Part 1 The height of a ball​ (in feet) after t seconds is given by the quadratic function h = -16(t-5)^2 + 119.

A. When does the ball reach its maximum​ height?
B. What is the maximum​ height?

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

The utilization of two or more additional numbers that compares is known as the ratio.

The ratio of red to blue in purple 1 and purple 2 will be 1:2 and 1:3, respectively. The table is given below.

Purple #1              Purple #2

Red: Blue             Red: Blue

  1      2                    1      3

 2      4                   2      6

 3      6                   3      9

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

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The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

The term "operation" in mathematics refers to the process of computing a value utilising operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds.

The prime factorization of 12 is 2² x 3, and the prime factorization of 30 is 2 x 3 x 5.

To find the smallest common multiple, we need to take the highest power of each prime factor that appears in either factorization. Thus, the smallest common multiple of 12 and 30 are:

2² x 3 x 5 = 60

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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Answer:

300

Step-by-step explanation:

because you do it for 1 hundred years you multiply it by 100 and it would be 3x100=300

There is approximately a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 3 odd numbers among the possible outcomes of each die (1, 3, 5), so there are 3 x 3 = 9 ways to obtain an odd sum:

(1,2), (1,4), (1,6), .... (6,1), (6,3), (6,5)

There are 6 possible outcomes for rolling the same number on both dice, so there are 6 ways to obtain doubles:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

We counted (1,1), (3,3), and (5,5) twice in the above two categories, so we need to subtract 2 from the total count.

Therefore, there are 9 + 6 - 2 = 13 ways to obtain an odd sum or doubles.

Therefore, the probability of rolling an odd sum or doubles is:

P(odd sum or doubles) = 13/36

Thus, there is about a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

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The answer of the given question based on to determine that the quadrilateral must be a parallelogram the answer is given below.

A parallelogram is  type of quadrilateral ( polygon with four sides) with two pairs of parallel sides. This means that the opposite sides of parallelogram are parallel and congruent.

Yes, we can determine that the given quadrilateral is a parallelogram based on the information given.

We are told that opposite sides of the quadrilateral are congruent (that is, AB is congruent to CD, and BC is congruent to DA), which is a property of parallelograms. We are also told that opposite angles of the quadrilateral are congruent (that is, angle A is congruent to angle C, and angle B is congruent to angle D), which is another property of parallelograms.

Therefore, based on these two pieces of information, we can conclude that the quadrilateral must be a parallelogram. This is because these properties are unique to parallelograms and do not apply to other types of quadrilaterals, such as rectangles, rhombuses, or trapezoids.

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A reasonable prediction for the number of times a dime will be drawn is approximately 90.

Probability is the measure of how likely it is that an event will happen. The event is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. Probability is used in many areas, such as mathematics, science, engineering, and finance. For example, in mathematics, probability is used to determine the likelihood of an event occurring or a certain outcome occurring.

When 2 dimes, 2 nickels, and 1 penny are placed into a bag, there are 5 total coins. Therefore, the probability of drawing a dime is 2/5. When a coin is drawn and replaced 175 times, the probability of drawing a dime will remain the same (2/5) and the expected value of drawing a dime is 175*2/5 = 90. Since this is a reasonable prediction, it is a valid solution.

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In   linear equation, you can get 4 cookies for $1.00 at the Math munch cafe.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

If you can get 6 cookies for $1.50, then the cost of each cookie is:

$1.50 ÷ 6 = $0.25

This means that for $1.00, you can get:

$1.00 ÷ $0.25 per cookie = 4 cookies

Therefore, you can get 4 cookies for $1.00 at the Math munch cafe.

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Answer:

onomatopoeia

Step-by-step explanation:

onomatopoeia are words that are sounds

Answer:

Onomatopoeia

Step-by-step explanation:

The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.

Household refers to a single dwelling unit occupied by a family or other group of people who share common living arrangements. This includes a home, apartment, condominium, or other dwelling. Households can be single-family, multi-family, or even a group of unrelated people. They are typically headed by one or more adults, and may include children, elderly family members, and other dependents.

The total number of households surveyed is 1000 and is represented by the circle outside the two others. The circle on the left represents the number of households with an Aggie fan and it is 670. The circle on the right represents the number of households with a Longhorn fan and it is 450. The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.

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In accordance with the provided assertion, (A) the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches (B) the longer leg is 4√3 cm and the hypotenuse is 8 cm.

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object.

