.

A scatterplot allows us to visually observe the relationship between the two variables by plotting the data points on the graph. The categorical variable is represented on one axis, while the quantitative variable is represented on the other axis. Each dot on the scatterplot represents an observation or data point.

By examining the distribution of the dots on the scatterplot, we can identify patterns, trends, and any potential association between the categorical and quantitative variables. This helps us understand the relationship, including its direction and strength.

On the other hand, a bar graph is typically used to compare categorical data by displaying the frequencies or percentages of different categories. It is not ideal for examining the association between a categorical variable and a quantitative variable.

Similarly, a pie chart is useful for displaying proportions or percentages of different categories within a whole but does not effectively represent the relationship between a categorical variable and a quantitative variable.

A line graph is commonly used to show trends over time or continuous data. While it can represent a quantitative variable, it may not be the best choice for examining the association claim with a categorical variable.

In summary, a scatterplot is the most appropriate graph format for examining the association claim between a categorical variable and a quantitative variable as it allows for the visual analysis of individual data points and their relationship.

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Answer:110.5inches2

Step-by-step explanation:

to find the area of a triangle use the formula 1/2(base times height) where in this case  base is 17 and height is 13. applying this formula= 1/2(17x13)=1/2(221)=110.5inches2