Suppose that Joe put a cup of hot coffee in the refrigerator. The coffee is 196°F and the refrigerator is a constant 36°F. He waits 10 minutes and check the temperature and it is now 173. How long until the temperature is 120°F?(round-off to the nearest integer & if you round k use at least 3 significant digits) Newton's Law of cooling: T(t) = Aekt +T,

The width of the rectangle with a length of 42 inches is 70 inches.

To find the width of a rectangle that has a length of 42 inches, we can use the concept of proportions based on the given table.

First, we observe that the length and width of the rectangles are proportional. We can set up a proportion using the values from the table:

Length (in inches): 6, 9, 18, 24

Width (in inches): 10, 15, 30, 40

Using the proportion, we have:

Length / Width = Length / Width

We can select any corresponding pair of length and width values to set up the proportion. Let's choose the first pair: 6 and 10.

6 / 10 = 42 / x

To find the width (x) when the length is 42, we can solve the proportion:

6 / 10 = 42 / x

Cross-multiplying:

6x = 10 * 42

6x = 420

Dividing both sides by 6:

x = 420 / 6

x = 70

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Answer:

y^5

Step-by-step explanation:

you subtract the exponents

Answer:

{x | x = -1, 2, 3}

Step-by-step explanation:

There are only 3 x-values in the domain of this function because there are only 3 points where the function is defined.

These points occur when x = -1, x = 2, and x = 3.

We can represent these x-values in set notation as:

D = {x | x = -1, 2, 3}

This reads: "The domain of the function is a variable x such that x equals -1, 2, or 3."

___________________________________________________________

Note that you could also add that x is an element of all real numbers before the "such that" statement. This would be denoted:

D = {x ∈ R | x = -1, 2, 3}

This set reads: "The domain of the function is a variable x that is a set of all real numbers such that x equals -1, 2, or 3."

Answer:

Domain:  {-1, 2, 3}

Range:  {-4, 3}

Step-by-step explanation:

The diagram shows a Cartesian plane with (x, y) points:

The domain is the set of x-values.

The x-values of the plotted points are -1, 2 and 3.

Therefore, the domain in set notation is:

\(\large\boxed{\textsf{Domain:} \quad \{-1, 2, 3\}}\)

The range is the set of y-values.

The y-values of the plotted points are -4, 3 and -4.

Therefore, the range in set notation is:

\(\large\boxed{\textsf{Range:} \quad \{-4, 3\}}\)

\(\hrulefill\)

Note: Sets are defined by unique elements, and duplicates are not included. Therefore, in set notation, the repetition of elements is not necessary.

Answer:

747.5

Step-by-step explanation:

Answer:

$26.40

Step-by-step explanation:

Answer:

$26.40

Step-by-step explanation:

1 paper flower=$0.55

Therefore,48 paper flowers=?

cross multiplying,we have 0.55×48=$26.40

To find the Annual Percentage Rate (APR) of 18.60% compounded daily, we need to convert the nominal interest rate to an annual rate.  The formula to calculate the effective annual rate, or APR, when interest is compounded daily is:

APR = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1 In this case, the nominal interest rate is 18.60% and it is compounded daily. Therefore, the number of compounding periods in a year is 365.

Plugging in the values into the formula, we have:

APR = (1 + (0.1860 / 365))^365 - 1 Calculating this expression, we find:

APR ≈ 0.1934 Rounded to two decimal places, the APR of 18.60% compounded daily is approximately 19.34. Therefore, the APR is 19.34 (without the percent symbol).

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Answer:

61

Step-by-step explanation:

180 - 119 =

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

Suppose that the given function is

\(f:X\rightarrow Y\)

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

\(f^{-1}: Y \rightarrow X\)

such that:

\(\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X\)

(and vice versa).

It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'

The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.

Hence, the correct option is A.

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The equation of a line can be written as:

y = mx + b

Where m is the slope and b is the y-intercept.

For the word problem, the slope is -10 and the intercept is 50, thus the equation is:

y = -10x + 50

If x is the number of weeks, then y decreases by 10 when x increases by 1. We expect that the value of y goes from 50 down to 40, 30, 20, etc.

The example of the friend is that he started with

Answer:

No. pp you can fit in a van: 6,

No. pp you can fit in a bus: 20

Step-by-step explanation:

Let v = # of pp in vans, and let b = # of pp in buses:

8v + 9b = 228,

4v + 5b = 124

If we solve this system of equations by substitution, we isolate the first eq. for v and then substitute into the bottom eq:

v = 228-9b/8,

Substitute v = 228-9b/8 into bottom eq:

[4 * 228-9b/8 + 5b = 125]

[228+b/2=124]

[228+b = 248]

[b = 20]

Now substitute 20 to find no. of pp in the vans:

v = 228 - 9(20)/8 = 228  - 180/8 = 48/8 = 6

An expression in terms of a to indicate Emily's total outlay is 1.2753x when Emily visits a restaurant, and the bill's subtotal was one dollar.

