About how many cups or juice does this container hole? Hint: 1 cup=14.44in^3)

The value of dz/ dt using Chain Rule is (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex].

The chain rule states that the derivative D of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x).

In other words, the first factor on the right, Df(g(x)), indicates that the derivative of f(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x).

Given:

By chain rule we can write z= f(x, y) = f( x(t), y(t))

dz/ dt = df/ dx . dx/ dt + df/ dy. dy/dt

So, df/ dx = [tex]e^y[/tex]

df/dy =   [tex]e^y[/tex] + (x+ y)  [tex]e^y[/tex]

x(t)=5t, while y(t)=1-t², So,

So, dx/dt = 5

and, dy/dt = -2t

Now, dz/ dt = 5 . [tex]e^y[/tex] + -2t ( [tex]e^y[/tex] + (x+ y)  [tex]e^y[/tex])

                   = (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex]

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Answer:

Step-by-step explanation:

In response to the given question, we have that Therefore, on Tuesday, equation the yield was 2.92%, and on Monday, it was 2.96%.

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.

Divide the yearly dividend by the share price to determine the yield, then multiply the result by 100 to get the percentage:

Tuesday's yield is calculated as (Annual dividend / Share Price) times 100.

Tuesday's yield is calculated as ($2.10 / $72) times 100, which is 2.92%.

Tuesday's closing price minus Monday's closing price is the difference.

The price on Monday was $72 minus $0.95.

$71.05 was the final price on Monday.

We apply the same procedure as previously to determine the yield as of Monday's close:

Monday's yield is calculated as (annual dividend / share price) x 100.

Yield on Monday is equal to ($2.10 / $71.05) times 100, or 2.96%.

Therefore, on Tuesday, the yield was 2.92%, and on Monday, it was 2.96%.

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Answer:

AC = 14.9

BC = 10.5

Step-by-step explanation:

The triangle is a isosceles right triangle with ∠B = 90o, ∠A = ∠C = 45o.

Therefore AB = BC = 10.5

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, which is AC.

AC^2 = AB^2 + BC^2

AC^2 = 2AB^2

AC^2 = 2(10.5)^2

AC^2 = 220.5

AC = √220.5 = 14.85 or 14.9

Answer:

To write 2x(x+4) in standard form, we need to expand the product and simplify:

2x(x+4) = 2x^2 + 8x

Therefore, the standard form of 2x(x+4) is 2x^2 + 8x.

Step-by-step explanation:

Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.

What are the levels of measurement?

You may find out how accurately variables are recorded using levels of measurement, also known as scales of measurement. A variable in scientific research is anything that can have several values depending on the data collection.

Four levels of measuring exist:

You might only be able to perform a limited amount of data analysis depending on the level of measurement of the variable. From low (nominal) to high, there is a hierarchy in the complexity and precision of the level of measurement (ratio).

We have to find the appropriate level of measurement for the data course grades from A to F.

Here there is an order for ranking. This is because A is the highest grade followed by B, C, D, E and F respectively.

So nominal level of measurement is out of the question.

Now, there are no numerical values associated with the grades. We have no means to find the difference between the two grades.

Therefore the most appropriate level of measurement for Course grades from A to F is,

Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.

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Answer:

The probability that a randomly chosen cancer patient who has received chemotherapy has also had elective surgery can be expressed as P(E|C), where "P" represents probability and the vertical bar "|" indicates "given." So, P(E|C) represents the probability of event E given that event C has occurred.

Step-by-step explanation:

Answer: (a) Since the time to get the order follows a uniform distribution between 19 to 35 minutes, the probability of getting the order in any interval of time within this range is proportional to the length of that interval. Therefore, the probability of taking at least 23 minutes to get the order is:

P(X ≥ 23) = (35 - 23) / (35 - 19) = 0.4

Rounding to 4 decimal places, the probability is:

P(X ≥ 23) ≈ 0.4000

(b) If you arrive at Tim Horton's at 7:30am and your friends show up at 8:00am, you have 30 minutes to receive your order. Since the time to get the order follows a uniform distribution, the probability of receiving the order before your friends show up is the probability of getting the order in 30 minutes or less, which is:

P(X ≤ 30) = (30 - 19) / (35 - 19) = 0.5789

Rounding to 4 decimal places, the probability is:

P(X ≤ 30) ≈ 0.5789

(c) Let's call the time in minutes to get the order that is longer than 10% of the time as t. Since the distribution is uniform, we know that the probability of taking longer than t minutes is 0.1. Therefore, we can write:

(35 - t) / (35 - 19) = 0.1

Solving for t, we get:

t = 19 + 0.9(35 - 19) = 32.4

Rounding to 2 decimal places, we get:

t ≈ 32.40 minutes

Therefore, 10% of the time it takes longer than 32.40 minutes to get the order.

