Solve for b:
10abc - 2d = 3d​

Answer:

a. One angle measures 90 degrees.

Answer:

Rate = Amount / Time

R = (2/3 * 10) / (5/4) oz/hr

R = (80 / 15) oz / hr = 16 / 3 oz / hr = 5 1/3 oz / hr

Check:  

5 1/3 * 5/4 = 16 / 3 * 5 / 4 = 80 / 12 = 20 / 3 = 6 2/3    oz in 1 1/4 hr

2/3 * 10 = 20 / 3 = 6 2/3 oz in 1 1/4 hr

In one hour, Amadou drinks \(4\frac{7}{12}\) ounces of water.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Amadou drinks 2/3 of a 10-ounce glass of water in 1 1/4 hours,

So, Amadou drinks (2/3)×10 = 5/3 ounces of water in 11/4 hours.

∴ In 1 hour he drinks (5/3)/(11/4) ounces of water.

= 55/12 ounces.

= \(4\frac{7}{12}\) ounces.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ2

Answer:

6.32455532034

Rounded: 6.32

Hope this helps! :)

Answer:

X = 0

Step-by-step explanation:

Because if X equaled 0 then both sides would be equaled to 16.

Answer:

- changing the order of the numbers we are multiplying, does not change the product

Step-by-step explanation:

7 x 8 x 11 x 2 = 11 x 7 x 2 x 8

1232 = 1232

Hope it helps!

1. f(x) =\(1 - 4x^2 + 8(x^2)^2/2! - ...\) this represents a power series representation for the function f(x) = \(1 - 4x^2.\)

2.f(x) = \(-3 - x^6 + (x^6)^2/2! - ...\) this represents a power series representation for the function f(x) =\(-3 - x^6.\)

1. For the function f(x) =\(1 - 4x^2,\) we can express it as a power series by expanding the terms around x = 0. We can rewrite the function as f(x) =\(1 - 4x^2 = 1 - 4(x^2) = 1 - 4(x^2)^1.\)

By using the binomial series expansion, we have:

f(x) = \(1 - 4(x^2)^1 = 1 - 4(x^2)(1) + 4(1)(-1)(x^2)^2/2! + ...\)

Simplifying the terms, we get:

f(x) =\(1 - 4x^2 + 8(x^2)^2/2! - ...\)

The interval of convergence can be determined by considering the values of x for which the series converges. In this case, the power series representation of f(x) will converge for values of x within the interval (-1, 1). The endpoints x = -1 and x = 1 are excluded from the interval of convergence.

2. For the function f(x) = -\(3 - x^6,\)we can similarly express it as a power series by expanding the terms around x = 0. We can rewrite the function as f(x) =\(-3 - x^6 = -3 - (x^6)^1.\)

Expanding the series using the binomial series expansion, we have:

f(x) =\(-3 - (x^6)^1 = -3 - (x^6)(1) + (1)(-1)(x^6)^2/2! + ...\)

Simplifying the terms, we get:

f(x) = \(-3 - x^6 + (x^6)^2/2! - ...\)

The interval of convergence for this power series representation is the set of values of x for which the series converges. In this case, the power series representation will converge for all values of x since there are no terms dependent on x. Therefore, the interval of convergence is (-∞, ∞).

For more such information on: function

https://brainly.com/question/11624077

#SPJ8

The interpretation of the given compound interest expression is:

2400 is the amount of initial deposit

1.03 is the amount

12t is the number of times the account has compounded since it opened

The formula for compound interest is:

A = P(1 + (r/t))^(nt)

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We are given the equation as:

S = 2400(1.03)^(12t)

Thus:

2400 is the amount of initial deposit

1.03 is the amount

12t is the number of times the account has compounded since it opened

Read more about Compound Interest at: https://brainly.com/question/24274034

#SPJ1

Answer: Your answer should be C) 171! Hope this helps you!

Step-by-step explanation:

Answer:

The relation represented by the graph is not a function

Step-by-step explanation:

A function by definition is "a relation from a set of inputs to a set of outputs". For this graph there's no constant rate of change, you can't form a line with the points, and you can't write an equation or inequality from the points. There's no sort of relationship between the number of days and the number of students who are absent, so it's not a function.

Answer:

1. 1,7 2,10 3,5 4,7 5,9

2. 5

3. 2 10 Students were absent on day 2.

4.The graph is a function because each x-value is paired with a single y-value.

You can put 14 boxes of candy weighing 3/4 lb each in the bin.

To determine how many 3/4 lb boxes of candy can fit in a bin, we divide the total weight of the bin by the weight of each box.