Given that,

Emily visits a restaurant, and the bill's subtotal was one dollar. The bill is subject to a 9% tax. Emily chooses to add 18% to the total price as a tip (including the tax).

We have to create an expression in terms of a to indicate Emily's total outlay.

We know that,

Let x represent the bill's subtotal.

The bill is subject to a 9% tax.

Therefore, the final bill amount after tax is

x+9% of x

= x+9/100 x

= x+0.09x

= 1.09x

Juan chooses to add a 18% tip to the total bill (including the tax).

Thus, the final sum after tip is

(1.09x)+18% of 1.09x

= 1.09x+ 18/100(1.09x)

= 1.09x+ 0.18(1.09x)

= 1.09x+ 0.1853x

= 1.2753x

Therefore, an expression in terms of a to indicate Emily's total outlay is 1.2753x when Emily visits a restaurant, and the bill's subtotal was one dollar.

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\(36-18=18\)

So, 18 more.

Answer:

<

Step-by-step explanation:

Step 1: Evaluate 2√40

2√40 = 12.6491

Step 2: Evaluate 7 + √63

7 + √63 = 14.9373

Step 3: Fill in inequality symbol

12.6491 < 14.9373

Answer: The simplified form of 2x · 5z · y is 10xzy.

Step-by-step explanation:

Answer: The answer is C(3,11)

Step-by-step explanation:

If you replace x with 3 that will be 3 to the third power 3 x 3 is 9 so 9 plus 2 is 11 you can use 11 in y, therefor your answer is C.(3,11)

Answer:

JAMAL NEEDS 14 MORE PEOPLE .

Step-by-step explanation:

FIRSTLY: TAKE 5 ×3

=15 PEOPLE

15 PEOPLE -1 PEOPLE

=14 PEOPLE

MINUS 1 BECAUSE YOU INCLUDE JAMAL AS 1

Option B. $9,255.75, Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of

To find the present value of an infinite stream of cash flows, we can use the formula:

PV = CF / r

where PV is the present value, CF is the cash flow per period, and r is the interest rate per period.

In this case, CF = $100 (received at the end of each year forever) and r = 10%.

Plugging in the numbers, we get:

PV = $100 / 0.10 = $1,000

So the present value of the infinite stream of cash flows is $1,000.

However, we need to adjust for the fact that the cash flows are received at the end of each year, not at the beginning. To do this, we can use the formula:

PV = CF / (r - g)

where g is the growth rate of the cash flows, which in this case is 0 (since the cash flows are constant).

Plugging in the numbers, we get:

PV = $100 / (0.10 - 0) = $1,000

So the present value of the infinite stream of cash flows received at the end of each year is also $1,000.

Therefore, the answer must include the present value of an infinite stream of cash flows. Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of cash flows.

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Answer: Whats your snap i think I'm simping :)

Step-by-step explanation:

Answer:

answers are in the picture

A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.

Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.

The diameter of the semicircle is also the length of the rectangle, so it is 3x.

The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.

The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:

3x^2 + (9/8)πx^2 = 750

(21/8)πx^2 = 750

x^2 = 750/(21/8)*π

x = √(750/(21/8)*π)

To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:

x = √(750/(21/8)*3.14)

= √(750/6.71)

= √(112.64)

= approximately 10.65 inches.

The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.

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The expected value of the gain for this game is -0.88. This means that on average, a player can expect to lose about

88 cents per game.

To find the expected value of the gain, E[Y], we first need to calculate the probability of each possible outcome and the

corresponding gain.

Since the probability of heads is 0.4, the probability of tails is 0.6.

If X = 0 (no heads), the probability is \((0.6)^3 = 0.216\), and the gain is -5 (losing the bet).

If X = 1 (one head), the probability is \(3× (0.4)×(0.6)^2 = 0.432\), and the gain is -1 (losing 1).

If X = 2 (two heads), the probability is \(3×(0.4)^2×(0.6) = 0.288\), and the gain is -1 (losing 1) or 3 (winning 4).

If X = 3 (three heads), the probability is \((0.4)^3 = 0.064\), and the gain is 5 (winning 10).

Now we can calculate the expected value of the gain by multiplying each gain by its probability and summing them up:

E[Y] = (-5)×(0.216) + (-1)×(0.432 + 0.288) + 5×(0.064)

      = -0.88

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(a+b+c)^3=a^3 +b^3+c^3-2(ab+ac+bc)

216=a^3+b^3+c^3-2(11)

a^3+b^3+c^3=238

but ıdk how can ı find -3abc :/

===============================================

Work Shown:

a+b+c = 6

(a+b+c)^2 = 6^2

(a+b+c)(a+b+c) = 36

a(a+b+c)+b(a+b+c)+c(a+b+c) = 36

a^2+ab+ca+ab+b^2+ca+bc+c^2 = 36

a^2+b^2+c^2+2ab+2bc+2ca = 36

a^2+b^2+c^2+2(ab+bc+ca) = 36

a^2+b^2+c^2+2*11 = 36

a^2+b^2+c^2+22 = 36

a^2+b^2+c^2 = 36-22

a^2+b^2+c^2 = 14

-----------------------

a^3+b^3+c^3-3abc = (a+b+c)*(a^2+b^2+c^2 - (ab+bc+ca) )

a^3+b^3+c^3-3abc = 6*(14 - 11)

a^3+b^3+c^3-3abc = 18

There were _22_ cars in the first train, _24_ cars in the second train, and _26_ cars in the third train

We know that the trains have 418, 456, and 494 seats. And are made of the same train cars, so the number of seats on each train car is a common factor of 418, 456 and 494.