For a 30°−60°−90° triangle, the ratios of the side lengths are:

Using these ratios, we can solve the problems:

Longer leg = x√3 = 9

x = 9/√3 = 3√3

Shorter leg = x = 3√3

Hypotenuse = 2x = 2(3√3) = 6√3

Therefore, the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches.

    2. If the shorter leg is 4 cm, we have:

Shorter leg = x = 4

Longer leg = x√3 = 4√3

Hypotenuse = 2x = 2(4) = 8

Therefore, the longer leg is 4√3 cm and the hypotenuse is 8 cm.

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From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Amount of coffee in A bag of ground coffee = 11 ounces

Number of bags = 250 bags

Number of bags which contain 10.9 ounces of coffee = 50

The percentage of bags which contain 10.9 ounces of coffee

= (50/250) × 100 = 20%

This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.

Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

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The possible value of angle M is 30.6°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle LMN.

Given,  m = 4.1 inches, I = 3.9 inches

∠L = 151°. We have to find ∠M.

Using law of sines,

l / sin L = m / sin M

3.9 / sin (151°) = 4.1 / sin (M)

sin (M) = [4.1 × sin (151°)] / 3.9

           = 0.5097

M = sin⁻¹ (0.5097) = 30.64° ≈ 30.6°

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The question is incomplete. The complete question is,

In triangle LMN, m = 4.1 inches, I = 3.9 inches and ∠L = 151°. Find all possible values of ∠M to the nearest 10th of a degree.

The radius of the frame is approximately 1.27 inches

First, we can start by using the formula for the circumference of a circle:

C = 2πr

Where

We know that 75% of the circumference is 6 inches, so we can set up the following equation:

0.75C = 6

Simplifying this equation by dividing both sides by 0.75, we get:

C = 8

Now we can use this value of the circumference and the formula for the circumference to solve for the radius:

C = 2πr

8 = 2πr

Dividing both sides by 2π, we get:

r = 8/(2π)

Using a calculator, we can evaluate this expression to get:

r ≈ 1.27

Therefore, the radius of the frame is approximately 1.27 inches.

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Answer:

p ≈ 11.3 , q ≈ 4.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{p}{12}[/tex] ( multiply both sides by 12 )

12 × cos20° = p , then

p ≈ 11.3 ( to 1 decimal place )

using the sine ratio in the right triangle

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{12}[/tex] ( multiply both sides by 12 )

12 × sin20° = q , then

q ≈ 4.1 ( to 1 decimal place )

You therefore paid $21.26 to travel to the beach.

One mile is 5,280 feet long. To determine how many steps this should require walking a mile, simply split 5,280 feet by the length of your typical stride. For instance, if your typical stride is 2 feet, walking a mile will need 2,640 steps.

a) We must divide the total amount of miles travelled by the quantity of gas consumed in order to compute mpg (miles per gallon). If 141 miles are covered by 3/8 of a tank, we may calculate the tank's total capacity as follows:

18 gallons = 8/8 tank (full tank)

So, 3/8 tank = (3/8) x 18 = 6.75 gallons

Therefore, the mpg is:

mpg = distance traveled ÷ gas used

mpg = 141 miles ÷ 6.75 gallons

mpg = 20.89 miles per gallon (rounded to two decimal places)

b) The entire amount of gas consumed must be multiplied by the gallon price in order to get the cost of gas. Gas is expensive at:

Cost of gas = gas used x price per gallon

Cost of gas = 6.75 gallons x $3.15/gallon

Cost of gas = $21.26

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Answer:

Step-by-step explanation:

Using the remainder theorem we get:

[tex]f(-2)=-5[/tex],  [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]

So we get

[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]

                 [tex]-8p+8+4p-2q+r=-5[/tex]

                              [tex]-4p-2q+r=-13[/tex]  [tex](a)[/tex]

[tex]f(1)=(p-1)+p+q+r=4[/tex]

                       [tex]2p+q+r=5[/tex]               [tex](b)[/tex]

[tex]f(-1)=-(p-1)+p-q+r=0[/tex]

                                 [tex]-q+r=-1[/tex]    [tex](c)[/tex]

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from [tex](c)[/tex]  [tex]r=q-1[/tex]. Sub this into (a) and (b):

[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex]    [tex](d)[/tex]

      [tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex]              [tex](e)[/tex]

Sub (e) into (d) we get

[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]

Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]

Sub  [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]

SOLUTION: [tex]p=3,q=0,r=-1[/tex]    

So [tex]f(x)=2x^3+3x^2-1[/tex]

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

[tex]f(x)=(x+1)(2x^2+x-1)[/tex]

[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]

So, the codomain of the function is the set of all real numbers: codomain = R.