Step-by-step explanation:

We can write the diameter and circumference of the base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

Mathematically, we can write,

y = f(x) = ax + b.

Given is to find the diameter and height of the tin can.

Assume the density of coffee as {ρ}. We can write the volume of the tin can as -

Volume = mass x density

Volume = 750ρ

We can write -

πr²h = 750ρ

r = √(750ρ/πh)

D = 2r

D = 2√(750ρ/πh)

Now, we can write the circumference as -

C = 2πr

C = 2π√(750ρ/πh)

Therefore, we can write the diameter and circumference of the base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

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Therefore, the height range that encompasses 99.7% of adolescent women is roughly between 55.9 and 68.1 inches.

It reveals the average deviation of each number from the norm. When it comes to normally distributed, a large standard deviation denotes that values are typically out of the mean, whereas a smaller standard deviation denotes that values are grouped closely around the mean.

The 68-95-99.7 rule is a way to remember the percentage of data that falls within certain numbers of standard deviations from the mean in a normal distribution. Specifically:

Using this rule, we can answer the following questions:

About 68% of young women have heights within 1 standard deviation of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 1 standard deviation from the mean:

64 inches ± 2.7 inches

So the range of heights that includes about 68% of young women is approximately 61.3 inches to 66.7 inches.

    2. What is the range of heights that includes about 95% of young women?

About 95% of young women have heights within 2 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 2 standard deviations from the mean:

64 inches ± 2(2.7 inches)

So the range of heights that includes about 95% of young women is approximately 58.6 inches to 69.4 inches.

     3. What is the range of heights that includes about 99.7% of young women?

About 99.7% of young women have heights within 3 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 3 standard deviations from the mean:

64 inches ± 3(2.7 inches)

So the range of heights that includes about 99.7% of young women is approximately 55.9 inches to 68.1 inches.

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Answer: [3, 2.5]

Step-by-step explanation:

Based on the given information, the graph of the function will shift 6 units up from the parent graph, f(x).

A function is a mathematical rule that relates one input value to one output value. The parent graph of a function is the simplest form of the graph that shows the basic behavior of the function.

In this case, the function is being shifted vertically by 6 units. This means that all points on the graph will be shifted upward by 6 units compared to the parent graph.

The shape of the graph will remain the same, but its position will change. Understanding how functions are transformed is important in mathematics and can be used to model a wide range of real-world phenomena.

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Answer

The shape of sampling distribution of ^p is approximately normal because n < greater than 0.05N and np (1-p) > less than 10.

Step-by-step explanation:

The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.

The distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n is defined by the central limit theorem, where:

As long as these two conditions are respected:

n≤ N

np(1-p) > 10.

Here, we have the parameters

n= 700, p = 0.172, N= 15, 000

So, n/N = 0.0466 < 0.05

and, np(1-p)

= 700 x 0.172 ( 1- 0.172)

= 99.69 >10

Then the shape is approximately normal.

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Answer:

52 - 13 = 39 so p = 39

Step-by-step explanation:

Answer:

P=25

Step-by-step explanation:

180=52+90+p+30

180=155+P

180-155=p

p=25

Answer:

No solution

Step-by-step explanation:

[tex]\sqrt{x-45} =\sqrt{x-3} \\(\sqrt{x-45} )^2=(\sqrt{x-3} )^2\\x-45 = x-3\\x-x = 45-3\\0 = 42\\[/tex]

The volume of the right cone below is 1152π/3 cubic units then the value of x is 24.

The volume of a right circular cone is given by the formula:

V = (1/3)πr²h

where π is pi (approximately equal to 3.14), r is the radius of the circular base, and h is the height of the cone.

In this problem, we are given that the volume of the cone is 1152π/3 cubic units and that the value of x is related to the radius and height of the cone.

Let's first write the formula for the volume of the cone in terms of x:

V = (1/3)π(x/3)²(x/3)

Simplifying this expression, we get:

V = (1/27)πx²

We are given that V = 1152π/3, so we can substitute this into the formula above and solve for x:

1152π/3 = (1/27)πx³

Multiplying both sides by 27/π, we get:

x³ = 1152*27/3

x³ = 27648

Taking the cube root of both sides, we get:

x = 24

Therefore, the value of x is 24.