First, let's convert the mixed number 10 1/2 lbs to an improper fraction.

10 1/2 lbs = (10 * 2 + 1) / 2 = 21/2 lbs

Next, we divide the total weight of the bin (21/2 lbs) by the weight of each box (3/4 lb):

(21/2 lbs) / (3/4 lb) = (21/2) * (4/3) = (21 * 4) / (2 * 3) = 84/6 = 14

As a result, you can fill the bin with 14 boxes of sweets that each weigh 3/4 lb.

Learn more about capacity at https://brainly.com/question/14828811

#SPJ11

Ingrid needs to deposit approximately $558.95 at the end of each quarter to have enough money to buy the $17,000 car in 6 years.

To calculate the amount Ingrid needs to deposit at the end of each quarter, we can use the future value of an annuity formula. The future value (FV) of an annuity is given by the formula:

FV = P * ((1 + r/n)(n*t) - 1) / (r/n)

Where:

P is the periodic deposit

r is the annual interest rate (as a decimal)

n is the number of compounding periods per year

t is the number of years

In this case, Ingrid wants to accumulate $17,000 in 6 years, with a quarterly compounding rate of 5.5% (0.055) and 4 compounding periods per year. Plugging these values into the formula:

17,000 = P * ((1 + 0.055/4)²⁴ - 1) / (0.055/4)

By solving this equation, we find that Ingrid needs to deposit approximately $558.95 at the end of each quarter to accumulate enough money to pay for her car.

learn more about intrest rate here:

https://brainly.com/question/29222674

#SPJ11

The equation for a circle with center located at (a,b) and radius r is given by:

(x - a)² + (y - b)² = r²

Therefore, if a circle has radius r = 2 and is centered at (3,2), its equation is given by:

Option D: (x - 3)² + (y - 2)² = 4

The required answer is the y = 3x - 7.

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept. To find the equation of a line when you know the slope and y-intercept, simply substitute the values into the equation.

step-by-step explanation:

1. Start with the equation y = mx + b, where m is the slope and b is the y-intercept.
2. Identify the given slope and y-intercept values.
3. Substitute the given values into the equation.
  - Replace the variable m with the given slope value.
  - Replace the variable b with the given y-intercept value.
4. Simplify the equation by performing any necessary calculations.

For example, the slope is 3 and the y-intercept is -7. substitute these values into the equation:

y = 3x - 7.

The equation of the line, given the slope of 3 and the y-intercept of -7, is y = 3x - 7.

To know about linear equation. To click the link.

https://brainly.com/question/29111179.

#SPJ11

We can say with 95% confidence that the true proportion of adults who have read a book in either print or digital format in the preceding 12 months lies between 0.

to calculate the confidence interval for the population proportion of adults who have read a book in either print or digital format in the preceding 12 months, we need to know the sample proportion, sample size, and confidence level. let's assume that a random sample of n adults was selected and p is the sample proportion of adults who have read a book in either print or digital format in the preceding 12 months. we will use the formula:

(lower bound, upper bound) = (p - z*sqrt((p*(1-p))/n), p + z*sqrt((p*(1-p))/n))

where z is the z-score corresponding to the desired confidence level. for example, if we want a 95% confidence interval, z = 1.96. if we want a 99% confidence interval, z = 2.58.

let's assume that a sample of 500 adults was selected and 300 of them reported having read a book in either print or digital format in the preceding 12 months. then the sample proportion is:

p = 300/500 = 0.6

if we want a 95% confidence interval, the z-score is 1.96. substituting these values into the formula, we get:

(lower bound, upper bound) = (0.6 - 1.96*sqrt((0.6*(1-0.6))/500), 0.6 + 1.96*sqrt((0.6*(1-0.6))/500))

simplifying this expression, we get:

(lower bound, upper bound) = (0.5516, 0.6484) 5516 and 0.6484.

Learn more about proportion here:

 https://brainly.com/question/31548894

#SPJ11

To obtain a 40% alcohol solution from a 22% solution, you need to add 18% more alcohol.

100 ml of 22% alcohol solution contains 22 ml of pure alcohol and 78 ml of other ingredients.

Therefore, to obtain a 40% solution, you need 40 ml of pure alcohol in every 100 ml of solution.

So, 18 ml of pure alcohol should be added to 100 ml of 22% solution to obtain 40% solution.

Another way to calculate this is:

You can calculate the amount of pure alcohol you need to add by multiplying the initial volume of the solution (100ml) by the percentage increase in alcohol content (18%) .

100ml * 18% = 18ml

So you would need to add 18ml of pure alcohol to 100ml of 22% alcohol solution to obtain a 40% alcohol solution.