In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.

Here,

The codomain is the set of all possible output values of a function.

For the given function, f(x) = x² - 4, we can see that the output values are obtained by squaring the input value, subtracting 4, and therefore can be any real number.

To find the codomain of the function f(x) = x² - 4, we need to determine the range of the function, which is the set of all possible output values.

Let y = f(x) = x² - 4.

To find the range, we need to solve for y:

y = x² - 4

y + 4 = x²

Taking the square root of both sides, we get:

x = ±√(y + 4)

Therefore, the range of the function is the set of all real numbers greater than or equal to -4, since y + 4 must be non-negative for real values of y:

range = {y | y + 4 ≥ 0} = {y | y ≥ -4}

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Answer:

The guitar Francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive?

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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So, by resolving the given, we obtain the : As a result, subtracting As a percentage result, subtracting $332.03 from $1,000 results in a loss of 66.797%.$332.03 from $1,000 results in a loss of 66.797%.

A ratio or value stated as a percentage of 100 is referred to as a percentage in mathematics. The abbreviations "pct.," "pct," and "pc" are also sporadically used. Nonetheless, the percentage symbol "%" is frequently used to denote it. The percentage amount is dimensionally empty. When the denominator is 100, percentages are essentially fractions. To show that a number is a percentage, a percent symbol (%) should be used next to it. For instance, you receive a 75% grade if you correctly answer 75 out of 25 questions (75/100) on a test. For percentage calculations, multiply the outcome by 100 after dividing the amount by the total. The percentage is calculated by multiplying (value/total) by 100%.  

You may use the following calculation to get the percentage change between $1,000 and $332.03:

(|new value - old value| / old value|) x 100% represents the percentage change.

In this instance, the new value is $332.03 while the previous value was $1,000.

percentage change = (|332.03 - 1000| / 1000| x 100% = f 66.797%.

As a result, subtracting $332.03 from $1,000 results in a loss of 66.797%.

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The growth percentage for the given function is 92.2%.

What is the percentage?

A number can be represented as a fraction of 100 using a percentage. "%" is used to represent it.

For instance, when we state that 20% of a class is made up of guys, we mean that 20 of the class's 100 pupils are male. In other words, there are 20 out of 100 boys in the class, or 0.2.

We can multiply by 100 to change a fraction or decimal into a percentage. For instance, we can multiply the fraction 3/5 by 100 to achieve the following percentage conversion:

3/5 × 100% = 60%

Now,

The given function is [tex]y = 990^{(1.922)}[/tex]

We can compare this to the standard form of an exponential function y = abˣ, where "a" represents the initial value or starting point, "b" represents the growth or decay factor, and "x" represents the time or number of periods.

In this case, we have:

a = 990 (the initial value)

b = 1.922 (the growth factor)

To find the growth percentage, we can subtract the initial value from the final value and divide by the initial value:

(1.922 - 1) / 1 × 100% = 92.2%

Therefore, the growth percentage for the given function is 92.2%.

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a) The altitude of the plane is approximately 8.4 kilometers.

b) The pilot has approximately 11.2 minutes before he has to land.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides (the legs).

In mathematical terms, if we have a right triangle with legs a and b and hypotenuse c, the Pythagorean theorem can be written as:

[tex]a^2 + b^2 = c^2[/tex]

This theorem is named after the ancient Greek mathematician Pythagoras, who was the first to prove it. The Pythagorean theorem has numerous applications in geometry, trigonometry, physics, and engineering, among other fields.

The Pythagorean theorem can also be used to determine whether a triangle is a right triangle or not. If the lengths of the three sides of a triangle satisfy the equation [tex]a^2 + b^2 = c^2,[/tex] then the triangle is a right triangle with sides a and b and hypotenuse c.

a) In the given image, we can see that the slant range, ground range, and altitude form a right triangle. We can use the Pythagorean theorem to find the altitude of the plane.

Pythagorean theorem: In a right triangle, the square of the hypotenuse (slant range in this case) is equal to the sum of the squares of the other two sides (ground range and altitude in this case).

