The Garcia family started the day with 222 gallons of milk. They drank 111 quart of milk for breakfast and 3 pints for lunch. How many pints of milk did the Garcia family have left after lunch?

a) John withdraws $1,300.

b) The annual effective yield rate for John's six-year investment is 2.09%.

a) To find the amount that John withdraws, we need to calculate the future value of his deposits after six years.

For the first three years, the deposits gain interest at a force of interest of 0.06. So after three years, the balance becomes $500 * (1 + 0.06)^3 = $595.44.

After three years, the interest rate changes to an effective rate of discount of 8%. Using the formula for the future value of a single sum with a discount rate, we can calculate the balance after six years:

$595.44 * (1 - 0.08)^3 = $429.97.

Therefore, John withdraws $429.97.

b) The annual effective yield rate can be found by calculating the rate of return on John's initial deposit over six years.

Let's assume John's initial deposit is $D. After three years, it grows to $D * (1 + 0.06)^3 = $1.191D. After six years, it becomes $1.191D * (1 - 0.08)^3 = $0.924D.

To find the annual effective yield rate, we need to solve the equation:

$D * (1 + r)^6 = $0.924D,

where r is the annual effective yield rate.

Simplifying the equation:

(1 + r)^6 = 0.924,

Taking the sixth root of both sides:

1 + r = 0.924^(1/6),

r = 0.0209.

Therefore, the annual effective yield rate for John's six-year investment is 2.09%.

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Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

Answer:

path =2m

Step-by-step explanation:

Answer:

I believe the answer should be 2m

Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3

Answer:

7.9

Step-by-step explanation:

7.87400787401

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Answer:

2

Step-by-step explanation:

\(x + 17 = - 2x + 23 \\ \\ x + 2x = 23 - 17 \\ \\ 3x = 6 \\ \\ x = \frac{6}{3} \\ \\ x = 2\)

Answer:

x = 2

Step-by-step explanation:

First, we will move all the xs to one side and everything else to the other side.

x + 17 = -2x + 23

+2x       +2x

-17         -17

This gives us:

x + 2x = 23-17

Then we can just combine like terms:

3x = 6

And divide both sides by three:

x = 2

Answer:

\( \boxed{Values \: true \: of \: 'x' \: for \: equation \: {x}^{2} + 2x = 24 \: is \: -6 \: and \: 4} \)

Step-by-step explanation:

\( = > {x}^{2} + 2x = 24 \\ \\ = > {x}^{2} + 2x - 24 = 0 \\ \\ = > {x}^{2} + (6 - 4)x - 24 = 0 \\ \\ = > {x}^{2} + 6x - 4x - 24 = 0 \\ \\ = > x(x + 6) - 4(x + 6) = 0 \\ \\ = > (x + 6)(x - 4) = 0 \\ \\ = > x + 6 = 0 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: x - 4 = 0 \\ \\ = > x = - 6 \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: x = 4\)

Values true of 'x' for equation x² + 2x = 24 is -6 and 4

Answer:

1. 4hrs and 10mnts

2. 13 builders

3. 25 walls

4. 52 toy soldiers

Step-by-step explanation:

1. then, one man can do it in 16hrs and 40mnts, so, 4 men would take 4hrs and 10mnts

2. one builder can build 4 houses in a year, so 13 builders are needed to build 52 houses

3. they can do it at a rate of 2 walls per person for 3 days, so 10 ppl can make 25 walls in 3.75 days

4. 4 toys per person for 2 weeks, so 7 makers can make 52 toys for 3 weeks

Answer:

Picture #1

Triangles ΔJKL and ΔXYZ have:

∠X is corresponding to ∠J, since they are different (90° vs 38°), the triangles can't be similar

Picture #2

Perimeter is the sum of the sides each has same ratio.

The ratio of the perimeters will be same as the ratio of each corresponding pair.

Correct choice is C. 3:5

Picture #3

Use ratios of corresponding sides:

Correct choice is B

Answer:

b. 22

Step-by-step explanation:

1.6 x 14 = 22.4

22.4 rounded is 22

a. The number of people that enjoyed only skiing is 129

b. The number of people that enjoyed snow boarding and ice skating only is 13

c. The number of people that enjoyed snow board or ice skating is 221

d. The number of people that enjoyed none is 35

e. The number of people that enjoyed at least two is 62

sets is a collection of well-defined objects or elements.