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the answer is 283.4

I can't write a formula

The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.

Total revenue = Price per vetkoek x Number of vetkoek sold

Total revenue = 10 x 300 = 3000

Total cost = Cost per vetkoek x Number of vetkoek sold

Total cost = 3.80 x 300 = 1140

Profit = Total revenue - Total cost

Profit = 3000 - 1140 = 1860

Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

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Answer:

0

Step-by-step explanation:

for x x^2+x-6=-4. x2+x−6=−4 x 2 + x - 6 = - 4. Step 1. Add 4 4 to both sides of the equation. x2+x−6+4=0 x 2 + x - 6 + 4 = 0.

(hope it helps!)

We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).

A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.

from the question;

We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function

y = 2 + log2(x - 1).

The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:

lim x→∞ 2 + log2(x - 1) = ∞

Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:

lim x→1+ 2 + log2(x - 1) = -∞

This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):

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By answering the above question, we may state that As a result, in 2006, equation Mexico's population was expanding at a pace of around 2.708 million people each year.

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

We must enter t = 2006 - 1900 = 106 into the population model and do the following calculations to get the population of Mexico in 2006:

p(106) = 8.028e (0.025 * 106) million individuals

108.191 million individuals, or p(106) (rounded to three decimal places)

Finding the derivative of the population model with respect to time t will allow us to determine how quickly Mexico's population was rising in 2006:

Each year, p'(t) = 0.025 * 8.028e(0.025t) million individuals.

We may then calculate the derivative at time t = 106 as follows:

P'(106) = 0.025 * 8.028e(0.025*106) million individuals annually P'(106) 2.708 million individuals annually (rounded to three decimal places)

As a result, in 2006, Mexico's population was expanding at a pace of around 2.708 million people each year.

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The answer is 6

but specifically, it can land on green 6.8181%

The required quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.

Arithmetic involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

Here,
To simplify the given expression, we can start by factoring out the common factor of 2x from the numerator. This gives:

(16x⁻² - 8x⁻² - 2x⁻⁹) / 2x

Next, we can simplify the terms in the numerator by combining the like terms:

= (4x⁻² - x⁻⁹) / x

= 4x⁻²⁻¹ - x⁻⁹⁻¹
= 4x⁻³ - x⁻¹⁰

= 4x⁻³ - x⁻¹⁰

Therefore, the quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.

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Therefore , the solution of the given problem of unitary method comes out to be she actually paid more for the same quantity of milk in the end.

Divide the measures of just this microsecond portion by two  variable in order to complete the task using the unitary technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method expression when a wanted item is present. For example, 40 pens with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this.

Here,

4 gallons of milk make up a gallon of milk. Four pints would cost $1.19 each, or

=> $1.19 x 4 = $4.76.

Instead of purchasing a gallon of milk for $4.66,

Aisha opted to purchase four pints for $4.76.

Thus, by purchasing four pints rather than a gallon, Aisha did not save money.

She actually paid more for the same quantity of milk in the end.

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An equation that represents this problem "Anthony read 5/6 hour each day for 2 days." is: A. 2 × 5/6 = 10/12.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we can reasonably infer and logically deduce that Anthony's reading rate is 5/6 hour on a daily basis and for a period of 2 days only:

Total number of hours = 2 × 5/6

Total number of hours = 10/12 hours.

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Answer:

Step-by-step explanation:

Therefore, 12 minutes of play awards 4.5 points.

The constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that for every 4 minutes of play, 1/2 point is awarded.

For every 12 minutes of play, 1 1/2 points are awarded.

We can set up a proportion to find the constant of proportionality:

(1/2 point) / (4 minutes) = (3/2 points) / (12 minutes)

Simplifying the left side, we get:

1/8 = (3/2 points) / (12 minutes)

Multiplying both sides by 12, we get:

1.5 = (3/2)P

P = (1.5) x (2/3) = 1

Therefore, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded.

By constant of proportionality, the equation that represents the relationship between the number of points awarded and the amount of time played:

P = (1/4)t

To find the number of points awarded for 20 minutes of play, we can use the equation P = (1/4)t:

P = (1/4)(20)

= 5

Hence, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.

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Answer would be shifted up

Step-by-step explanation:

hence the +9 you would be going up 9 units :)