Read more about percentages here:

https://brainly.com/question/24877689

#SPJ1

Answer: The total amount at the end of 6 years would be $47,971.27.

Step-by-step explanation:

1. Calculate the quarterly interest rate (1.5/4) = 0.375%

2. Calculate the number of quarters (6 years * 4 quarters) = 24 quarters

3. Calculate the amount after 6 years = $40,000 * (1 + 0.00375)^24 = $47,737.91

The greatest water depth is 12 feet

The least water depth is 6 feet

The positive difference is

12 - 6 = 6 feet

The answer is G

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

Learn more about Congruent polygons here:

https://brainly.com/question/2096633

#SPJ1

The value of a is -4 from the given system of linear equations.

The system of given equations are ax+12y=-6 and 2x-6y=4.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here, ax+12y=-6 -------(I) and 2x-6y=4 -------(II)

Given, no solution for the system

So, (a1/a2) = (b1/b2) ≠ (c1/c2)

Now, a/2 = 12/(-6)

a=-4

Hence, the value of a is -4 from the given system of linear equations.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ1

Answer:17.4 ft

Step-by-step explanation:

When the ladder is pulled 4 feet farther from the house, it will reach up  32 feet along the side of the house.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the Pythagorean theorem to solve this problem. Let's call the distance that the ladder reaches up the side of the house "x".

According to the problem, we know that the ladder is 40 feet long and reaches up 24 feet when it's set against the side of the house.

So, we can set up the following equation:

40² = 24² + x²

Simplifying this equation, we get:

1600 = 576 + x²

1024 = x²

Take square root on both sides

x = 32

Hence,  when the ladder is pulled 4 feet farther from the house, it will reach up approximately 32 feet along the side of the house.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ2

Answer:

f(0)=1

Step-by-step explanation:

The question asks us to find f(0). We want to find what f(x), or y is, when x is equal to 0.

f(x)=3^x

Therefore, we can substitute 0 in for x.

f(0)=3^0

Evaluate the exponent, 3^0.

Any number raised to the power of zero is equal to 1.

f(0)=1

Answer:

1

Step-by-step explanation:

f(0) = 3^0

f(0) = 1

anything to the 0th power = 1

Answer:

2.625

Step-by-step explanation:

Last week Thomas ran 5 1/4 miles

This week he plans to run 1/2 miles as far

Therefore the number of miles he plans to run cann be calculated as follows

= 5 1/4 × 1/2

= 21/4 × 1/2

= 21/8

= 2.625

Hence Thomas plans to run 2.625 miles

Yes, the test in an "if" function must evaluate to either a True or a False value.

An "if" function, also known as a conditional statement, is used to perform specific actions based on whether a certain condition is met or not. The test or condition within the "if" function needs to be evaluated as either True or False in order for the program to decide which action to execute. If the test evaluates to True, the program will perform the action within the "if" block, and if it evaluates to False, it will either execute the action in the "else" block (if present) or simply skip the "if" block.

When using an "if" function in programming, it is essential for the test or condition within the statement to result in a boolean value, which is either True or False. This is because the program needs to determine whether the condition is met or not, so it can decide which set of actions to execute. If the condition evaluates to True, the code within the "if" block will be executed, while if it evaluates to False, the code within the "else" block (if present) will be executed, or the "if" block will be skipped altogether.

To know more about function visit:-

https://brainly.com/question/30721594

#SPJ11

Answer:

76+76=152

Step-by-step explanation:

The formula for the nth partial sum of the series is equal to Sn = ln √(n+1), and the series diverges.

Get a formula for the nth partial sum of the series, by writing out the first few terms,

S₁ = (ln √2 - ln √1)

   = ln √2

S₂ = (ln √3 - ln √2) + (ln √2 - ln √1)

   = ln √3 - ln √1

S₃= (ln √4 - ln √3) + (ln √3 - ln √2) + (ln √2 - ln √1)

   = ln √4 - ln √1

Pattern here expressed the nth partial sum is equal to

ln √(n+1) - ln √1.

Simplify this to,

ln (√(n+1)/√1)

= ln √(n+1).

nth partial sum is equal to,

Sn = ln √(n+1)

Series converges or diverges,

Take the limit of the nth partial sum as n approaches infinity we have,

\(\lim_{n \to \infty}\) ln √(n+1)

= ln ∞

= ∞

Here, the limit of the nth partial sum diverges to infinity, the series itself diverges.

⇒the series does not have a sum.

Therefore, the nth partial sum of the series is Sn = ln √(n+1), and the series diverges.

Learn more about series here

brainly.com/question/28144066

#SPJ4