The total number of visitors is 350

n(ski and snow board only) = 49-2 = 47

n( ski and skating) only= 2-2 = 0

n( snow board and skating) = 15-2 = 13

n( snow board only) = 154-(47+13+2) = 92

n( skating only) = 57-(13+2) = 32

a. The number of that that enjoyed skiing only = 178-(47+2) = 129

b. n( skating and snow board) only= 13

c. n ( ski or snow board) only = 129+92 = 221

d. the number of people that didn't enjoy any = 350-(129+47+92+13+32+2)

= 350-315 = 35

e. the number of people that enjoyed at least two = 13+2+47 = 62

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To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Answer:B

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

its a graph

Answer:

No

Step-by-step explanation:

It isn't a positive linear association nor a negative linear association. If you were to connect those lines, it would not be a linear function of any kind of association.

∂z/∂s = 3cos(t)/y, ∂z/∂t = 3s*cos(t)/y - sin(s)/x (using the chain rule to differentiate each term and substituting the given expressions for x and y)

To find ∂z/∂s and ∂z/∂t using the chain rule, we start by finding the partial derivatives of z with respect to x and y, and then apply the chain rule.

First, let's find ∂z/∂x and ∂z/∂y.

∂z/∂x = ∂/∂x [ln(5x^3y)]

= (1/5x^3y)  ∂/∂x [5x^3y]

= (1/5x^3y) 15x^2y

= 3/y

∂z/∂y = ∂/∂y [ln(5x^3y)]

= (1/5x^3y) ∂/∂y [5x^3y]

= (1/5x^3y)  5x^3

= 1/x

Now, using the chain rule, we can find ∂z/∂s and ∂z/∂t.

∂z/∂s = (∂z/∂x)  (∂x/∂s) + (∂z/∂y)  (∂y/∂s)

= (3/y)  (cos(t)) + (1/x)  (0)

= 3cos(t)/y

∂z/∂t = (∂z/∂x)  (∂x/∂t) + (∂z/∂y)  (∂y/∂t)

= (3/y) * (scos(t)) + (1/x)  (-sin(s))

= 3scos(t)/y - sin(s)/x

Therefore, ∂z/∂s = 3cos(t)/y and ∂z/∂t = 3s*cos(t)/y - sin(s)/x.

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Out of 50 people, 4 had a mispriced item.

For every 50 people, there are 4 mispriced item.

So in 600 people, which is 600/50 = 12 times more.

The number of mispriced item is 12 x 4 = 48.

ANSWER :

48 mispriced items

A poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. The dimensions that maximize the printed area are 500 cm x 23.52 cm.

The problem can be solved using the following concept:

Suppose we have a function f(x), then at the maximum/minimum point, it holds:

          f '(x) = 0

In the given problem, let:

q = length of the poster

p = width of the poster

Then,

p x q = 11760

or q = 11760/p

Let f(p,q) be the function of printed area, then:

f(p,q) = (p - 20)(q - 12)

f(p) = (p - 20) (11760/p - 12)

f(p) = -p² + 1000p - 980 x 20

At the maximum point:

f '(p) = 0

-2p + 1000 = 0

p = 500

Substitute p = 500 to get q:

q = 11760/p = 11760/500 = 23.52

Hence, the maximum printed area obtained if the dimensions are 500 cm x 23.52 cm

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The letter used to represent Pearson's product-moment correlation coefficient is "r".

This coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear correlation.

To calculate Pearson's correlation coefficient, we first standardize the variables by subtracting their means and dividing by their standard deviations. Then, we calculate the product of the standardized values for each pair of corresponding data points. The sum of these products is divided by the product of the standard deviations of the two variables. The resulting value is the correlation coefficient "r".

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Answer:

2

Step-by-step explanation:

√20 ÷ √5

√20/√5

=> √(20/5)

=> √4

=> 2

Answer:

.75t=180

Step-by-step explanation:

75% of the book = 180

We're looking for 100%. (t)

Let's write a proportion.

\(\frac{75}{100} =\frac{180}{x}\)

Cross-multiply.

75(x)=180(100)

75x=18000

x = 240

The equation is:

.75t=180

\( \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } \)

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is (\(x^2 - 3x - 10\)). We need to solve the equation:

\(x^2 - 3x - 10 = 0\)

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

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Rearrange first

9,13,37,39

median=13+37÷2

=25

median is 25

mean=9+13+37+39÷4

=98÷4=24.5

Mean=24.5

Answer:

3 (4 x + 6): Each side length is 4 x + 6 units.

Step-by-step explanation:

Perimeter of equilateral triangle = 12x + 18 = 3(4x + 6) units

Answer:

B

Step-by-step explanation:

An equilateral triangle has a perimeter of 12 x + 18 units. Which expression can be used to show the length of one side of the triangle?

  6 (2 x + 3): Each side length is 2 x + 3 units.

✔3 (4 x + 6): Each side length is 4 x + 6 units.

  2 (6 x + 9): Each side length is 6 x + 9 units.

  x (12 + 18): Each side length is 12 + 18 units.

Answer:

the variables are x and y

Step-by-step explanation:

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

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A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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