We also know that no train car has more than 25 seats.

First, let's decompose the given numbers as a product of prime numbers:

418 = 2*11*19

456 = 2*2*2*3*19

494 = 2*13*19

As you can see, the factors 2 and 19 appear in the 3 numbers, 19 is the largest one that is also smaller than 25, so we conclude that each train car has 19 seats.

Then:

The first train, which has 418 seats, has:

418/19 = 22 train cars.

The second train has 456 seats, so it has:

456/19 = 24 train cars

The third train has 494 seats, so it has:

494/19 = 26 train cars.

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Answer:

It's AAS congruent theorem.

Answer:

\(\huge\boxed{\sf AAS\ postulate}\)

Step-by-step explanation:

The two triangles have:

So, 2 angles and 1 side congruency makes it AAS postulate (Angle-Angle-Side).

\(\rule[225]{225}{2}\)

To determine if a given value is a solution to an equation, we substitute the value into the equation and check if it satisfies the equation. 1. For the equation 45x - 478 = -2, we substitute x = 45

45(45) - 478 = -2

2025 - 478 = -2

1547 = -2

Since the left side of the equation is not equal to the right side, x = 45 is not a solution to the equation 45x - 478 = -2.

2. For the equation 0.25x + 10(x - 3) = 0.05(22), we substitute x = 4:

0.25(4) + 10(4 - 3) = 0.05(22) 1 + 10(1) = 1.1 1 + 10 = 1.1 Since the left side of the equation is not equal to the right side, x = 4 is not a solution to the equation 0.25x + 10(x - 3) = 0.05(22).

3. For the equation x/2 - 1 = (2/3)x - 3, we substitute x = 12:

12/2 - 1 = (2/3)(12) - 3 6 - 1 = 8 - 3

5 = 5 Since both sides of the equation are equal, x = 12 is a solution to the equation x/2 - 1 = (2/3)x - 3.

4. For the equation 2x = 48 + 6x, we substitute x = -12:

2(-12) = 48 + 6(-12) -24 = 48 - 72 -24 = -24 Since both sides of the equation are equal, x = -12 is a solution to the equation 2x = 48 + 6x.

5. For the equation 5x - 2.6 = 2(x + 0.8), we substitute x = 4.4: 5(4.4) - 2.6 = 2(4.4 + 0.8) 22 - 2.6 = 2(5.2) 19.4 = 10.4 Since the left side of the equation is not equal to the right side, x = 4.4 is not a solution to the equation 5x - 2.6 = 2(x + 0.8).

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The given

system of equations

is:

5x + y = 10   ... (1)

x + (1/5)y = 2   ... (2)

To solve this system, we can use the method of

elimination

. Let's multiply equation (2) by 5 to eliminate the fraction:

5(x + (1/5)y) = 5(2)

5x + y = 10   ... (3)

Comparing equations (1) and (3), we can see that they are identical. This means that equation (3) is just a multiple of equation (1), and therefore the two equations are dependent. The system does not have a unique solution; instead, it has

infinitely many solutions.

To see this, we can rewrite equation (1) as:

y = 10 - 5x

Now, we can substitute this expression for y into either equation (1) or (2). Let's substitute it into equation (1):

5x + (10 - 5x) = 10

10 = 10

As we can see, this equation is always true, regardless of the value of x. This means that for any real value of x, the equation is satisfied. Therefore, the solution set is {x | x is any real number}.

In summary, the given system of equations is

dependent

and has infinitely many solutions. The solution set is {x | x is any real number}.

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When gathering data through a survey, companies can save money by surveying 100% of a population. False

Survey an activity in which many people are asked a question or a series of questions in order to gather information about what most people do or think about something.

Survey research has historically included large population-based data collection. The primary purpose of this type of survey research was to obtain information describing characteristics of a large sample of individuals of interest relatively quickly.

Therefore when gathering data through survey there is not 100% sure that companies can make alot of save.

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Answer:

Step-by-step explanation:

Oh then you just multiply it

Range is the set of all values which the given function can output. The correct option is A.

Since y is the output for the given function, and the only outputs that can be seen for the function are 0, 2, and 4. Therefore, the range of the function is {0,2,4}.

Hence, the correct option is A.

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