Therefore, we can write:

[tex]Slant range^2 = Ground range^2 + Altitude^2[/tex]

Substituting the given values, we get:

[tex]14.5^2 = 10.15^2 + Altitude^2[/tex]

Simplifying and solving for altitude, we get:

Altitude ≈ 8.4 km (rounded to the nearest meter)

Therefore, the altitude of the plane is approximately 8.4 kilometers.

b) If the plane descends suddenly at a rate of 750 meters per minute, we can use the altitude of the plane (calculated in part a)) to find the time the pilot has before landing.

Time = Altitude/Descent rate

Substituting the values, we get:

Time = [tex]\frac{8.4 }{0.75}[/tex] ≈ 11.2 minutes

Therefore, the pilot has approximately 11.2 minutes before he has to land.

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Answer: 37.21 dollars

Step-by-step explanation: 25% of 45 is 11.25 so after the sale it is 33.75 then you multiply by .1025 which gives you 3.46 rounded then add it
33.75+3.46= 37.21

The cost of 6 sets of cards is $105.95

Each set has 100 cards, then in 6 sets there are 6*100 = 600 cards.

We know that the first 200 cards costs $49.95, and from then, the cost per set is $14.

So we have a piecewise function which can be written as:

y = $49.95   if x ≤ 200

y = $49.95 + $14*(x - 200) if x > 200.

Then we have 200 cards and 4 sets, then the total cost will be:

$49.95 + 4*$14 = $105.95

That is the cost of the 6 sets.

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The slope of the line passing through (- 1, 3) and (1, - 2) is - 5/2.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the steeper its graph or the rate of change is large.

From the given line we can identify two coordinate points,

(- 1, 3) and (1, - 2).

Now, We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

slope(m) = (- 2 - 3)/(1 + 1).

slope(m) = - 5/2.

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Answer:

We can use the formula for the future value of an annuity to solve this problem. An annuity is a series of equal payments made at regular intervals. In this case, we are making a single lump-sum deposit now to grow into the desired future value.

The formula for the future value of a lump-sum deposit is:

FV = PV x (1 + r/n)^(n*t)

Where:

FV = future value

PV = present value (the amount to be deposited now)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, we want to find the present value (PV) required to grow into the future value (FV) of $800,000 in 25 years with an annual interest rate of 5% compounded monthly, so:

FV = $800,000

r = 5% = 0.05 (annual interest rate)

n = 12 (monthly compounding)

t = 25 (number of years)

Substituting these values into the formula, we get:

$800,000 = PV x (1 + 0.05/12)^(12*25)

Simplifying the exponent on the right-hand side, we get:

$800,000 = PV x (1.004167)^300

Dividing both sides by (1.004167)^300, we get:

PV = $800,000 / (1.004167)^300

Using a calculator or spreadsheet, we can evaluate this expression to find:

PV ≈ $267,227.92

Therefore, you would need to deposit approximately $267,227.92 now into the account to reach your retirement goal of $800,000 in 25 years with an annual interest rate of 5% compounded monthly.

The speed at which the water level is rising when the water is 20 cm deep is 0.04285 m/min

Using differentiation:

dV/dt = 0.3

find dh/dt

the width of the water level is dependent on the height

at height 0, width of 20

height 60, width of 80

when height increases by 1, width increases by 1

dh/dt = dw/dt

V = 0.5*(0.2 + (0.2+h))*h*10

V = 5*(0.4 + h)*h

V = 5h^2 + 2h

dV/dt = 5*2h(dh/dt) + 2(dh/dt)

when h = 0.5

0.1 = 5*2*0.5*(dh/dt) + 2(dh/dt)

0.1 = 5(dh/dt) + 2(dh/dt)

7(dh/dt) = 0.3

dh/dt = 0.04285 m/min

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The probability both will be peanut butter sandwiches will be 1/6.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true.

here, we have,

The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability that John picks a peanut butter sandwich from the first bag is 6/12 = 1/2.

The probability that John picks a peanut butter sandwich from the second bag is 4/12 = 1/3.

The probability that John picks a peanut butter sandwich from both bags is (1/2) * (1/3) = 1/6.

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Sergio's new balance is $87

Sergio's savings showed a previous balance of $234.95 and interest of $1.06

The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09

The new balance can be calculated by adding the previous balance, interest, deposits in the statement and then subtract the sum total from the withdrawal amount

234.95 + 1.06 + 123.42 + 50.66 - 323.09

= 410.09 - 323.09

= 87

Hence Sergio's new balance after adding the deposits, previous balance then subtracting from the withdrawal is $87

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